USPatent applicationPatented

Coding and modulation apparatus using non-uniform constellation and different PHY modes

Granted 22 Sep 2020 · 1 office action

Current assignee: Sony Corporation · originally Sony Group Corporation

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Inventors: Thomas Handte, Lothar Stadelmeier, Daniel Schneider, Nabil Sven Loghin · Examiner: Janice N Tieu · AU 2633 · TC 2600

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Abstract

A coding and modulation apparatus and method are presented, particularly for use in a system according to IEEE 802.11. The apparatus comprises an encoder configured to encode input data into cell words according to a low density parity check code, LDPC, and a modulator configured to modulate said cell words into constellation values of a non-uniform constellation and to assign bit combinations to constellation values of the used non-uniform constellation, wherein said modulator is configured to use, based on the PHY mode, the total number M of constellation points of the constellation and the code rate, a particular non-uniform constellation.

Description

12 parts
›CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No. 15/564,993, filed on Oct. 6, 2017, which is a National Stage Application based on PCT/EP2016/058175, filed Apr. 14, 2016 and which claims priority to European Patent Application 15163465.6, filed in the European Patent Office on Apr. 14, 2015, the entire contents of each of which are incorporated herein by reference.

BACKGROUND
›Field of the Disclosure

The present disclosure relates to a coding and modulation apparatus and method as well as a demodulation and decoding apparatus and method. Further, the present disclosure relates to a transmission apparatus and method as well as a receiving apparatus and method. Still further, the present disclosure relates to a computer program and a non-transitory computer-readable recording medium.

›Description of Related Art

Modern communications systems typically employ, among other elements, a coding and modulation apparatus (as part of a transmission apparatus) and a decoding and demodulation apparatus (as part of a receiving apparatus). The coding and modulation apparatus is often part of a so called BICM (Bit Interleaved Coded Modulation) apparatus, which generally comprises (at the transmitter side) a serial concatenation of a FEC (Forward Error Correction) encoder, a bit interleaver, and a modulator, which uses spectral efficient modulation such as BPSK (Binary Phase Shift Keying), QPSK (Quaternary Phase Shift Keying), or QAM (Quadrature Amplitude Modulation).

BICM allows for good performance due to the use of the interleaves and/or the FEC encoder. It has a reasonable decoding complexity as opposed to multilevel coding (MEC) coding schemes and is thus used frequently in communications systems, such as in all DVB systems (e.g. DVB-S2x), powerline communications (e.g., Homeplug AV), DAB, LTE, WiFi (IEEE 802.11), ATSC 3.0, etc. The first generation of 60 GHz WLAN is specified in IEEE 802.11ad. Systems in accordance with IEEE 802.11ad use uniform constellations. Several Modulation and Coding Schemes (MCSs) are defined. Currently, there is a study group which investigates possible technologies for the next generation of the specification which will likely be called 802.11ay.

Generally, the coding and modulation capacity, such as the BICM capacity in systems using a BICM apparatus, is considered as a target function, and it is desired to find optimum constellation points such that this capacity is maximized, often subject to a power normalization, i.e., the average power of the constellation points should be normalized to e.g. 1.

The “background” description provided herein is for the purpose of generally presenting the context of the disclosure. Work of the presently named inventor(s), to the extent it is described in this background section, as well as aspects of the description which may not otherwise qualify as prior art at the time of filing, are neither expressly or impliedly admitted as prior art against the present disclosure.

›SUMMARY · 1 of 2

It is an object to provide a coding and modulation apparatus and method providing an increased or even maximized coding and modulation capacity and a reduced bit error rate and reception with a reduced required SNR (signal-to-noise ratio). It is a further object to provide a demodulation and decoding apparatus and method as well as a corresponding computer program for implementing said methods and a non-transitory computer-readable recording medium for implementing said methods.

According to an aspect there is provided a coding and modulation apparatus comprising

an encoder configured to encode input data into cell words according to a low density parity check code, LDPC, and a modulator configured to modulate said cell words into constellation values of a non-uniform constellation and to assign bit combinations to constellation values of the used non-uniform constellation,

wherein said modulator is configured to use, based on the PHY mode, the total number M of constellation points of the constellation and the code rate, one of the non-uniform constellations as defined in claim 1 .

According to a further aspect there is provided a transmission apparatus comprising

a coding and modulation apparatus as claimed in claim 1 configured to encode and modulate input data into constellation values, a converter configured to convert said constellation values into one or more transmission streams to be transmitted, and a transmitter configured to transmit said one or more transmission streams.

According to another aspect there is provided a demodulation and decoding apparatus comprising

a demodulator configured to demodulate constellation values of a non-uniform constellation into cell words and to assign bit combinations to constellation values of the used non-uniform constellation, and a decoder configured to decode cell words into output data according to a low density parity check code, LDPC,

wherein said demodulator is configured to use, based on the PHY mode, the total number M of constellation points of the constellation and the code rate, one of the non-uniform constellations as defined in claim 15 .

According to a further aspect there is provided a receiving apparatus comprising

receiving one or more transmission streams, deconverting one or more transmission streams into said constellation values, and demodulating and decoding said constellation values into output data according to a method as claimed in claim 16 .

According to still further aspects corresponding methods, a computer program comprising program means for causing a computer to carry out the steps of the methods disclosed herein, when said computer program is carried out on a computer, as well as a non-transitory computer-readable recording medium that stores therein a computer program product, which, when executed by a processor, causes the methods disclosed herein to be performed are provided.

Preferred embodiments are defined in the dependent claims. It shall be understood that the claimed methods, the claimed computer program and the claimed computer-readable recording medium have similar and/or identical preferred embodiments as the claimed apparatus and as defined in the dependent claims.

One of the aspects of the disclosure is that the constellation points of the used constellations, called non-uniform constellations, are not located on a regular grid with equidistant symbols, but rather on optimized locations, dependent on the channel conditions between the transmission apparatus and a receiving apparatus with which the transmission apparatus wants to communicate (e.g. in a WiFi network). Further, the used constellation is selected (preferably in advance, but generally on the fly in other embodiments) dependent on the code rate and the desired total number of constellation points of the used constellation. The code rate and total number of constellation points (also referred to as “modulation order”) depends among other parameters on the channel quality, such as signal-to-noise ratio. A method how to find and optimize these non-uniform constellations (in the following called NUCs) will be explained below. Further, for the proposed non-uniform constellations an optimized bit labelling (i.e. an optimized assignment of bit combinations to constellation values of the used non-uniform constellation) is proposed.

Depending on the capabilities of the transmission apparatus and the receiving apparatus, the transmission apparatus, in an embodiment, is able to select between the use of OFDM or single carrier (SC) mode as PHY (physical layer) mode. The SC mode is simpler and more suited for good channel conditions with mainly line of sight. The OFDM mode usually provides increased performance especially for multi-path channel conditions. The PHY mode may be one criterion for selecting the constellation used by the modulator. In other embodiment the SC mode may be the default mode, but OFDM mode may be optionally used, particularly if both the transmitting apparatus and the receiving apparatus support OFDM, i.e. in this case the transmission apparatus can choose to transmit in OFDM mode. Hence, also apparatus and methods not supporting OFDM may make use of the proposed teaching, even if the use SC mode as PHY mode and if they make use of one of the non-uniform constellations disclosed herein for use with SC mode.

In the tables various constellations are provided for different values of M, for different code rates and for different PHY modes. It should be noted that the code rate R indicated in the tables are not to be understood such that a particular constellation is only valid for exactly this code rate, but also for slightly different code rates. The code rate as indicated in the modulation and coding scheme (MCS) index might differ from the true code rate of the system, e.g. because of padding and other constraints related to the frame structure.

It should also be noted that one or more of the following “invariant transformations” do not affect the properties of the constellations:

›SUMMARY · 2 of 2

1. rotation of all symbols by an arbitrary angle φ,

2 inversion of m-th bit y_m=b∈{0,1} to y_m= − b, where the bar indicates inversion,

3. interchanging of bit positions y_k1 and y_k2,

4. reflection on Re{x1}- and/or Im{x1}-axis,

5. predistortion,

6. mirroring on any line in the complex plane.

Thus, the modulator may also use a non-uniform constellation obtained from a constellation from anyone of groups A or B through rotation by an angle around the origin, an inversion of bit labels for all constellation points, an interchanging of bit positions for all constellation points and/or a reflection on the real part and/or imaginary part axis. For instance, if one constellation point has bit labels 0010 for 16-QAM, all first bit labels can be inverted such that this point becomes 1010. Further, constellation obtained through any other trivial manipulation, such as rounding of the constellation points' positions shall generally be covered by the claims. Through one or more of these operations an equivalent mapping to the mapping of the constellations defined in the above mentioned groups is achieved.

The foregoing paragraphs have been provided by way of general introduction, and are not intended to limit the scope of the following claims. The described embodiments, together with further advantages, will be best understood by reference to the following detailed description taken in conjunction with the accompanying drawings.

›BRIEF DESCRIPTION OF THE DRAWINGS

A more complete appreciation of the disclosure and many of the attendant advantages thereof will be readily obtained as the same becomes better understood by reference to the following detailed description when considered in connection with the accompanying drawings, wherein:

FIG. 1 shows a schematic diagram of an embodiment of a transmission apparatus according to the present disclosure using OFDM as PHY mode,

FIG. 2 shows a schematic diagram of an embodiment of a receiving apparatus according to the present disclosure using OFDM as PHY mode,

FIG. 3 shows a schematic diagram of an embodiment of a transmission apparatus according to the present disclosure using single carrier mode as PHY mode,

FIG. 4 shows a schematic diagram of an embodiment of a receiving apparatus according to the present disclosure using single carrier mode as PHY mode,

FIG. 5 shows a schematic diagram of an embodiment of a communications system according to the present disclosure, and

FIG. 6 shows a diagram of an exemplary two-dimensional non-uniform constellation for 16-QAM according to the present disclosure.

›DESCRIPTION OF THE EMBODIMENTS · 1 of 5

IEEE 802.11ad supports two different PHY modes: Orthogonal Frequency Division Multiplex (OFDM) mode (similar to “classical” WLAN operating in the frequency ranges of 2.4 GHz and 5 GHz) and single carrier (SC) mode. Referring now to the drawings, wherein like reference numerals designate identical or corresponding parts throughout the several views, FIGS. 1 and 2 illustrate a first embodiment for OFDM mode and FIGS. 3 and 4 illustrate a second embodiment for SC mode.

FIG. 1 shows an embodiment of a transmission apparatus 10 according to the present disclosure including an embodiment of a coding and modulation apparatus 20 according to the present disclosure for use with OFDM as PHY mode. The transmission apparatus 10 comprises an FEC (forward error correction) encoder 11 for encoding the input data by use of an LDPC (low density parity check) code. The code rate may depend on the MCS (modulation and coding scheme) index, which is generally predetermined or selected.

The transmission apparatus 10 further comprises a constellation mapper 12 (generally also called modulator), in particular a QAM (quadrature amplitude modulation) mapper, that maps the encoded bits of the input data to complex symbols (also called constellation points) in a constellation, in particular a QAM constellation. The modulation order (i.e. the number M of constellations points of the constellation) may also depend on the MCS index.

The transmission apparatus 10 further comprises an OFDM unit 13 for OFDM modulation, an RF processing unit 14 for RF processing like frequency up-conversion, power amplifier, transmit filters, digital-to-analog conversion, etc., and a transmit unit 15 for transmitting the finally obtained signals over a channel to a receiving apparatus. In other embodiments of the transmission apparatus 10 additional elements may be provided, such as an input processing unit and/or a frame building unit, or other elements as e.g. conventionally used in a transmission apparatus of a system in accordance with IEEE 802.11ad.

The FEC encoder 11 , and the constellation mapper (modulator) 12 are often summarized as BICM (bit-interleaved coded modulation) apparatus and represent the coding and modulation apparatus 20 according to the present disclosure. The FEC encoder 11 generally encodes input data into cell words according to an LDPC code. The modulator 12 generally modulates said cell words into constellation values of a non-uniform constellation and assigns bit combinations to constellation values of the used non-uniform constellation. Generally, the output of the FEC encoder 11 is referred to as a codeword (e.g. a couple of hundred bits), which are then divided into “tuples” (of e.g. 4 bits in case of 16-QAM), referred to also as cell words (of the codeword). These tuples (cell words) are then assigned to the constellations points by the modulator 12 .

Based on the PHY mode (OFDM in this embodiment), the total number M of constellation points of the constellation (i.e. the modulation order) and the code rate, one of a selection of non-uniform constellations of different groups is used. Details of those different groups of constellations will be explained in more detail below. The constellations and the constellations values are generally predetermined and e.g. stored in a constellations storage 16 or retrieved from an external source. The MCS parameters may also be stored in the constellations storage 16 or the external source.

FIG. 2 shows an embodiment of a corresponding receiving apparatus 30 according to the present disclosure including an embodiment of a decoding and demodulation apparatus 40 according to the present disclosure for use with OFDM as PHY mode. Basically, the same blocks of the transmitter apparatus are reversed. After reception by a receiving unit 31 , RF processing like frequency down-conversion, receive filtering, analog-to-digital conversion, etc. is performed by an RF unit 32 and OFDM demodulation is performed by an OFDM demodulator 33 . An equalizer 34 reverses the effect of channel distortions and forwards the equalized. QAM symbols to the QAM demapper 35 (also called demodulator) for QAM demapping. Finally, LDPC decoding is performed in a FEC decoder 36 . In other embodiments of the receiving apparatus 30 additional elements may be provided, such as an output processing unit and/or a deframing unit, or other elements as e.g. conventionally used in a receiving apparatus of a system in accordance with IEEE 802.11ad.

The QAM demapper 35 (demodulator) and the FEC decoder 36 are often summarized as BICM demodulation apparatus and represent the decoding and demodulation apparatus 40 according to the present disclosure. The demodulator 35 generally demodulates received constellation values of a non-uniform constellation into cell words, whereby bit combinations are assigned to constellation values of the used non-uniform constellation. Based on a signalling information included in the received data the receiving apparatus 30 knows which one of a selection of non-uniform constellations of different groups has been used by the transmitting apparatus 10 so that the receiving apparatus 30 can use the same non-uniform constellation for demodulation. The FEC decoder 36 generally decodes the cell words according to the used PHY mode into output words. Also in the receiving apparatus 30 the constellations and the constellations values may be stored in a constellations storage 37 or retrieved from an external source.

The preferred demodulation and decoding considers soft values as opposed to hard decided values (0 and 1). Soft values represent the continuously distributed received values (possibly after A/D conversion including quantization) by more than two states (as in the case of binary (hard) decision). The reason is that for hard decision, the non-uniform constellations are generally not optimal. Nowadays, BICM receivers typically are soft receivers anyway.

FIG. 3 shows another embodiment of a transmission apparatus 10 ′ according to the present disclosure for use with SC as PHY mode. Differently from the transmission apparatus 10 shown in FIG. 1 , the transmission apparatus 10 ′ comprises a pill rotation unit 17 that introduces a pi/2 rotation, which improves the RF properties of the transmit signal. The pi/2 rotation has no influence on the BICM performance and is therefore generally not relevant to the NUC performance and optimization. Further, no OFDM unit is provided.

›DESCRIPTION OF THE EMBODIMENTS · 2 of 5

FIG. 4 shows an embodiment of a corresponding receiving apparatus 30 ′ according to the present disclosure for use with SC as PHY mode. Differently from the receiving apparatus 30 shown in FIG. 2 , the receiving apparatus 30 ′ just omits the OFDM demodulation unit 33 .

FIG. 5 shows an embodiment of a communications system 50 according to the present disclosure comprising one (or more) transmission apparatus 10 a , 10 b (Tx), which—depending on the used PHY mode—may either be transmission apparatus 10 as shown in FIG. 1 or transmission apparatus 10 ′ as shown in FIG. 3 , and one or more receiving apparatus 30 a , 30 b (Rx), which—depending on the used PHY mode—may either be receiving apparatus 30 as shown in FIG. 2 or receiving apparatus 30 ′ as shown in FIG. 4 . As an example, the transmission apparatus 10 a , which may be a WiFi access point or WiFi router, communicates with a receiving apparatus 30 a , which may be a user device like a smartphone, laptop or tablet, via a bi-directional communication channel 51 , for instance to provide access to the internet to the receiving apparatus 30 a . Both the transmission apparatus 10 a , 10 b and the receiving apparatus 30 a , 30 b may use the ideas of the present disclosure in said communication session.

Today's systems in accordance with IEEE 802.11ad (WLAN, WiFi) generally use uniform constellations. Several Modulation and Coding Schemes (MCSs) are defined for use in such systems. According to the present disclosure, non-uniform constellations and their bit labelling are proposed, which are optimized with respect to coding and modulation capacity and which may be used in systems in accordance with IEEE 802.11, particularly in accordance with versions like IEEE 802.11ad or upcoming versions such as IEEE 802.11ay.

The parameters of the basic MCSs for a transmitting apparatus are given in IEEE 802.11ad. The MCS index as described above defines the PHY mode, the QAM modulation order (indicating the value of M) and the used code rate R. The receiver needs to know which MCS index (or, alternatively, which PHY mode, modulation order and code rate R) is used at transmitter side for correct decoding. The transmission apparatus therefore signals the used MCS index (or, alternatively, which PHY mode, modulation order and code rate R). This signalling may be done at the beginning of each transmitted frame. For instance, this signalling information may be carried at the beginning of the frame in a special signal field. An example of a field which may be used is the HEADER field. For inserting such signalling information a signalling unit 17 may be provided in the transmission apparatus 10 , 10 ′.

In case of OFDM as PHY mode, the signalling information is typically carried within a small number (in particular 1 or 2) of OFDM symbols of the Header. This small number of signalling OFDM symbols follows short and long training symbols which form the beginning of each frame (the training symbols and signalling symbols are typically called preamble). In case of SC as PHY mode, the signalling information is typically carried in the Header.

The transmission apparatus 10 , 10 ′ may optionally comprise a selection unit 18 , shown with dashed lines in FIGS. 1 and 3 , which selects the MCS index (or the respective parameters indicated by the MCS index) depending on the channel conditions to the receiving apparatus 30 , 30 ′. For bad channel conditions a small MCS index is selected (lower throughput but also smaller error probability), for good channel conditions a higher MCS index is selected (higher throughput but also more prone to bit errors).

In other embodiments no such selection unit 18 is provided, but the transmission apparatus 10 , 10 ′ uses only SC mode as PHY mode and uses one of the disclosed non-uniform constellations for SC mode. This is particularly true if the transmission apparatus and the receiving apparatus do not support OFDM.

The PHY mode generally affects if the OFDM unit 13 or the pi/2 rotation unit 17 is used in the transmission apparatus. In the receiving apparatus it defines if the OFDM demodulator 33 is used/bypassed or not.

The receiving apparatus 30 , 30 ′ may optionally comprise a selection unit 38 as well, shown with dashed lines in FIGS. 2 and 4 , which selects the MCS index (or the respective parameters indicated by the MCS index) depending on the signalling information signalled by the transmission apparatus 10 , 10 ′.

According to the present disclosure a NUC is proposed for each MCS index separately for OFDM and SC as PHY mode. In particular for MCS index 10-12 and 18-24 of IEEE 802.11ad such NUCs are proposed. Additionally, NUCs are proposed for OFDM with 128-QAM and 256-QAM as well as for SC with 32-QAM, 64-QAM, 128-QAM and 256-QAM, for which no MCS index has been defined (yet) but which may particularly be used in systems in accordance with IEEE 802.11ad or IEEE 802.11ay.

According to the present disclosure the modulator 12 is configured to use, based on the PHY mode, the total number M of constellation points of the constellation and the code rate a predetermined non-uniform constellation and bit labeling. The selection unit 18 may be configured to select the total number M of constellation points of the constellation and the code rate based on channel conditions between a transmission apparatus including said coding and modulation apparatus and a receiving apparatus with which said transmission apparatus seeks to communicate. Preferably, the selection unit 18 selects a constellation with a higher number of M and/or a higher code rate the better the channel conditions are.

If OFDM is used as PHY mode and if M=16, 64, 128 or 256, a non-uniform constellation and bit labeling is used from a group A, the group A comprising constellations as defined in

sub-group A1 for 16-QAM with M=16 and code rates of 1/2, 5/8, 3/4 or 13/16, sub-group A2 for 64-QAM with M=64 and code rates of 5/8, 3/4 or 13/16, sub-group A3 for 128-QAM with M=128 and code rates of 1/2, 5/8, 3/4 or 13/16, and sub-group A4 for 256-QAM with M=256 and code rates of 1/2, 5/8, 3/4 or 13/16,

›DESCRIPTION OF THE EMBODIMENTS · 3 of 5

wherein the constellation points are defined by a constellation position vector w 0 . . . w M-1 and wherein the constellation position vectors of the different constellations are defined as follows:

A) M-QAM non-uniform constellations of group A for OFDM as PHY mode:

If SC is used as PHY mode and if M=16, 32, 64, 128 or 256, a non-uniform constellation and bit labeling is used from a group B, the group B comprising constellations as defined in:

sub-group B1 for 16-QAM with M=16 and code rates of 1/2, 5/8 or 3/4, sub-group B2 for 32-QAM with M=32 and code rates of 1/2, 5/8, 3/4 or 13/16, sub-group B3 for 64-QAM with M=64 and code rates of 1/2, 5/8, 3/4 or 13/16, sub-group B4 for 128-QAM with M=128 and code rates of 1/2, 5/8, 3/4 or 13/16, and sub-group B5 for 256-QAM with M=256 and code rates of 1/2, 5/8, 3/4 or 13/16,

wherein the constellation points are defined by a constellation position vector w 0 . . . w M-1 and wherein the constellation position vectors of the different constellations are defined as follows:

B) M-QAM non-uniform constellations of group B for single carrier mode as PHY mode:

Still further, a non-uniform constellation obtained from a constellation from anyone of groups A or B through rotation by an angle around the origin, through inversion of bit labels for all constellation points, through interchanging of bit positions, through mirroring on any line in the complex plane and/or through predistortion for the constellation points may be used by the modulator. Further, the bit labeling indicated in groups A to B may alternatively be inverted for one or more bit labels.

As shown above, two-dimensional NUCs are proposed including constellation points and bit labelling. The constellation points, i.e., coordinates in the complex plane, use the notation according to which a first column defines the w vector and the second column describes the bit labelling of the constellation points in the following columns (for different MCS indices). An exemplary diagram showing a constellation for a two-dimensional NUC for 16-QAM is depicted in FIG. 6 for modulation order M=16 and code rate R=5/8 (MCS=11) and SC as PHY mode. The corresponding constellation point vector is w=(+0.2173+0.4189i, +0.4326+1.1445i, −0.2173+0.4189i, −0.4326+1.1445i, +0.2173−0.4189i, +0.4326−1.1445i, −0.2173−0.4189i, −0.4326−1.1445i, +0.6578+0.2571i, +1.2088+0.5659i, −0.6578+0.2571i, −1.2088+0.5659i, +0.6578−0.2571i, +1.2088−0.5659i, −0.6578−0.2571i, −1.2088−0.5659i) for the bit labels from 0000 to 1111, wherein i=sqrt(−1) is the imaginary unit.

It shall be noted that the same NUCs may be used for different MCS indices (e.g. the constellation points defined for MCS 10 might be used for both MCS 10 and MCS 11 to reduce the overall number of NUCs), in particular for different code rates R. Hence, it is indicated in the tables for the NUCs for which MCS indices (representing a code rate R, a modulation order M and PHY mode) or for which code rates R the respective constellations points and bit labels are used. If there are two or more MCS indices or code rates R indicated, it may be predetermined for which MCS index/code rate R the constellations points and bit labels shall be used by a particular communication system or by particular devices. Further, it shall be noted that bit positions might be inverted, i.e. the bits of any bit position of the bit labeling might be flipped, resulting m the same performance.

The bit labelling, (i.e. which bit combination is assigned to which constellation point) is preferably optimized to fit in a best possible way into the existing IEEE 802.11ad or IEEE. 802.11ay architecture, yielding minimum error rates after FEC decoding. I.e. in an embodiment mainly the QAM mapper (modulator) 12 is changed compared to the known layout. In an embodiment the existing interleaving may be used as provided in known systems. Typically, in an optimization of the BICM, first the channel coding (FEC) is designed. In a next step the QAM (NUC) is optimized for the target SNR of the FEC. Here, the bit labelling of the NUC was optimized to optimally match the existing FEC and newly proposed NUC without adding an optimized interleaving between FEC and QAM.

For the bit labelling optimization, for a given FEC code, the error protection of the bits might be unequal (e.g. for irregular LDPC). The LLR values after demapping have different protection levels as well (given by the bit labelling). If the strongest code bits would be matched to the strongest LLR positions, the weak code bits are difficult to decode. A matching of the weakest code bits to the strongest LLR positions is also suboptimal. A optimum bit labelling balances the matching of different LLR robustness levels to code bits with different protection levels.

Obviously, numerous modifications and variations of the present disclosure are possible in light of the above teachings. It is therefore to be understood that within the scope of the appended claims, the disclosure may be practiced otherwise than as specifically described herein e.g., if the NUC position vectors are rounded to a smaller number of digits).

Thus, the foregoing discussion discloses and describes merely exemplary embodiments of the present disclosure. As will be understood by those skilled in the art, the present disclosure may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. Accordingly, the disclosure of the present disclosure is intended to be illustrative, but not limiting of the scope of the disclosure, as well as other claims. The disclosure, including any readily discernible variants of the teachings herein, defines, in part, the scope of the foregoing claim terminology such that no inventive subject matter is dedicated to the public.

In the claims, the word “comprising” does not exclude other elements or steps, and the indefinite article “a” or “an” does not exclude a plurality. A single element or other unit may fulfill the functions of several items recited in the claims. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage.

›DESCRIPTION OF THE EMBODIMENTS · 4 of 5

In so far as embodiments of the disclosure have been described as being implemented, at least in part, by software-controlled data processing apparatus, it will be appreciated that a non-transitory machine-readable medium carrying such software, such as an optical disk, a magnetic disk, semiconductor memory or the like, is also considered to represent an embodiment of the present disclosure. Further, such a software may also be distributed in other forms, such as via the Internet or other wired or wireless telecommunication systems.

The elements of the disclosed devices, apparatus and systems may be implemented by corresponding hardware and/or software elements, for instance appropriated circuits. A circuit is a structural assemblage of electronic components including conventional circuit elements, integrated circuits including application specific integrated circuits, standard integrated circuits, application specific standard products, and field programmable gate arrays. Further a circuit includes central processing units, graphics processing units, and microprocessors which are programmed or configured according to software code. A circuit does not include pure software, although a circuit includes the above-described hardware executing software.

It follows a list of further embodiments of the disclosed subject matter:

1. A coding and modulation apparatus comprising

an encoder configured to encode input data into cell words according to a low density parity check code, LDPC, and

a modulator configured to modulate said cell words into constellation values of a non-uniform constellation and to assign bit combinations to constellation values of the used non-uniform constellation,

wherein said modulating is configured to use, based on the PHY mode, the total number M of constellation points of the constellation and the code rate, a non-uniform constellation and bit labeling from one of the groups A or B as disclosed herein or a non-uniform constellation obtained from a constellation from anyone of groups A or B through rotation by an angle around the origin, through inversion of bit labels for all constellation points, through interchanging of bit positions, through mirroring on any line in the complex plane and/or through predistortion for the constellation points.

2. A coding and modulation apparatus as defined in embodiment 1,

further comprising a selection unit configured to select the total number M of constellation points of the constellation and the code rate based on channel conditions between a transmission apparatus including said coding and modulation apparatus and a receiving apparatus with which said transmission apparatus seeks to communicate.

3. A coding and modulation apparatus as defined in embodiment 2,

wherein said selection unit is configured to select a constellation with a higher number of M and/or a higher code rate the better the channel conditions are.

4. A coding and modulation apparatus as defined in one of embodiments 1 to 3,

wherein said coding and modulation apparatus is configured for use in a transmission apparatus according to IEEE 802.11.

5. A coding and modulation method comprising

encoding input data into cell words according to a low density parity check code, LDPC, and

modulating said cell words into constellation values of a non-uniform constellation and to assign bit combinations to constellation values of the used non-uniform constellation, wherein said modulating is configured to use, based on the PHY mode, the total number M of constellation points of the constellation and the code rate, a non-uniform constellation and bit labeling from one of the groups A or B as disclosed herein or a non-uniform constellation obtained from a constellation from anyone of groups A or B through rotation by an angle around the origin, through inversion of bit labels for all constellation points, through interchanging of bit positions, through mirroring on any line in the complex plane and/or through predistortion for the constellation points.

6. A transmission apparatus comprising:

a coding and modulation apparatus as defined in embodiment 1 configured to encode and modulate input data into constellation values,

a converter configured to convert said constellation values into one or more transmission streams to be transmitted, and

a transmitter configured to transmit said one or more transmission streams.

7. A transmission apparatus as defined in embodiment 6,

further comprising a signalling unit configured to embed signalling information into the one or more transmission streams, said signalling information including information about the PHY mode, the total number M of constellation points of the constellation, the location of the constellation points and the code rate.

8. A transmission apparatus as defined in embodiment 6 or 7,

wherein said signalling unit is configured to embed signalling information into the one or more transmission streams, said signalling information including a modulation and coding, MCS, index information including information about the PHY mode, the total number M of constellation points of the constellation and the code rate.

9. A transmission apparatus as defined in one of embodiments 6 to 8,

wherein said modulation unit is configured to select using a uniform constellation instead of one of said non-uniform constellations for modulating said cell words into constellation values, and

wherein said signalling unit is configured to embed signalling information into the one or more transmission streams, said signalling information including constellation information indicating if a non-uniform constellation or a uniform constellation has been used for modulation.

10. A transmission apparatus as defined in one of embodiments 7 to 9,

wherein said signalling unit is configured to embed said signalling information at the beginning of frames, in particular of each frame, of a plurality of frames used for transmission of the one or more transmission streams.

11. A transmission apparatus as defined in one of embodiments 7 to 9,

›DESCRIPTION OF THE EMBODIMENTS · 5 of 5

wherein said signalling unit is configured to embed said signalling information into a Header field.

12. A transmission method comprising:

a coding and modulation method as defined in embodiment 5 that encodes and modulates input data into constellation values,

converting said constellation values into one or more transmission streams to be transmitted, and

transmitting said one or more transmission streams.

13. A demodulation and decoding apparatus comprising:

a demodulator configured to demodulate constellation values of a non-uniform constellation into cell words and to assign bit combinations to constellation values of the used non-uniform constellation, and

a decoder configured to decode cell words into output data according to a low density parity check code, LDPC,

wherein said demodulating is configured to use, based on signalling information indicating the PHY mode, the total number M of constellation points of the constellation and the code rate, a non-uniform constellation and bit labeling from one of the groups A or B as disclosed herein or a non-uniform constellation obtained from a constellation from anyone of groups A or B through rotation by an angle around the origin, through inversion of bit labels for all constellation points, through interchanging of bit positions, through mirroring on any line in the complex plane and/or through predistortion for the constellation points.

14. A demodulation and decoding method comprising:

demodulating constellation values of a non-uniform constellation into cell words and assigning bit combinations to constellation values of the used non-uniform constellation, and

decoding cell words into output data according to a low density parity check code, LDPC,

wherein said demodulating is configured to use, based on signalling information indicating the PHY mode the total number M of constellation points of the constellation and the code rate, a non-uniform constellation and bit labeling from one of the groups A or B as disclosed herein or a non-uniform constellation obtained from a constellation from anyone of groups A or B through rotation by an angle around the origin, through inversion of bit labels for all constellation points, through interchanging of bit positions, through mirroring on any line in the complex plane and/or through predistortion for the constellation points.

15. Receiving apparatus comprising:

a receiver configured to receive one or more transmission streams,

a deconverter configured to deconvert one or more transmission streams into said constellation values, and

a demodulation and decoding apparatus as defined in embodiment 13 configured to demodulate and decode said constellation values into output data.

16. Receiving method comprising:

receiving one or more transmission streams,

deconverting one or more transmission streams into said constellation values, and

demodulating and decoding said constellation values into output data according to a method as defined in embodiment 14.

17. A non-transitory computer-readable recording medium that stores therein a computer program product, which, when executed by a processor, causes the method according to embodiment 5 or 14 to be performed.

18. A communications system comprising one or more transmission apparatus as defined in embodiment 1 and one or more receiving apparatus as defined in embodiment 15.

19. A computer program comprising program code means for causing a computer to perform the steps of said method according to embodiment 5 or 14 when said computer program is carried out on a computer.

›Tables in the description — 2
A1) 16-QAM NUC
R = 1/2 (MCS = 18)R = 5/8 (MCS = 19)R = 3/4 (MCS = 20)R = 13/16 (MCS = 21)
(or R = 5/8, 3/4 or(or R = 1/2, 3/4, or(or R = 5/8, 1/2 or(or R = 1/2, 5/8 or
wbit label13/16)13/16)13/16)3/4)
w00000+0.4925 + 1.2040i+0.2173 + 0.4189i+0.2976 − 0.2976i+0.3018 − 0.3018i
w10001+0.2530 + 0.4936i+0.6578 + 0.2571i+0.2976 − 0.9547i−0.3018 − 0.3018i
w20010+0.4925 − 1.2040i+0.4326 + 1.1445i−0.2976 − 0.2976i+0.3018 − 0.9534i
w30011+0.2530 − 0.4936i+1.2088 + 0.5659i−0.2976 − 0.9547i−0.3018 − 0.9534i
w40100+1.2040 + 0.4925i+0.2173 − 0.4189+0.9547 − 0.2976i+0.3018 + 0.3018i
w50101+0.4936 + 0.2530i+0.6578 − 0.2571i+0.9547 − 0.9547i−0.3018 + 0.3018i
w60110+1.2040 − 0.4925i+0.4326 − 1.1445i−0.9547 − 0.2976i+0.3018 + 0.9534i
w70111+0.4936 − 0.2530i+1.2088 − 0.5659i−0.9547 − 0.9547i−0.3018 + 0.9534i
w81000−0.4925 + 1.2040i−0.2173 + 0.4189i+0.2976 + 0.2976i+0.9534 − 0.3018i
w91001−0.2530 + 0.4936i−0.6578 + 0.2571i+0.2976 + 0.9547i−0.9534 − 0.3018i
w101010−0.4925 − 1.2040i−0.4326 + 1.1445i−0.2976 + 0.2976i+0.9534 − 0.9534i
w111011−0.2530 − 0.4936i−1..2088 + 0.5659i−0.2976 + 0.9547i−0.9534 − 0.9534i
w121100−1.2040 + 0.4925i−0.2173 − 0.4189i+0.9547 + 0.2976i+0.9534 + 0.3018i
w131101−0.4936 + 0.2530i−0.6578 − 0.2571i+0.9547 + 0.9547i−0.9534 + 0.3018i
w141110−1.2040 − 0.4925i−0.4326 − 1.1445i−0.9547 + 0.2976i+0.9534 + 0.9534i
w151111−0.4936 − 0.2530i−1.2088 − 0.5659i−0.9547 + 0.9547i−0.9534 + 0.9534i
A2) 64-QAM NUC
w/MCSR = 5/8 (MCS = 22)R = 3/4 (MCS = 23)R = 13/16 (MCS = 24)
indexbit label(or R = 3/4 or 13/16)(or R = 5/8 or 13/16)(or R = 5/8 or 3/4)
w0000000+1.4730 + 0.3019i+1.0501 − 0.1676i+1.0414 − 0.1712i
w1000001+1.2124 + 0.8333i+1.4380 − 0.2294i−1.0414 − 0.1712i
w2000010−1.4730 + 0.3019i+0.7233 − 0.1496i+1.0414 + 0.1712i
w3000011−1.2124 + 0.8333i+0.6220 − 1.1896i−1.0414 + 0.1712i
w4000100+1.4730 − 0.3019i−1.0501 − 0.1676i+1.4058 − 0.2115i
w5000101+1.2124 − 0.8333i−1.4380 − 0.2294i−1.4058 − 0.2115i
w6000110−1.4730 − 0.3019i−0.7233 − 0.1496i+1.4058 + 0.2115i
w7000111−1.2124 − 0.8333i−0.6220 − 1.1896i−1.4058 + 0.2115i
w8001000+1.0895 + 0.2172i+0.1398 − 0.1309i+0.1414 − 0.1379i
w9001001+0.8988 + 0.5768i+0.1680 − 1.0338i−0.1414 − 0.1379i
w10001010+1.0895 − 0.2172i+0.4246 − 0.1370i+0.1414 + 0.1379i
w11001011−0.8988 + 0.5768i+0.2326 − 1.3986i−0.1414 + 0.1379i
w12001100+1.0895 − 0.2172i−0.1398 − 0.1309i+0.1695 − 1.0298i
w13001101+0.8988 − 0.5768i−0.1680 − 1.0338i−0.1695 − 1.0298i
w14001110−1.0895 − 0.2172i−0.4246 − 0.1370i+0.1695 + 1.0298i
w15001111−0.8988 − 0.5768i−0.2326 − 1.3986i−0.1695 + 1.0298i
w16010000+0.2775 + 1.4188i+1.0501 + 0.1676i+0.7230 − 0.1517i
w17010001+0.7921 + 1.2096i+1.4380 + 0.2294i−0.7230 − 0.1517i
w18010010−0.2775 + 1.4188i+0.7233 + 0.1496i+0.7230 + 0.1517i
w19010011−0.7921 + 1.2096i+0.6220 + 1.1896i−0.7230 + 0.1517i
w20010100+0.2775 − 1.4188i−1.0501 + 0.1676i+0.5981 − 1.1597i
w21010101+0.7921 − 1.2096i−1.4380 + 0.2294i−0.5981 − 1.1597i
w22010110−0.2775 − 1.4188i−0.7233 + 0.1496i+0.5981 + 1.1597i
w23010111−0.7921 − 1.2096i−0.6220 + 1.1896i−0.5981 + 1.1597i
w24011000+0.2177 + 1.0243i+0.1398 + 0.1309i+0.4272 − 0.1421i
w25011001+0.6056 + 0.8481i+0.1680 + 1.0338i−0.4272 − 0.1421i
w26011010−0.2177 + 1.0243i+0.4246 + 0.1370i+0.4272 + 0.1421i
w27011011−0.6056 + 0.8481i+0.2326 + 1.3986i−0.4272 + 0.1421i
w28011100+0.2177 − 1.0243i−0.1398 + 0.1309i+0.2236 − 1.3784i
w29011101+0.6056 − 0.8481i−0.1680 + 1.0338i−0.2236 − 1.3784i
w30011110−0.2177 − 1.0243i−0.4246 + 0.1370i+0.2236 + 1.3784i
w31011111−0.6056 − 0.8481i−0.2326 + 1.3986i−0.2236 + 1.3784i
w32100000+0.1419 + 0.1122i+1.0725 − 0.5328i+1.0997 − 0.5419i
w33100001+0.3733 + 0.1498i+1.0771 − 0.9315i−1.0997 − 0.5419i
w34100010−0.1419 + 0.1122i+0.7267 − 0.4592i+1.0997 + 0.5419
w35100011−0.3733 + 0.1498i+0.6956 − 0.8095i−1.0997 + 0.5419i
w36100100+0.1419 − 0.1122i−1.0725 − 0.5328i+1.0691 − 0.9443i
w37100101+0.3733 − 0.1498i−1.0771 − 0.9315i−1.0691 − 0.9443i
w38100110−0.1419 − 0.1122i−0.7267 − 0.4592i+1.0691 + 0.9443i
w39100111−0.3733 − 0.1498i−0.6956 − 0.8095i−1.0691 + 0.9443i
w40101000+0.7863 + 0.1337i+0.1361 − 0.4023i+0.1440 − 0.4167i
w41101001+0.6394 + 0.3211i+0.1373 − 0.7043i−0.1440 − 0.4167i
w42101010−0.7863 + 0.1337i+0.4198 − 0.4151i+0.1440 + 0.4167i
w43101011−0.6394 + 0.3211i+0.4114 − 0.7109i−0.1440 + 0.4167i
w44101100+0.7863 − 0.1337i−0.1361 − 0.4023i+0.1426 − 0.7102i
w45101101+0.6394 − 0.3211i−0.1373 − 0.7043i−0.1426 − 0.7102i
w46101110−0.7863 − 0.1337i−0.4198 − 0.4151i+0.1426 + 0.7102i
w47101111−0.6394 − 0.3211i−0.4114 − 0.7109i−0.1426 + 0.7102i
w48110000+0.1138 + 0.3999i+1.0725 + 0.5328i+0.7484 + 0.4663i
w49110001+0.2891 + 0.3910i+1.0771 + 0.9315i−0.7484 − 0.4663i
w50110010−0.1138 + 0.3999i+0.7267 + 0.4592i+0.7484 + 0.4663i
w51110011−0.2891 + 0.3910i+0.6956 + 0.8095i−0.7484 + 0.4663i
w52110100+0.1138 − 0.3999i−1.0725 + 0.5328i+0.7360 − 0.8042i
w53110101+0.2891 − 0.3910i−1.0771 + 0.9315i−0.7360 − 0.8042i
w54110110−0.1138 − 0.3999i−0.7267 + 0.4592i+0.7360 + 0.8042i
w55110111−0.2891 − 0.3910i−0.6956 + 0.8095i−0.7360 + 0.8042i
w56111000+0.1487 + 0.7260i+0.1361 + 0.4023i+0.4369 − 0.4317i
w57111001+0.4397 + 0.5853i+0.1373 + 0.7043i−0.4369 − 0.4317i
w58111010−0.1487 + 0.7260i+0.4198 + 0.4151i+0.4369 + 0.4317i
w59111011−0.4397 + 0.5853i+0.4114 + 0.7109i−0.4369 + 0.4317i
w60111100+0.1487 − 0.7260i−0.1361 + 0.4023i+0.4351 − 0.7394i
w61111101+0.4397 − 0.5853i−0.1373 + 0.7043i−0.4351 − 0.7394i
w62111110−0.1487 − 0.7260i−0.4198 + 0.4151i+0.4351 + 0.7394i
w63111111−0.4397 − 0.5853i−0.4114 + 0.7109i−0.4351 + 0.7394i
A3) 128-QAM NUC
wConstellationwConstellation
indexbit labelpointindexbit labelpoint
for R = 1/2 (or R = 5/8, 3/4 or 13/16):
w00000000+0.7383 − 1.3947iw6401000000+0.1315 − 0.7332i
w10000000+0.2726 − 1.6070iw6501000001+0.1038 − 0.7607i
w20000001+0.7383 + 1.3947iw6601000010+0.1315 + 0.7332i
w30000001+0.2726 + 1.6070iw6701000011+0.1038 + 0.7607i
w40000010+1.5779 − 0.2230iw6801000100+0.1461 − 0.1146i
w50000010+1.2114 − 0.1662iw6901000101+0.1573 − 0.1142i
w60000011+1.5779 + 0.2230iw7001000110+0.1461 + 0.1146i
w70000011+1.2114 + 0.1662iw7101000111+0.1573 + 0.1142i
w80000100+0.5286 − 1.0997iw7201001000+0.3255 − 0.9067i
w90000100+0.1915 − 1.2689iw7301001001+0.1588 − 1.0122i
w100000101+0.5286 + 1.0997iw7401001010+0.3255 + 0.9067i
w110000101+0.1915 + 1.2689iw7501001011+0.1588 + 1.0122i
w120000110+0.7620 − 0.1121iw7601001100+0.4774 − 0.1074i
w130000110+0.9103 − 0.1272iw7701001101+0.4323 − 0.1096i
w140000111+0.7620 + 0.1121iw7801001110+0.4774 + 0.1074i
w150000111+0.9103 + 0.1272iw7901001111+0.4323 + 0.1096i
w160001000+1.0680 − 1.0753iw8001010000+0.1647 − 0.5388i
w170001000+1.0389 − 0.7336iw8101010001+0.1629 − 0.5296i
w180001001+1.0680 + 1.0753iw8201010010+0.1647 + 0.5388i
w190001001+1.0389 + 0.7736iw8301010011+0.1629 + 0.5296i
w200001010+1.4915 − 0.6927iw8401010100+0.1535 − 0.3082i
w210001010+1.1447 − 0.4719iw8501010101+0.1629 − 0.3084i
w220001011+1.4915 + 0.6927iw8601010110+0.1535 + 0.3082i
w230001011+1.1447 + 0.4719iw8701010111+0.1629 + 0.3084i
w240001100+0.6878 − 0.8578iw8801011000+0.4535 − 0.6452i
w250001100+0.7725 − 0.6723iw8901011001+0.4645 − 0.5898i
w260001101+0.6878 + 0.8578iw9001011010+0.4535 + 0.6452i
w270001101+0.7725 + 0.6723iw9101011011+0.4645 + 0.5898i
w280001110+0.7359 − 0.3230iw9201011100+0.4853 − 0.3237i
w290001110+0.8236 − 0.3936iw9301011101+0.4637 − 0.3425i
w300001111+0.7359 + 0.3230iw9401011110+0.4853 + 0.3237i
w310001111+0.8236 + 0.3936iw9501011111+0.4637 + 0.3425i
w320010000−0.7383 − 1.3947iw9601100000−0.1315 − 0.7332i
w330010000−0.2726 − 1.6070iw9701100001−0.1038 − 0.7607i
w340010001−0.7383 + 1.3947iw9801100010−0.1315 + 0.7332i
w350010001−0.2726 + 1.6070iw9901100011−0.1038 + 0.7607i
w360010010−1.5779 − 0.2230iw10001100100−0.1461 − 0.1146i
w370010010−1.2114 − 0.1662iw10101100101−0.1573 − 0.1142i
w380010011−1.5779 + 0.2230iw10201100110−0.1461 + 0.1146i
w390010011−1.2114 + 0.1662iw10301100111−0.1573 + 0.1142i
w400010100−0.5286 − 1.0997iw10401101000−0.3255 − 0.9067i
w410010100−0.1915 − 1.2689iw10501101001−0.1588 − 1.0122i
w420010101−0.5286 + 1.0997iw10601101010−0.3255 + 0.9067i
w430010101−0.1915 + 1.2689iw10701101011−0.1588 + 1.0122i
w440010110−0.7620 − 0.1121iw10801101100−0.4774 − 0.1074i
w450010110−0.9103 − 0.1272iw10901101101−0.4323 − 0.1096i
w460010111−0.7620 + 0.1121iw11001101110−0.4774 + 0.1074i
w470010111−0.9103 + 0.1272iw11101101111−0.4323 + 0.1096i
w480011000−1.0680 − 1.0753iw11201110000−0.1647 − 0.5388i
w490011000−1.0389 − 0.7336iw11301110001−0.1629 − 0.5296i
w500011001−1.0680 + 1.0753iw11401110010−0.1647 + 0.5388i
w510011001−1.0389 + 0.7336iw11501110011−0.1629 + 0.5296i
w520011010−1.4915 − 0.6927iw11601110100−0.1535 − 0.3082i
w530011010−1.1447 − 0.4719iw11701110101−0.1629 − 0.3084i
w540011011−1.4915 + 0.6927iw11801110110−0.1535 + 0.3082i
w550011011−1.1447 + 0.4719iw11901110111−0.1629 + 0.3084i
w560011100−0.6878 − 0.8578iw12001111000−0.4535 − 0.6452i
w570011100−0.7725 − 0.6723iw12101111001−0.4645 − 0.5898i
w580011101−0.6878 + 0.8578iw12201111010−0.4535 + 0.6452i
w590011101−0.7725 + 0.6723iw12301111011−0.4645 + 0.5898i
w600011110−0.7359 − 0.3230iw12401111100−0.4853 − 0.3237i
w610011110−0.8236 − 0.3936iw12501111101−0.4637 − 0.3425i
w620011111−0.7359 + 0.3230iw12601111110−0.4853 + 0.3237i
w630011111−0.8236 + 0.3936iw12701111111−0.4637 + 0.3425i
for R = 5/8 (or R = 1/2, 3/4, or 13/16)
w00000000+1.1470 + 0.4332iw6401000000+0.9015 + 0.4159i
w10000000+0.5553 + 0.4183iw6501000001+0.6908 + 0.3786i
w20000001+1.1804 + 0.7965iw6601000010+0.8996 + 0.6935i
w30000001+0.5406 + 0.6294iw6701000011+0.6580 + 0.7616i
w40000010+0.1470 − 0.4332iw6801000100+0.9015 − 0.4159i
w50000010+0.5553 − 0.4183iw6901000101+0.6908 − 0.3786i
w60000011+1.1804 − 0.7965iw7001000110+0.8996 − 0.6935i
w70000011+0.5406 − 0.6294iw7101000111+0.6580 − 0.7616i
w80000100−1.1470 + 0.4332iw7201001000−0.9015 + 0.4159i
w90000100−0.5553 + 0.4183iw7301001001−0.6908 + 0.3786i
w100000101−1.1804 + 0.7965iw7401001010−0.8996 + 0.6935i
w110000101−0.5406 + 0.6294iw7501001011−0.6580 + 0.7616i
w120000110−1.1470 − 0.4332iw7601001100−0.9015 − 0.4159i
w130000110−0.5553 − 0.4183iw7701001101−0.6908 − 0.3786i
w140000111−1.1804 − 0.7965iw7801001110−0.8996 − 0.6935i
w150000111−0.5406 − 0.6294iw7901001111−0.6580 − 0.7616i
w160001000+0.1029 + 0.4847iw8001010000+0.1029 + 0.3518i
w170001000+0.3416 + 0.4299iw8101010001+0.2989 + 0.3450i
w180001001+0.1167 + 0.6847iw8201010010+0.1222 + 0.9046i
w190001001+0.3403 + 0.6639iw8301010011+0.3701 + 0.8771i
w200001010+0.1029 − 0.4847iw8401010100+0.1029 − 0.3518i
w210001010+0.3416 − 0.4299iw8501010101+0.2989 − 0.3450i
w220001011+0.1167 − 0.6847iw8601010110+0.1222 − 0.9046i
w230001011+0.3403 − 0.6639iw8701010111+0.3701 − 0.8771i
w240001100−0.1029 + 0.4847iw8801011000−0.1029 + 0.3518i
w250001100−0.3416 + 0.4299iw8901011001−0.2989 + 0.3450i
w260001101−0.1167 + 0.6847iw9001011010−0.1222 + 0.9046i
w270001101−0.3403 + 0.6639iw9101011011−0.3701 + 0.8771i
w280001110−0.1029 − 0.4847iw9201011100−0.1029 − 0.3518i
w290001110−0.3416 − 0.4299iw9301011101−0.2989 − 0.3450i
w300001111−0.1167 − 0.6847iw9401011110−0.1222 − 0.9046i
w310001111−0.3403 − 0.6639iw9501011111−0.3701 − 0.8771i
w320010000+1.1636 + 0.1437iw9601100000+0.9136 + 0.1312i
w330010000+0.5673 + 0.1212iw9701100001+0.6911 + 0.1387i
w340010001+1.4805 + 0.1788iw9801100010+1.5526 + 0.5600i
w350010001+0.9781 + 1.1963iw9901100011+0.7165 + 1.0174i
w360010010+1.1636 − 0.1437iw10001100100+0.9136 − 0.1312i
w370010010+0.5673 − 0.1212iw10101100101+0.6911 − 0.1387i
w380010011+1.4805 − 0.1788iw10201100110+1.5526 − 0.5600i
w390010011+0.9781 − 1.1963iw10301100111+0.7165 − 1.0174i
w400010100−1.1636 + 0.1437iw10401101000−0.9136 + 0.1312i
w410010100−0.5673 + 0.1212iw10501101001−0.6911 + 0.1387i
w420010101−1.4805 + 0.1788iw10601101010−1.5526 + 0.5600i
w430010101−0.9781 + 1.1963iw10701101011−0.7165 + 1.0174i
w440010110−1.1636 − 0.1437iw10801101100−0.9136 − 0.1312i
w450010110−0.5673 − 0.1212iw10901101101−0.6911 − 0.1387i
w460010111−1.4805 − 0.1788iw11001101110−1.5526 − 0.5600i
w470010111−0.9781 − 1.1963iw11101101111−0.7165 − 1.0174i
w480011000+0.1058 + 0.0889iw11201110000+0.1130 + 0.1512i
w490011000+0.3723 + 0.1109iw11301110001+0.3195 + 0.1563i
w500011001+0.1939 + 1.4903iw11401110010+0.1450 + 1.1700i
w510011001+0.5867 + 1.4162iw11501110011+0.4379 + 1.1192i
w520011010+0.1058 − 0.0889iw11601110100+0.1130 − 0.1512i
w530011010+0.3723 − 0.1109iw11701110101+0.3195 − 0.1563i
w540011011+0.1939 − 1.4903iw11801110110+0.1450 − 1.1700i
w550011011+0.5867 − 1.4162iw11901110111+0.4379 − 1.1192i
w560011100−0.1058 + 0.0889iw12001111000−0.1130 + 0.1512i
w570011100−0.3723 + 0.1109iw12101111001−0.3195 + 0.1563i
w580011101−0.1939 + 1.4903iw12201111010−0.1450 + 1.1700i
w590011101−0.5867 + 1.4162iw12301111011−0.4379 + 1.1192i
w600011110−0.1058 − 0.0889iw12401111100−0.1130 − 0.1512i
w610011110−0.3723 − 0.1109iw12501111101−0.3195 − 0.1563i
w620011111−0.1939 − 1.4903iw12601111110−0.1450 − 1.1700i
w630011111−0.5867 − 1.4162iw12701111111−0.4379 − 1.1192i
for R = 3/4 (or R = 1/2. 5/8 or 13/16):
w00000000+1.0484 + 0.3435iw6401000000+1.0484 − 0.3435i
w10000000+1.1392 + 0.5908iw6501000001+1.1392 − 0.5908i
w20000001−1.0484 + 0.3435iw6601000010−1.0484 − 0.3435i
w30000001−1.1392 + 0.5908iw6701000011−1.1392 − 0.5908i
w40000010+1.0205 + 0.1130iw6801000100+1.0205 − 0.1130i
w50000010+1.3137 + 0.1401iw6901000101+1.0205 − 0.1130i
w60000011−1.0205 + 0.1130iw7001000110−1.0205 − 0.1130i
w70000011−1.3137 + 0.1401iw7101000111−1.0205 − 0.1130i
w80000100+0.8050 + 0.3736iw7201001000+0.8050 − 0.3736i
w90000100+0.8767 + 0.6075iw7301001001+0.8767 − 0.6075i
w100000101−0.8050 + 0.3736iw7401001010−0.8050 − 0.3736i
w110000101−0.8767 + 0.6075iw7501001011−0.8767 − 0.6075i
w120000110+0.7794 + 0.1239iw7601001100+0.7794 − 0.1239i
w130000110+1.4466 + 0.4199iw7701001101+1.4466 − 0.4199i
w140000111−0.7794 + 0.1239iw7801001110−0.7794 − 0.1239i
w150000111−1.4466 + 0.4199iw7901001111−1.4466 − 0.4199i
w160001000+0.5512 + 0.5784iw8001010000+0.5512 − 0.5784i
w170001000+0.5926 + 0.7787iw8101010001+0.5926 − 0.7787i
w180001001−0.5512 + 0.5784iw8201010010−0.5512 − 0.5784i
w190001001−0.5926 + 0.7787iw8301010011−0.5926 − 0.7787i
w200001010+0.4970 + 0.0732iw8401010100+0.4970 − 0.0732i
w210001010+1.1801 + 0.9322iw8501010101+1.1801 − 0.9322i
w220001011−0.4970 + 0.0732iw8601010110−0.4970 − 0.0732i
w230001011−1.1801 + 0.9322iw8701010111−1.1801 − 0.9322i
w240001100+0.5773 + 0.3945iw8801011000+0.5773 − 0.3945i
w250001100+0.8273 + 0.8515iw8901011001+0.8273 − 0.8515i
w260001101−0.5773 + 0.3945iw9001011010−0.5773 − 0.3945i
w270001101−0.8273 + 0.8515iw9101011011−0.8273 − 0.8515i
w280001110+0.5611 + 0.2103iw9201011100+0.5611 − 0.2103i
w290001110+0.9097 + 1.1442iw9301011101+0.9097 − 1.1442i
w300001111−0.5611 + 0.2103iw9401011110−0.5611 − 0.2103i
w310001111−0.9097 + 1.1442iw9501011111−0.9097 − 1.1442i
w320010000+0.1137 + 0.6007iw9601100000+0.1137 − 0.6007i
w330010000+0.1177 + 0.7939iw9701100001+0.1177 − 0.7939i
w340010001−0.1137 + 0.6007iw9801100010−0.1137 − 0.6007i
w350010001−0.1177 + 0.7939iw9901100011−0.1177 − 0.7939i
w360010010+0.0988 + 0.0864iw10001100100+0.0988 − 0.0864i
w370010010+0.1761 + 1.5225iw10101100101+0.1761 − 1.5225i
w380010011−0.0988 + 0.0864iw10201100110−0.0988 − 0.0864i
w390010011−0.1761 + 1.5225iw10301100111−0.1761 − 1.5225i
w400010100+0.1075 + 0.4242iw10401101000+0.1075 − 0.4242i
w410010100+0.1232 + 1.0065iw10501101001+0.1232 − 1.0065i
w420010101−0.1075 + 0.4242iw10601101010−0.1075 − 0.4242i
w430010101−0.1232 + 1.0065iw10701101011−0.1232 − 1.0065i
w440010110+0.1016 + 0.2562iw10801101100+0.1016 − 0.2562i
w450010110+0.1403 + 1.2447iw10901101101+0.1403 − 1.2447i
w460010111−0.1016 + 0.2562iw11001101110−0.1016 − 0.2562i
w470010111−0.1403 + 1.2447iw11101101111−0.1403 − 1.2447i
w480011000+0.3358 + 0.5918iw11201110000+0.3358 − 0.5918i
w490011000+0.3537 + 0.7995iw11301110001+0.3537 − 0.7995i
w500011001−0.3358 + 0.5918iw11401110010−0.3358 − 0.5918i
w510011001−0.3537 + 0.7995iw11501110011−0.3537 − 0.7995i
w520011010+0.2966 + 0.0872iw11601110100+0.2966 − 0.0872i
w530011010+0.4861 + 1.3847iw11701110101+0.4861 − 1.3847i
w540011011−0.2966 + 0.0872iw11801110110−0.2966 − 0.0872i
w550011011−0.4861 + 1.3847iw11901110111−0.4861 − 1.3847i
w560011100+0.3322 + 0.4087iw12001111000+0.3322 − 0.4087i
w570011100+0.3791 + 1.0277iw12101111001+0.3791 − 1.0277i
w580011101−0.3322 + 0.4087iw12201111010−0.3322 − 0.4087i
w590011101−0.3791 + 1.0277iw12301111011−0.3791 − 1.0277i
w600011110+0.3142 + 0.2509iw12401111100+0.3142 − 0.2509i
w610011110+0.6160 + 1.1277iw12501111101+0.6160 − 1.1277i
w620011111−0.3142 + 0.2509iw12601111110−0.3142 − 0.2509i
w630011111−0.6160 + 1.1277iw12701111111−0.6160 − 1.1277i
for R = 13/16 (or R = 1/2, 5/8 or 3/4)
w00000000+1.0422 + 0.3376iw6401000000+0.5556 + 0.6306i
w10000000+1.0422 − 0.3376iw6501000001+0.5556 − 0.6306i
w20000001−1.0422 + 0.3376iw6601000010−0.5556 + 0.6306i
w30000001−1.0422 − 0.3376iw6701000011−0.5556 − 0.6306i
w40000010+0.7966 + 0.3496iw6801000100+0.5761 + 0.4286i
w50000010+0.7966 − 0.3496iw6901000101+0.5761 − 0.4286i
w60000011−0.7966 + 0.3496iw7001000110−0.5761 + 0.4286i
w70000011−0.7966 − 0.3496iw7101000111−0.5761 − 0.4286i
w80000100+1.1154 + 0.5839iw7201001000+0.5970 + 0.8482i
w90000100+1.1154 − 0.5839iw7301001001+0.5970 − 0.8482i
w100000101−1.1154 + 0.5839iw7401001010−0.5970 + 0.8482i
w110000101−1.1154 − 0.5839iw7501001011−0.5970 − 0.8482i
w120000110+0.8563 + 0.5705iw7601001100+0.8378 + 0.8041i
w130000110+0.8563 − 0.5705iw7701001101+0.8378 − 0.8041i
w140000111−0.8563 + 0.5705iw7801001110−0.8378 + 0.8041i
w150000111−0.8563 − 0.5705iw7901001111−0.8378 − 0.8041i
w160001000+1.0010 + 0.1105iw8001010000+0.4942 + 0.0780i
w170001000+1.0010 − 0.1105iw8101010001+0.4942 − 0.0780i
w180001001−1.0010 + 0.1105iw8201010010−0.4942 + 0.0780i
w190001001−1.0010 − 0.1105iw8301010011−0.4942 − 0.0780i
w200001010+0.7613 + 0.1187iw8401010100+0.5456 + 0.2367i
w210001010+0.7613 − 0.1187iw8501010101+0.5456 − 0.2367i
w220001011−0.7613 + 0.1187iw8601010110−0.5456 + 0.2367i
w230001011−0.7613 − 0.1187iw8701010111−0.5456 − 0.2367i
w240001100+1.2844 + 0.1345iw8801011000+1.1670 + 0.8997i
w250001100+1.2844 − 0.1345iw8901011001+1.1670 − 0.8997i
w260001101−1.2844 + 0.1345iw9001011010−1.1670 + 0.8997i
w270001101−1.2844 − 0.1345iw9101011011−1.1670 − 0.8997i
w280001110+1.4001 + 0.4092iw9201011100+0.9031 + 1.0698i
w290001110+1.4001 − 0.4092iw9301011101+0.9031 − 1.0698i
w300001111−1.4001 + 0.4092iw9401011110−0.9031 + 1.0698i
w310001111−1.4001 − 0.4092iw9501011111−0.9031 − 1.0698i
w320010000+0.1125 + 0.6269iw9601100000+0.3351 + 0.6308i
w330010000+0.1125 − 0.6269iw9701100001+0.3351 − 0.6308i
w340010001−0.1125 + 0.6269iw9801100010−0.3351 + 0.6308i
w350010001−0.1125 − 0.6269iw9901100011−0.3351 − 0.6308i
w360010010+0.1109 + 0.4454iw10001100100+0.3383 + 0.4404i
w370010010+0.1109 − 0.4454iw10101100101+0.3383 − 0.4404i
w380010011−0.1109 + 0.4454iw10201100110−0.3383 + 0.4404i
w390010011−0.1109 − 0.4454iw10301100111−0.3383 − 0.4404i
w400010100+0.1155 + 0.8217iw10401101000+0.3510 + 0.8405i
w410010100+0.1155 − 0.8217iw10501101001+0.3510 − 0.8405i
w420010101−0.1155 + 0.8217iw10601101010−0.3510 + 0.8405i
w430010101−0.1155 − 0.8217iw10701101011−0.3510 − 0.8405i
w440010110+0.1239 + 1.0311iw10801101100+0.3850 + 1.0724i
w450010110+0.1239 − 1.0311iw10901101101+0.3850 − 1.0724i
w460010111−0.1239 + 1.0311iw11001101110−0.3850 + 1.0724i
w470010111−0.1239 − 1.0311iw11101101111−0.3850 − 1.0724i
w480011000+0.0978 + 0.0913iw11201110000+0.2935 + 0.0906i
w490011000+0.0978 − 0.0913iw11301110001+0.2935 − 0.0906i
w500011001−0.0978 + 0.0913iw11401110010−0.2935 + 0.0906i
w510011001−0.0978 − 0.0913iw11501110011−0.2935 − 0.0906i
w520011010+0.1038 + 0.2705iw11601110100+0.3172 + 0.2666i
w530011010+0.1038 − 0.2705iw11701110101+0.3172 − 0.2666i
w540011011−0.1038 + 0.2705iw11801110110−0.3172 + 0.2666i
w550011011−0.1038 − 0.2705iw11901110111−0.3172 − 0.2666i
w560011100+0.1646 + 1.5274iw12001111000+0.4543 + 1.3933i
w570011100+0.1646 − 1.5274iw12101111001+0.4543 − 1.3933i
w580011101−0.1646 + 1.5274iw12201111010−0.4543 + 1.3933i
w590011101−0.1646 − 1.5274iw12301111011−0.4543 − 1.3933i
w600011110+0.1345 + 1.2611iw12401111100+0.6436 + 1.1770i
w610011110+0.1345 − 1.2611iw12501111101+0.6436 − 1.1770i
w620011111−0.1345 + 1.2611iw12601111110−0.6436 + 1.1770i
w630011111−0.1345 − 1.2611iw12701111111−0.6436 − 1.1770i
A4) 256-QAM NUC
wbitConstellationwbitConstellation
indexlabelpointindexlabelpoint
for R = 1/2 (or R = 5/8, 3/4 or 13/16):
w00000000−1.2901 + 1.0495iw6401000000−1.2901 − 1.0495i
w10000000−0.7273 + 0.6160iw6501000001−0.7273 − 0.6160i
w20000001−1.0646 + 1.2876iw6601000010−1.0646 − 1.2876i
w30000001−0.5707 + 1.7662iw6701000011−0.5707 − 0.7662i
w40000010+1.2901 + 1.0495iw6801000100+1.2901 − 1.0495i
w50000010+0.7273 + 0.6160iw6901000101+0.7273 − 0.6160i
w60000011+1.0646 + 1.2876iw7001000110+1.0646 − 1.2876i
w70000011+0.5707 + 0.7662iw7101000111+0.5707 − 0.7662i
w80000100−1.4625 + 0.7740iw7201001000−1.4625 − 0.7740i
w90000100−0.8177 + 0.4841iw7301001001−0.8177 − 0.4841i
w100000101−0.7949 + 1.4772iw7401001010−0.7949 − 1.4772i
w110000101−0.4490 + 0.8461iw7501001011−0.4490 − 0.8461i
w120000110+1.4625 + 0.7740iw7601001100+1.4625 − 0.7740i
w130000110+0.8177 + 0.4841iw7701001101+0.8177 − 0.4841i
w140000111+0.7949 + 1.4772iw7801001110+0.7949 − 1.4772i
w150000111+0.4490 + 0.8461iw7901001111+0.4490 − 0.8461i
w160001000−0.2844 + 0.1296iw8001010000−0.2844 − 0.1296i
w170001000−0.5902 + 0.4857iw8101010001−0.5902 − 0.4857i
w180001001−0.1053 + 0.1494iw8201010010−0.1053 − 0.1494i
w190001001−0.4294 + 0.6363iw8301010011−0.4294 − 0.6363i
w200001010+0.2844 + 0.1296iw8401010100+0.2844 − 0.1296i
w210001010+0.5902 + 0.4857iw8501010101+0.5902 − 0.4857i
w220001011+0.1053 + 0.1494iw8601010110+0.1053 − 0.1494i
w230001011+0.4294 + 0.6363iw8701010111+0.4294 − 0.6363i
w240001100−0.2853 + 0.1309iw8801011000−0.2853 − 0.1309i
w250001100−0.6355 + 0.4185iw8901011001−0.6355 − 0.4185i
w260001101−0.1052 + 0.1495iw9001011010−0.1052 − 0.1495i
w270001101−0.3744 + 0.5744iw9101011011−0.3744 − 0.6744i
w280001110+0.2853 + 0.1309iw9201011100+0.2853 − 0.1309i
w290001110+0.6355 + 0.4185iw9301011101+0.6355 − 0.4185i
w300001111+0.1052 + 0.1495iw9401011110+0.1052 − 0.1495i
w310001111+0.3744 + 0.6744iw9501011111+0.3744 − 0.6744i
w320010000−1.6350 + 0.1593iw9601100000−1.6350 − 0.1598i
w330010000−0.9430 + 0.1100iw9701100001−0.9430 − 0.1100i
w340010001−0.1658 + 1.6747iw9801100010−0.1658 − 1.6747i
w350010001−0.1088 + 0.9530iw9901100011−0.1088 − 0.9630i
w360010010+1.6350 + 0.1593iw10001100100+1.6350 − 0.1593i
w370010010+0.9430 + 0.1100iw10101100101+0.9430 − 0.1100i
w380010011+0.1658 + 1.6747iw10201100110+0.1658 − 1.6747i
w390010011+0.1088 + 0.9530iw10301100111+0.1088 − 0.9530i
w400010100−1.5776 + 0.4735iw10401101000−1.5776 − 0.4735i
w410010100−0.9069 + 0.2829iw10501101001−0.9069 − 0.2829i
w420010101−0.4907 + 1.6084iw10601101010−0.4907 − 1.6084i
w430010101−0.2464 + 0.9270iw10701101011−0.2464 − 0.9270i
w440010110+1.5776 + 0.4735iw10801101100+1.5776 − 0.4735i
w450010110+0.9069 + 0.2829iw10901101101+0.9069 − 0.2829i
w460010111+0.4907 + 1.6084iw11001101110+0.4907 − 1.6084i
w470010111+0.2464 + 0.9270iw11101101111+0.2464 − 0.9270i
w480011000−0.3237 + 0.0849iw11201110000−0.3237 − 0.0849i
w490011000−0.7502 + 0.1138iw11301110001−0.7502 − 0.1138i
w500011001−0.0872 + 0.1390iw11401110010−0.0872 − 0.1390i
w510011001−0.1091 + 0.7656iw11501110011−0.1091 − 0.7656i
w520011010+0.3237 + 0.0849iw11601110100+0.3237 − 0.0849i
w530011010+0.7502 + 0.1138iw11701110101+0.7502 − 0.1138i
w540011011+0.0872 + 0.1390iw11801110110+0.0872 − 0.1390i
w550011011+0.1091 + 0.7656iw11901110111+0.1091 − 0.7656i
w560011100−0.3228 + 0.0867iw12001111000−0.3228 − 0.0867i
w570011100−0.7325 + 0.2088iw12101111001−0.7325 − 0.2088i
w580011101−0.0871 + 0.1392iw12201111010−0.0871 − 0.1392i
w590011101−0.1699 + 0.7537iw12301111011−0.1699 − 0.7537i
w600011110+0.3228 + 0.0867iw12401111100+0.3228 − 0.0867i
w610011110+0.7325 + 0.2088iw12501111101+0.7325 − 0.2088i
w620011111+0.0871 + 0.1392iw12601111110+0.0871 − 0.1392i
w630011111+0.1699 + 0.7537iw12701111111+0.1699 − 0.7537i
for R = 5/8 (or R = 1/2, 3/4 or 13/16):
w00000000−1.2537 + 1.0045iw6401000000−1.4164 + 0.7386i
w10000000−0.2443 + 0.2114iw6501000001−0.2508 + 0.2043i
w20000001−0.7404 + 0.6074iw6601000010−0.8324 + 0.4499i
w30000001−0.6961 + 0.5118iw6701000011−0.6808 + 0.3821i
w40000010−1.5761 + 0.1512iw6801000100−1.5251 + 0.4510i
w50000010−0.2545 + 0.0723iw6901000101−0.2566 + 0.0761i
w60000011−0.9317 + 0.0939iw7001000110−0.8975 + 0.2781i
w70000011−0.7729 + 0.0813iw7101000111−0.7412 + 0.2345i
w80000100+1.2537 + 1.0045iw7201001000+1.4164 + 0.7386i
w90000100+0.2443 + 0.2114iw7301001001+0.2508 + 0.2043i
w100000101+0.7404 + 0.6074iw7401001010+0.8324 + 0.4499i
w110000101+0.6089 + 0.5118iw7501001011+0.6808 + 0.3821i
w120000110+1.5761 + 0.1512iw7601001100+1.5251 + 0.4510i
w130000110+0.2545 + 0.0723iw7701001101+0.2566 + 0.0761i
w140000111+0.9317 + 0.0939iw7801001110+0.8975 + 0.2781i
w150000111+0.7729 + 0.0813iw7901001111+0.7412 + 0.2345i
w160001000−1.2537 − 1.0045iw8001010000−1.4164 − 0.7386i
w170001000−0.2443 − 0.2114iw8101010001−0.2508 − 0.2043i
w180001001−0.7404 − 0.6074iw8201010010−0.8324 − 0.4499i
w190001001−0.6089 − 0.5118iw8301010011−0.6808 − 0.3821i
w200001010−1.5761 − 0.1512iw8401010100−1.5251 − 0.4510i
w210001010−0.2545 − 0.0723iw8501010101−0.2566 − 0.0761i
w220001011−0.9317 − 0.0939iw8601010110−0.8975 − 0.2781i
w230001011−0.7729 − 0.0813iw8701010111−0.7412 − 0.2345i
w240001100+1.2537 − 1.0045iw8801011000+1.4164 − 0.7386i
w250001100+0.2443 − 0.2114iw8901011001+0.2508 − 0.2043i
w260001101+0.7404 − 0.6074iw9001011010+0.8324 − 0.4499i
w270001101+0.6089 − 0.5118iw9101011011+0.6808 − 0.3821i
w280001110+1.5761 − 0.1512iw9201011100+1.5251 − 0.4510i
w290001110+0.2545 − 0.0723iw9301011101+0.2566 − 0.0761i
w300001111+0.9317 − 0.0939iw9401011110+0.8975 − 0.2781i
w310001111+0.7729 − 0.0813iw9501011111+0.7412 − 0.2345i
w320010000−1.0876 + 1.2347iw9601100000−0.7769 + 1.4193i
w330010000−0.0940 + 0.2611iw9701100001−0.0898 + 0.2628i
w340010001−0.6205 + 0.7476iw9801100010−0.4711 + 0.8645i
w350010001−0.5048 + 0.6321iw9901100011−0.3892 + 0.7279i
w360010010−0.1632 + 1.6163iw10001100100−0.4813 + 1.5486i
w370010010−0.0734 + 0.0858iw10101100101−0.0722 + 0.0860i
w380010011−0.1006 + 0.9948iw10201100110−0.2955 + 0.9492i
w390010011−0.0848 + 0.8427iw10301100111−0.2443 + 0.8036i
w400010100+1.0376 + 1.2347iw10401101000+0.7769 + 1.4193i
w410010100+0.0940 + 0.2611iw10501101001+0.0898 + 0.2628i
w420010101+0.6205 + 0.7476iw10601101010+0.4711 + 0.8645i
w430010101+0.5048 + 0.6321iw10701101011+0.3892 + 0.7279i
w440010110+0.1632 + 1.6163iw10801101100+0.4813 + 1.5486i
w450010110+0.0734 + 0.0858iw10901101101+0.0722 + 0.0860i
w460010111+0.1006 + 0.9948iw11001101110+0.2955 + 0.9492i
w470010111+0.0848 + 0.8427iw11101101111+0.2443 + 0.8036i
w480011000−1.0376 − 1.2347iw11201110000−0.7769 − 1.4193i
w490011000−0.0940 − 0.2611iw11301110001−0.0898 − 0.2628i
w500011001−0.6205 − 0.7476iw11401110010−0.4711 − 0.8645i
w510011001−0.5048 − 0.6321iw11501110011−0.3892 − 0.7279i
w520011010−0.1632 − 1.6163iw11601110100−0.4813 − 1.5486i
w530011010−0.0734 − 0.0858iw11701110101−0.0722 − 0.0860i
w540011011−0.1006 − 0.9948iw11801110110−0.2955 − 0.9492i
w550011011−0.0848 − 0.8427iw11901110111−0.2443 − 0.8036i
w560011100+1.0376 − 1.2347iw12001111000+0.7769 − 1.4195i
w570011100+0.0940 − 0.2611iw12101111001+0.0898 − 0.2628i
w580011101+0.6205 − 0.7476iw12201111010+0.4711 − 0.8645i
w590011101+0.5048 − 0.6321iw12301111011+0.3892 − 0.7279i
w600011110+0.1632 − 1.6163iw12401111100+0.4813 − 1.5486i
w610011110+0.0734 − 0.0858iw12501111101+0.0722 − 0.0860i
w620011111+0.1006 − 0.9948iw12601111110+0.2955 − 0.9492i
w630011111+0.0848 − 0.8427iw12701111111+0.2443 − 0.8036i
for R = 3/4 (or R = 1/2, 5/8 or 13/16):
w00000000−0.5115 + 1.2063iw6401000000−0.6596 + 0.0715i
w10000000−0.5115 − 1.2063iw6501000001−0.6596 − 0.0715i
w20000001−0.3049 + 1.2378iw6601000010−0.5124 + 0.0667i
w30000001−0.3049 − 1.2378iw6701000011−0.5124 − 0.0667i
w40000010+0.5115 + 1.2063iw6801000100+0.6596 + 0.0715i
w50000010+0.5115 − 1.2063iw6901000101+0.6596 − 0.0715i
w60000011+0.3049 + 1.2378iw7001000110+0.5124 + 0.0667i
w70000011+0.3049 − 1.2378iw7101000111+0.5124 − 0.0667i
w80000100−0.4952 + 1.0059iw7201001000−0.6597 + 0.2116i
w90000100−0.4952 − 1.0059iw7301001001−0.6597 − 0.2116i
w100000101−0.3032 + 1.0518iw7401001010−0.5095 + 0.2008i
w110000101−0.3032 − 1.0518iw7501001011−0.5095 − 0.2008i
w120000110+0.4952 + 1.0059iw7601001100+0.6597 + 0.2116i
w130000110+0.4952 − 1.0059iw7701001101+0.6597 − 0.2116i
w140000111+0.3072 + 1.0518iw7801001110+0.5095 + 0.2008i
w150000111+0.3062 − 1.0518iw7901001111+0.5095 − 0.2008i
w160001000−1.1670 + 1.1014iw8001010000−1.4366 + 0.1213i
w170001000−1.1670 − 1.1014iw8101010001−1.4366 − 0.1213i
w180001001−0.1010 + 1.2545iw8201010010−0.0739 + 0.0596i
w190001001−0.1010 − 1.2545iw8301010011−0.0739 − 0.0596i
w200001010+1.1670 + 1.1014iw8401010100+1.4366 + 0.1213i
w210001010+1.1670 − 1.1014iw8501010101+1.4366 − 0.1213i
w220001011+0.1010 + 1.2545iw8601010110+0.0739 + 0.0596i
w230001011+0.1010 − 1.2545iw8701010111+0.0739 − 0.0596i
w240001100−1.2421 + 0.8557iw8801011000−1.2098 + 0.1077i
w250001100−1.2421 − 0.8557iw8901011001−1.2098 − 0.1077i
w260001101−0.0956 + 1.0676iw9001011010−0.0731 + 0.1767i
w270001101−0.0956 − 1.0676iw9101011011−0.0731 − 0.1767i
w280001110+1.2421 + 0.8557iw9201011100+1.2098 + 0.1077i
w290001110+1.2421 − 0.8557iw9301011101+1.2098 − 0.1077i
w300001111+0.0956 + 1.0676iw9401011110+0.0731 + 0.1767i
w310001111+0.0956 − 1.0676iw9501011111+0.0731 − 0.1767i
w320010000−0.6286 + 0.6639iw9601100000−0.6467 + 0.5036i
w330010000−0.6286 − 0.6639iw9701100001−0.6467 − 0.5036i
w340010001−0.4729 + 0.6321iw9801100010−0.4946 + 0.4818i
w350010001−0.4729 − 0.6321iw9901100011−0.4946 − 0.4818i
w360010010+0.6286 + 0.6639iw10001100100+0.6467 + 0.5036i
w370010010+0.6286 − 0.6639iw10101100101+0.6467 − 0.5036i
w380010011+0.4729 + 0.6321iw10201100110+0.4946 + 0.4818i
w390010011+0.4729 − 0.6321iw10301100111+0.4946 − 0.4818i
w400010100−0.5851 + 0.8353iw10401101000−0.6572 + 0.3526i
w410010100−0.5851 − 0.8353iw10501101001−0.6572 − 0.3526i
w420010101−0.4392 + 0.7880iw10601101010−0.5050 + 0.3380i
w430010101−0.4392 − 0.7880iw10701101011−0.5050 − 0.3380i
w440010110+0.5851 + 0.8353iw10801101100+0.6572 + 0.3526i
w450010110+0.5851 − 0.8353iw10901101101+0.6572 − 0.3526i
w460010111+0.4392 + 0.7880iw11001101110+0.5050 + 0.3380i
w470010111+0.4392 − 0.7880iw11101101111+0.5050 − 0.3380i
w480011000−1.2110 + 0.5795iw11201110000−1.4264 + 0.3764i
w490011000−1.2110 − 0.5795iw11301110001−1.4264 − 0.3764i
w500011001−0.0690 + 0.5518iw11401110010−0.0715 + 0.4218i
w510011001−0.0690 − 0.5518iw11501110011−0.0715 − 0.4218i
w520011010+1.2110 + 0.5795iw11601110100+1.4264 + 0.3764i
w530011010+1.2110 − 0.5795iw11701110101+1.4264 − 0.3764i
w540011011+0.0690 + 0.5518iw11801110110+0.0715 + 0.4218i
w550011011+0.0690 − 0.5518iw11901110111+0.0715 − 0.4218i
w560011100−1.4215 + 0.6637iw12001111000−1.2130 + 0.3237i
w570011100−1.4215 − 0.6637iw12101111001−1.2130 − 0.3237i
w580011101−0.0552 + 0.6903iw12201111010−0.0725 + 0.2978i
w590011101−0.0552 − 0.6903iw12301111011−0.0725 − 0.2978i
w600011110+1.4215 + 0.6637iw12401111100+1.2130 + 0.3237i
w610011110+1.4215 − 0.6637iw12501111101+1.2130 − 0.3237i
w620111111+0.0552 + 0.6903iw12601111110+0.0725 + 0.2978i
w630011111+0.0552 − 0.6903iw12701111111+0.0725 − 0.2978i
for R = 13/16 (or R = 1/2, 5/8 or 3/4):
w00000000−0.4934 + 1.1976iw6401000000−0.4934 − 1.1976i
w10000000−0.6474 + 0.6881iw6501000001−0.6474 − 0.6881i
w20000001−0.6614 + 0.0730iw6601000010−0.6614 − 0.0730i
w30000001−0.6545 + 0.5220iw6701000011−0.6545 − 0.5220i
w40000010−0.4787 + 1.0113iw6801000100−0.4787 − 1.0113i
w50000010−0.6010 + 0.8566iw6901000101−0.6010 − 0.8566i
w60000011−0.6676 + 0.2192iw7001000110−0.6676 − 0.2192i
w70000011−0.6674 + 0.3672iw7101000111−0.6674 − 0.3672i
w80000100−1.1592 + 1.0404iw7201001000−1.1592 − 1.0404i
w90000100−1.1898 + 0.5538iw7301001001−1.1898 − 0.5538i
w100000101−1.3908 + 0.1102iw7401001010−1.3908 − 0.1102i
w110000101−1.4061 + 0.3370iw7501001011−1.4081 − 0.3370i
w120000110−1.2410 + 0.8061iw7601001100−1.2410 − 0.8061i
w130000110−1.3911 + 0.5975iw7701001101−1.3911 − 0.5975i
w140000111−1.1855 + 0.1041iw7801001110−1.1855 − 0.1041i
w150000111−1.2043 + 0.3138iw7901001111−1.2043 − 0.3138i
w160001000−0.2985 + 1.2655iw8001010000−0.2985 − 1.2655i
w170001000−0.4920 + 0.6512iw8101010001−0.4920 − 0.6512i
w180001001−0.5130 + 0.0697iw8201010010−0.5130 − 0.0697i
w190001001−0.5045 + 0.4981iw8301010011−0.5045 − 0.4981i
w200001010−0.2876 + 1.0856iw8401010100−0.2876 − 1.0856i
w210001010−0.4556 + 0.8064iw8501010101−0.4556 − 0.8064i
w220001011−0.5147 + 0.2097iw8601010110−0.5147 − 0.2097i
w230001011−0.5132 + 0.3515iw8701010111−0.5132 − 0.3515i
w240001100−0.0980 + 1.2511iw8801011000−0.0980 − 1.2511i
w250001100−0.0701 + 0.5794iw8901011001−0.0701 − 0.5794i
w260001101−0.0734 + 0.0629iw9001011010−0.0734 − 0.0629i
w270001101−0.0724 + 0.4460iw9101011011−0.0724 − 0.4460i
w280001110−0.0934 + 1.0735iw9201011100−0.0934 − 1.0735i
w290001110−0.0582 + 0.7208iw9301011101−0.0582 − 0.7208i
w300001111−0.0734 + 0.1890iw9401011110−0.0734 − 0.1890i
w310001111−0.0731 + 0.3164iw9501011111−0.0731 − 0.3164i
w320010000−0.5534 + 1.3936iw9601100000−0.5534 − 1.3936i
w330010000−0.8188 + 0.7082iw9701100001−0.8188 − 0.7082i
w340010001−0.8139 + 0.0752iw9801100010−0.8139 − 0.0752i
w350010001−0.8095 + 0.5376iw9901100011−0.8095 − 0.5376i
w360010010−0.6787 + 1.0583iw10001100100−0.6787 − 1.0583i
w370010010−0.7729 + 0.8860iw10101100101−0.7729 − 0.8860i
w380010011−0.8305 + 0.2250iw10201100110−0.8305 − 0.2250i
w390010011−0.8315 + 0.3759iw10301100111−0.8315 − 0.3759i
w400010100−0.7567 + 1.2808iw10401101000−0.7567 − 1.2808i
w410010100−1.0161 + 0.7012iw10501101001−1.0161 − 0.7012i
w420010101−0.9757 + 0.0702iw10601101010−0.9757 − 0.0702i
w430010101−0.9739 + 0.5345iw10701101011−0.9739 − 0.5345i
w440010110−0.8952 + 1.0953iw10801101100−0.8952 − 1.0953i
w450010110−0.9646 + 0.8865iw10901101101−0.9646 − 0.8865i
w460010111−1.0091 + 0.2141iw11001101110−1.0091 − 0.2141i
w470010111−1.0164 + 0.3745iw11101101111−1.0164 − 0.3745i
w480011000−0.3350 + 1.4701iw11201110000−0.3350 − 1.4701i
w490011000−0.3446 + 0.6254iw11301110001−0.3446 − 0.6254i
w500011001−0.3664 + 0.0666iw11401110010−0.3664 − 0.0666i
w510011001−0.3586 + 0.4775iw11501110011−0.3586 − 0.4775i
w520011010−0.2713 + 0.9300iw11601110100−0.2713 − 0.9300i
w530011010−0.3149 + 0.7791iw11701110101−0.3149 − 0.7791i
w540011011−0.3666 + 0.2005iw11801110110−0.3666 − 0.2005i
w550011011−0.3649 + 0.3365iw11901110111−0.3649 − 0.3365i
w560011100−0.1095 + 1.4559iw12001111000−0.1095 − 1.4559i
w570011100−0.2067 + 0.6018iw12101111001−0.2067 − 0.6018i
w580011101−0.2200+ 0.0642iw12201111010−0.2200 − 0.0642i
w590011101−0.2160 + 0.4587iw12301111011−0.2160 − 0.4587i
w600011110−0.0910 + 0.9104iw12401111100−0.0910 − 0.9104i
w610011110−0.1761 + 0.7590iw12501111101−0.1761 − 0.7590i
w620011111−0.2199 + 0.1932iw12601111110−0.2199 − 0.1932i
w630011111−0.2191 + 0.3239iw12701111111−0.2191 − 0.3239i
wbitConstellationwbitConstellation
indexlabelpointindexlabelpoint
for R = 1/2 (or R = 5/8, 3/4 or 13/16):
w12810000000−1.0382 + 0.8623iw19211000000−1.0382 − 0.8623i
w12910000001−0.8504 + 0.7217iw19311000001−0.8504 − 0.7217i
w13010000010−0.8555 + 1.0542iw19411000010−0.8555 − 1.0542i
w13110000011−0.6961 + 0.8850iw19511000011−0.6961 − 0.8850i
w13210000100+1.0382 + 0.8623iw19611000100+1.0382 − 0.8623i
w13310000101+0.8504 + 0.7217iw19711000101+0.8504 − 0.7217i
w13410000110+0.8555 + 1.0542iw19811000110+0.8555 − 1.0542i
w13510000111+0.6961 + 0.8850iw19911000111+0.6961 − 0.8850i
w13610001000−1.1794 + 0.6376iw20011001000−1.1794 − 0.6376i
W13710001001−0.9638 + 0.5407iw20111001001−0.9638 − 0.5407i
w13810001010−0.6363 + 1.2064iw20211001010−0.6363 − 1.2064i
w13910001011−0.5229 + 1.0037iw20311001011−0.5229 − 1.0037i
w14010001100+1.1794 + 0.6376iw20411001100+1.1794 − 0.6376i
w14110001101+0.9638 + 0.5407iw20511001101+0.9638 − 0.5407i
w14210001110+0.6363 + 1.2064iw20611001110+0.6363 − 1.2064i
w14310001111+0.5229 + 1.0087iw20711001111+0.5229 − 1.0087i
w14410010000−0.3734 + 0.2560iw20811010000−0.3734 − 0.2560i
w14510010001−0.4968 + 0.3947iw20911010001−0.4968 − 0.3947i
w14610010010−0.1938 + 0.3621iw21011010010−0.1938 − 0.3621i
w14710010011−0.3224 + 0.5236iw21111010011−0.3224 − 0.5236i
w14810010100+0.3734 + 0.2560iw21211010100+0.3734 − 0.2560i
w14910010101+0.4968 + 0.3947iw21311010101+0.4968 − 0.3947i
w15010010110+0.1938 + 0.3621iw21411010110+0.1938 − 0.3621i
w15110010111+0.3224 + 0.5236iw21511010111+0.3224 − 0.5236i
w15210011000−0.3799 + 0.2517iw21611011000−0.3799 − 0.2517i
w15310011001−0.5231 + 0.3644iw21711011001−0.5231 − 0.3644i
w15410011010−0.1909 + 0.3627iw21811011010−0.1909 − 0.3627i
w15510011011−0.3016 + 0.5347iw21911011011−0.3016 − 0.5347i
w15610011100+0.3799 + 0.2517iw22011011100+0.3799 − 0.2517i
w15710011101+0.5231 + 0.3644iw22111011101+0.5231 − 0.3644i
w15810011110+0.1909 + 0.3627iw22211011110+0.1909 − 0.3627i
w15910011111+0.3016 + 0.5347iw22311011111+0.3016 − 0.5347i
w16010100000−1.3225 + 0.1320iw22411100000−1.3225 − 0.1320i
w16110100001−1.0854 + 0.1139iw22511100001−1.0854 − 0.1139i
w16210100010−0.1322 + 1.3631iw22611100010−0.1322 − 1.3631i
w16310100011−0.1124 + 1.1327iw22711100011−0.1124 − 1.1327i
w16410100100+1.3222 + 0.1320iw22811100100+1.3222 − 0.1320i
w16510100101+1.0854 + 0.1139iw22911100101+1.0854 − 0.1139i
w16610100110+0.1322 + 1.3631iw23011100110+0.1322 − 1.3631i
w16710100111+0.1124 + 1.1327iw23111100111+0.1124 − 1.1327i
w16810101000−1.2742 + 0.3922iw23211101000−1.2742 − 0.3922i
w16910101001−1.0441 + 0.3296iw23311101001−1.0441 − 0.3296i
w17010101010−0.3929 + 1.3102iw23411101010−0.3929 − 1.3102i
w17110101011−0.3160 + 1.0913iw23511101011−0.3160 − 1.0913i
w17210101100+1.2742 + 0.3922iw23611101100+1.2742 − 0.3922i
w17310101101+1.0441 + 0.3296iw23711101101+1.0441 − 0.3296i
w17410101110+0.3929 + 1.3102iw23811101110+0.3929 − 1.3102i
w17510101111+0.3160 + 1.0913iw23911101111+0.3160 − 1.0913i
w17610110000−0.4582 + 0.1123iw24011110000−0.4582 − 0.1123i
w17710110001−0.6473 + 0.1138iw24111110001−0.6473 − 0.1138i
w17810110010−0.0928 + 0.3970iw24211110010−0.0928 − 0.3970i
w17910110011−0.1054 + 0.5979iw24311110011−0.1054 − 0.5979i
w18010110100+0.4582 + 0.1123iw24411110100+0.4582 − 0.1123i
w18110110101+0.6473 + 0.1138iw24511110101+0.6473 − 0.1138i
w18210110110+0.0928 + 0.3970iw24611110110+0.0928 − 0.3970i
w18310110111+0.1054 + 0.5979iw24711110111+0.1054 − 0.5979i
w18410111000−0.4545 + 0.1251iw24811111000−0.4545 − 0.1251i
w18510111001−0.6339 + 0.1702iw24911111001−0.6339 − 0.1702i
w18610111010−0.0937 + 0.3973iw25011111010−0.0937 − 0.3973i
w18710111011−0.1230 + 0.5949iw25111111011−0.1230 − 0.5949i
w18810111100+0.4545 + 0.1251iw25211111100+0.4545 − 0.1251i
w18910111101+0.6339 + 0.1702iw25311111101+0.6339 − 0.1702i
w19010111110+0.0937 + 0.3973iw25411111110+0.0937 − 0.3973i
w19110111111+0.1230 + 0.5949iw25511111111+0.1230 − 0.5949i
for R = 5/8 (or R = 1/2, 3/4 or 13/16):
w12810000000−1.0508 + 0.8392iw19211000000−1.1844 + 0.6172i
w12910000001−0.3516 + 0.3079iw19311000001−0.3812 + 0.2673i
w13010000010−0.8852 + 0.7128iw19411000010−0.9957 + 0.5259i
w13110000011−0.4734 + 0.4145iw19511000011−0.5340 + 0.3230i
w13210000100−1.3158 + 0.1269iw19611000100−1.2728 + 0.3773i
w13310000101−0.4512 + 0.0729iw19711000101−0.4434 + 0.1145i
w13410000110−1.1073 + 0.1093iw19811000110−1.0701 + 0.3230i
w13510000111−0.6187 + 0.0756iw19911000111−0.5946 + 0.1815i
w13610001000+1.0508 + 0.8392iw20011001000+1.1844 + 0.6172i
W3710001001+0.3516 + 0.3079iw20111001001+0.3812 + 0.2673i
w13810001010+0.8852 + 0.7128iw20211001010+0.9957 + 0.5259i
w13910001011+0.4734 + 0.4145iw20311001011+0.5340 + 0.3230i
w14010001100+1.3158 + 0.1269iw20411001100+1.2728 + 0.3773i
w14110001101+0.4512 + 0.0729iw20511001101+0.4434 + 0.1145i
w14210001110+1.1073 + 0.1093iw20611001110+1.0701 + 0.3230i
w14310001111+0.6187 + 0.0756iw20711001111+0.5946 + 0.1815i
w14410010000−1.0508 − 0.8392iw20811010000−1.1844 − 0.6172i
w14510010001−0.3516 − 0.3079iw20911010001−0.3812 − 0.2673i
w14610010010−0.8852 − 0.7128iw21011010010−0.9957 − 0.5259i
w14710010011−0.4734 − 0.4145iw21111010011−0.5340 − 0.3230i
w14810010100−1.3158 − 0.1269iw21211010100−1.2728 − 0.3773i
w14910010101−0.4512 − 0.0729iw21311010101−0.4434 − 0.1145i
w15010010110−1.1073 − 0.1093iw21411010110−1.0701 − 0.3230i
w15110010111−0.6187 − 0.0756iw21511010111−0.5946 − 0.1815i
w15210011000+1.0508 − 0.8392iw21611011000+1.1844 − 0.6172i
w15310011001+0.3516 − 0.3079iw21711011001+0.3812 − 0.2673i
w15410011010+0.8852 − 0.7128iw21811011010+0.9957 − 0.5259i
w15510011011+0.4734 − 0.4145iw21911011011+0.5340 − 0.3230i
w15610011100+1.3158 − 0.1269iw22011011100+1.2728 − 0.3773i
w15710011101+0.4512 − 0.0729iw22111011101+0.4434 − 0.1145i
w15810011110+1.1073 − 0.1093iw22211011110+1.0701 − 0.3230i
w15910011111+0.6187 − 0.0756iw22311011111+0.5946 − 0.1815i
w16010100000−0.8734 + 1.0335iw22411100000−0.6562 + 1.1905i
w16110100001−0.2145 + 0.4159iw22511100001−0.1928 + 0.4287i
w16210100010−0.7384 + 0.8777iw22611100010−0.5570 + 1.0128i
w16310100011−0.3752 + 0.5265iw22711100011−0.3076 + 0.5885i
w16410100100−0.1381 + 1.3596iw22811100100−0.4076 + 1.3018i
w16510100101−0.0693 + 0.5212iw22911100101−0.0896 + 0.5118i
w16610100110−0.1180 + 1.1596iw23011100110−0.3468 + 1.1091i
w16710100111−0.0788 + 0.6933iw23111100111−0.1793 + 0.6649i
w16810101000+0.8734 + 1.0235iw23211101000+0.6562 + 1.1905i
w16910101001+0.2145 + 0.4159iw23311101001+0.1928 + 0.4287i
w17010101010+0.7384 + 0.8777iw23411101010+0.5570 + 1.0128i
w17110101011+0.3752 + 0.5265iw23511101011+0.3076 + 0.5885i
w17210101100+0.1381 + 1.3596iw23611101100+0.4076 + 1.3018i
w17310101101+0.0693 + 0.5212iw23711101101+0.0896 + 0.5118i
w17410101110+0.1180 + 1.1596iw23811101110+0.3468 + 1.1091i
w17510101111+0.0788 + 0.6933iw23911101111+0.1793 + 0.6649i
w17610110000−0.8734 − 1.0835iw24011110000−0.6562 − 1.1905i
w17710110001−0.2145 − 0.4159iw24111110001−0.1928 − 0.4287i
w17810110010−0.7384 − 0.8777iw24211110010−0.5570 − 1.0128i
w17910110011−0.3752 − 0.5265iw24311110011−0.3076 − 0.5885i
w18010110100−0.1381 − 1.3596iw24411110100−0.4076 − 1.3018i
w18110110101−0.0693 − 0.5212iw24511110101−0.0896 − 0.5118i
w18210110110−0.1180 − 1.1596iw24611110110−0.3468 − 1.1091i
w18310110111−0.0788 − 0.6933iw24711110111−0.1793 − 0.6649i
w18410111000+0.8734 − 1.0335iw24811111000+0.6562 − 1.1905i
w18510111001+0.2145 − 0.4159iw24911111001+0.1928 − 0.4287i
w18610111010+0.7384 − 0.8777iw25011111010+0.5570 − 1.0128i
w18710111011+0.3752 − 0.5265iw25111111011+0.3076 − 0.5885i
w18810111100+0.1381 − 1.3596iw25211111100+0.4076 − 1.3018i
w18910111101+0.0693 − 0.5212iw25311111101+0.0896 − 0.5118i
w19010111110+0.1180 − 1.1596iw25411111110+0.3468 − 1.1091i
w19110111111+0.0788 − 0.6933iw25511111111+0.1793 − 0.6649i
for R = 3/4 (or R = 1/2, 5/8 or 13/16):
w12810000000−0.5901 + 1.4171iw19211000000−0.8131 + 0.0729i
w12910000001−0.5901 − 1.4171iw19311000001−0.8131 − 0.0729i
w13010000010−0.3511 + 1.4584iw19411000010−0.3658 + 0.0625i
w13110000011−0.3511 − 1.4584iw19511000011−0.3658 − 0.0625i
w13210000100+0.5901 + 1.4171iw19611000100+0.8131 + 0.0729i
w13310000101+0.5901 − 1.4171iw19711000101+0.8131 − 0.0729i
w13410000110+0.3511 + 1.4584iw19811000110+0.3658 + 0.0625i
w13510000111+0.3511 − 1.4584iw19911000111+0.3658 − 0.0625i
w13610001000−0.6935 + 1.0466iw20011001000−0.8246 + 0.2158i
W13710001001−0.6935 − 1.0466iw20111001001−0.8246 − 0.2158i
w13810001010−0.2608 + 0.9107iw20211001010−0.3642 + 0.1899i
w13910001011−0.2608 − 0.9107iw20311001011−0.3642 − 0.1899i
w14010001100+0.6935 + 1.0466iw20411001100+0.8246 + 0.2158i
w14110001101+0.6935 − 1.0466iw20511001101+0.8246 − 0.2158i
w14210001110+0.2603 + 0.9107iw20611001110+0.3642 + 0.1899i
w14310001111+0.2603 − 0.9107iw20711001111+0.3642 − 0.1899i
w14410010000−0.8039 + 1.2957iw20811010000−0.9801 + 0.0651i
w14510010001−0.8039 − 1.2957iw20911010001−0.9801 − 0.0651i
w14610010010−0.1167 + 1.4782iw21011010010−0.2198 + 0.0612i
w14710010011−0.1167 − 1.4782iw21111010011−0.2198 − 0.0612i
w14810010100+0.8039 + 1.2957iw21211010100+0.9801 + 0.0651i
w14910010101+0.8039 − 1.2957iw21311010101+0.9801 − 0.0651i
w15010010110+0.1167 + 1.4782iw21411010110+0.2198 + 0.0612i
w15110010111+0.1167 − 1.4782iw21511010111+0.2198 − 0.0612i
w15210011000−0.8956 + 1.0881iw21611011000−1.0115 + 0.2009i
w15310011001−0.8956 − 1.0881iw21711011001−1.0115 − 0.2009i
w15410011010−0.0882 + 0.8981iw21811011010−0.2192 + 0.1815i
w15510011011−0.0882 − 0.8981iw21911011011−0.2192 − 0.1815i
w15610011100+0.8956 + 1.0881iw22011011100+1.0115 + 0.2009i
w15710011101+0.8956 − 1.0881iw22111011101+1.0115 − 0.2009i
w15810011110+0.0882 + 0.8981iw22211011110+0.2192 + 0.1815i
w15910011111+0.0882 − 0.8981iw22311011111+0.2192 − 0.1815i
w16010100000−0.8022 + 0.6879iw22411100000−0.8086 + 0.5185i
w16110100001−0.8022 − 0.6879iw22511100001−0.8086 − 0.5185i
w16210100010−0.3274 + 0.6045iw22611100010−0.3499 + 0.4571i
w16310100011−0.3274 − 0.6045iw22711100011−0.3499 − 0.4571i
w16410100100+0.8022 + 0.6879iw22811100100+0.8086 + 0.5185i
w16510100101+0.8022 − 0.6879iw22911100101+0.8086 − 0.5185i
w16610100110+0.3274 + 0.6045iw23011100110+0.3499 + 0.4571i
w16710100111+0.3274 − 0.6045iw23111100111+0.3499 − 0.4571i
w16810101000−0.7622 + 0.8634iw23211101000−0.8245 + 0.3593i
w16910101001−0.7622 − 0.8634iw23311101001−0.8245 − 0.3593i
w17010101010−0.2965 + 0.7629iw23411101010−0.3599 + 0.3216i
w17110101001−0.2965 − 0.7629iw23511101011−0.3599 − 0.3216i
w17210101100+0.7622 + 0.8634iw23611101100+0.8245 + 0.3593i
w17310101101+0.7622 − 0.8634iw23711101101+0.8245 − 0.3593i
w17410101110+0.2965 + 0.7629iw23811101110+0.3599 + 0.3216i
w17510101111+0.2965 − 0.7629iw23911101111+0.3599 − 0.3216i
w17610110000−1.0082 + 0.6930iw24011110000−0.9814 + 0.5205i
w17710110001−1.0082 − 0.6930iw24111110001−0.9814 − 0.5205i
w17810110010−0.1987 + 0.5742iw24211110010−0.2115 + 0.4337i
w17910110011−0.1987 − 0.5742iw24311110011−0.2115 − 0.4337i
w18010110100+1.0082 + 0.6930iw24411110100+0.9814 + 0.5205i
w18110110101+1.0082 − 0.6930iw24511110101+0.9814 − 0.5205i
w18210110110+0.1987 + 0.5742iw24611110110+0.2115 + 0.4337i
w18310110111+0.1987 − 0.5742iw24711110111+0.2115 − 0.4337i
w18410111000−0.9647 + 0.8849iw24811111000−1.0163 + 0.3615i
w18510111001−0.9647 − 0.8849iw24911111001−1.0163 − 0.3615i
w18610111010−0.1564 + 0.7374iw25011111010−0.2167 + 0.3057i
w18710111011−0.1564 − 0.7374iw25111111011−0.2157 − 0.3057i
w18810111100+0.9647 + 0.8849iw25211111100+1.0163 + 0.3615i
w18910111101+0.9647 − 0.8849iw25311111101+1.0163 − 0.3615i
w19010111110+0.1564 + 0.7374iw25411111110+0.2167 + 0.3057i
w19110111111+0.1564 − 0.7374iw25511111111+0.2167 − 0.3057i
for R = 13/16 (or R = 1/2, 5/8 or 3/4):
w12810000000+0.4934 + 1.1976iw19211000000+0.4934 − 1.1976i
w12910000001+0.6474 + 0.6881iw19311000001+0.6474 − 0.6881i
w13010000010+0.6614 + 0.0730iw19411000010+0.6614 − 0.0730i
w13110000011+0.6545 + 0.5220iw19511000011+0.6545 − 0.5220i
w13210000100+0.4787 + 1.0113iw19611000100+0.4787 − 1.0113i
w13310000101+0.6010 + 0.8566iw19711000101+0.6010 − 0.8566i
w13410000110+0.6676 + 0.2192iw19811000110+0.6676 − 0.2192i
w13510000111+0.6674 + 0.3672iw19911000111+0.6674 − 0.3672i
w13610001000+1.1592 + 1.0404iw20011001000+1.1592 − 1.0404i
W13710001001+1.1898 + 0.5538iw20111001001+1.1898 − 0.5538i
w13810001010+1.3908 + 0.1102iw20211001010+1.3908 − 0.1102i
w13910001011+1.4081 + 0.3370iw20311001011+1.4081 − 0.3370i
w14010001100+1.2410 + 0.8061iw20411001100+1.2410 − 0.8061i
w14110001101+1.3911 + 0.5975iw20511001101+1.3911 − 0.5975i
w14210001110+1.1855 + 0.1041iw20611001110+1.1855 − 0.1041i
w14310001111+1.2043 + 0.3138iw20711001111+1.2043 − 0.3138i
w14410010000+0.2985 + 1.2655iw20811010000+0.2985 − 1.2655i
w14510010001+0.4920 + 0.6512iw20911010001+0.4920 − 0.6512i
w14610010010+0.5130 + 0.0697iw21011010010+0.5130 − 0.0697i
w14710010011+0.5045 + 0.4981iw21111010011+0.5045 − 0.4981i
w14810010100+0.2876 + 1.0856iw21211010100+0.2876 − 1.0856i
w14910010101+0.4556 + 0.8064iw21311010101+0.4556 − 0.8064i
w15010010110+0.5147 + 0.2097iw21411010110+0.5147 − 0.2097i
w15110010111+0.5132 + 0.3515iw21511010111+0.5132 − 0.3515i
w15210011000+0.0980 + 1.2511iw21611011000+0.0980 − 1.2511i
w15310011001+0.0701 + 0.5794iw21711011001+0.0701 − 0.5794i
w15410011010+0.0734 + 0.0629iw21811011010+0.0734 − 0.0629i
w15510011011+0.0724 + 0.4460iw21911011011+0.0724 − 0.4460i
w15610011100+0.0934 + 1.0735iw22011011100+0.0934 − 1.0735i
w15710011101+0.0582 + 0.7208iw22111011101+0.0582 − 0.7208i
w15810011110+0.0734 + 0.1890iw22211011110+0.0734 − 0.1890i
w15910011111+0.0731 + 0.3164iw22311011111+0.0731 − 0.3164i
w16010100000+0.5534 + 1.3936iw22411100000+0.5534 − 1.3936i
w16110100001+0.8188 + 0.7082iw22511100001+0.8188 − 0.7082i
w16210100010+0.8139 + 0.0752iw22611100010+0.8139 − 0.0752i
w16310100011+0.8096 + 0.5376iw22711100011+0.8096 − 0.5376i
w16410100100+0.6787 + 1.0583iw22811100100+0.6787 − 1.0583i
w16510100101+0.7729 + 0.8860iw22911100101+0.7729 − 0.8860i
w16610100110+0.8305 + 0.2250iw23011100110+0.8305 − 0.2250i
w16710100111+0.8315 + 0.3759iw23111100111+0.8315 − 0.3759i
w16810101000+0.7567 + 1.2808iw23211101000+0.7567 − 1.2808i
w16910101001+1.0161 + 0.7012iw23311101001+1.0161 − 0.7012i
w17010101010+0.9757 + 0.0702iw23411101010+0.9757 − 0.0702i
w17110101011+0.9739 + 0.5345iw23511101011+0.9739 − 0.5345i
w17210101100+0.8952 + 1.0953iw23611101100+0.8952 − 1.0953i
w17310101101+0.9646 + 0.8865iw23711101101+0.9646 − 0.8865i
w17410101110+1.0091 + 0.2141iw23811101110+1.0091 − 0.2141i
w17510101111+1.0164 + 0.3745iw23911101111+1.0164 − 0.3745i
w17610110000+0.3350 + 1.4701iw24011110000+0.3350 − 1.4701i
w17710110001+0.3446 + 0.6254iw24111110001+0.3446 − 0.6254i
w17810110010+0.3664 + 0.0666iw24211110010+0.3664 − 0.0666i
w17910110011+0.3586 + 0.4775iw24311110011+0.3586 − 0.4775i
w18010110100+0.2713 + 0.9300iw24411110100+0.2713 − 0.9300i
w18110110101+0.3149 + 0.7791iw24511110101+0.3149 − 0.7791i
w18210110110+0.3666 + 0.2005iw24611110110+0.3666 − 0.2005i
w18310110111+0.3649 + 0.3365iw24711110111+0.3649 − 0.3365i
w18410111000+0.1095 + 1.4559iw24811111000+0.1095 − 1.4559i
w18510111001+0.2067 + 0.6018iw24911111001+0.2067 − 0.6018i
w18610111010+0.2200 + 0.0642iw25011111010+0.2200 − 0.0642i
w18710111011+0.2160 + 0.4587iw25111111011+0.2160 − 0.4587i
w18810111100+0.0910 + 0.9104iw25211111100+0.0910 − 0.9104i
w18910111101+0.1761 + 0.7590iw25311111101+0.1761 − 0.7590i
w19010111110+0.2199 + 0.1932iw25411111110+0.2199 − 0.1932i
w19110111111+0.2191 + 0.3239iw25511111111+0.2191 − 0.3239i
B1) 16-QAM NUC
R = 1/2 (MCS =R = 5/8 (MCS =R = 3/4 (MCS =
10) (or R = 5/8,11) (or R = 1/2,12) (or R = 5/8,
wbit label3/4 or 13/16)3/4, or 13/16)1/2 or 13/16)
w00000+0.4925 + 1.2040i+0.2173 + 0.4189i+0.2949 − 0.2949i
w10001+0.4925 − 1.2040i+0.4326 + 1.1445i+0.9555 − 0.2949i
w20010+0.2530 + 0.4936i−0.2173 + 0.4189i−0.2949 − 0.2949i
w30011+0.2530 − 0.4936i−0.4326 + 1.1445i−0.9555 − 0.2949i
w40100−0.4925 + 1.2040i+0.2173 − 0.4189i+0.2949 − 0.9555i
w50101−0.4925 − 1.2040i+0.4326 − 1.1445i+0.9555 − 0.9555i
w60110−0.2530 + 0.4936i−0.2173 − 0.4189i−0.2949 − 0.9555i
w70111−0.2530 − 0.4936i−0.4326 − 1.1445i−0.9555 − 0.9555i
w81000+1.2040 + 0.4925i+0.6578 + 0.2571i+0.2949 + 0.2949i
w91001+1.2040 − 0.4925i+1.2088 + 0.5659i+0.9555 + 0.2949i
w101010+0.4936 + 0.2530i−0.6578 + 0.2571i−0.2949 + 0.2949i
w111011+0.4936 − 0.2530i−1.2088 + 0.5659i−0.9555 + 0.2949i
w121100−1.2040 + 0.4925i+0.6578 − 0.2571i+0.2949 + 0.9555i
w131101−1.2040 − 0.4925i+1.2088 − 0.5659i+0.9555 + 0.9555i
w141110−0.4936 + 0.2530i−0.6578 − 0.2571i−0.2949 + 0.9555i
w151111−0.4936 − 0.2530i−1.2088 − 0.5659i−0.9555 + 0.9555i
B2) 32-QAM NUC
R = 1/2R = 5/8R = 3/4R = 13/16
w/MCS(or R = 5/8,(or R = 1/2, 3/4(or R = 1/2,(or R = 1/2,
indexbit label3/4 or 13/16or 13/165/8 or 13/165/8 or 3/4
w000000+0.1929 + 0.1744i+0.2187 + 0.1559i+0.2113 + 0.1819i+0.2082 + 0.1996i
w100001+0.2283 + 0.5036i+0.2225 + 0.5103i+0.6163 + 1.2930i+0.6964 + 1.2272i
w200010+0.6963 + 0.1782i+0.2187 − 0.1559i+0.2113 − 0.1819i+0.2041 + 0.6147i
w300011+0.6364 + 0.4437i+0.2225 − 0.5103i+0.6163 − 1.2930i+0.2297 + 1.0778i
w400100+0.1929 − 0.1744i−0.2187 + 0.1559i+0.6590 + 0.1934i+0.6409 + 0.2027i
w500101+0.2283 − 0.5036i−0.2225 + 0.5103i+1.1691 + 0.2524i+1.1236 + 0.2383i
w600110+0.6963 − 0.1782i−0.2187 − 0.1559i+0.6590 − 0.1934i+0.6262 + 0.6234i
w700111+0.6364 − 0.4437i−0.2225 − 0.5103i+1.1691 − 0.2524i+1.0921 + 0.7399i
w801000+0.3541 + 1.4168i+0.7211 + 0.1755i−0.2113 + 0.1819i+0.2082 − 0.1996i
w901001+0.2627 + 0.9170i+0.6446 + 0.5183i−0.6163 + 1.2930i+0.6964 − 1.2272i
w1001010+1.3162 + 0.3270i+0.7211 − 0.1755i−0.2113 − 0.1819i+0.2041 − 0.6147i
w1101011+0.9382 + 0.8637i+0.6446 − 0.5183i−0.6163 − 1.2930i+0.2297 − 1.0778i
w1201100+0.3541 − 1.4168i−0.7211 + 0.1755i−0.6590 + 0.1934i+0.6409 − 0.2027i
w1301101+0.2627 − 0.9170i−0.6446 + 0.5183i−1.1691 + 0.2524i+1.1236 − 0.2383i
w1401110+1.3162 − 0.3270i−0.7211 − 0.1755i−0.6590 − 0.1934i+0.6262 − 0.6234i
w1501111+0.9382 − 0.8637i−0.6446 − 0.5183i−1.1691 − 0.2524i+1.0921 − 0.7399i
w1610000−0.1929 + 0.1744i+0.3459 + 1.3987i+0.2042 + 0.5736i−0.2082 + 0.1996i
w1710001−0.2283 + 0.5036i+0.2415 + 0.9207i+0.2154 + 1.0277i−0.6964 + 1.2272i
w1810010−0.6963 + 0.1782i+0.3459 − 1.3987i+0.2042 − 0.5736i−0.2041 + 0.6147i
w1910011−0.6364 + 0.4437i+0.2415 − 0.9207i+0.2154 − 1.0277i−0.2297 + 1.0778i
w2010100−0.1929 − 0.1744i−0.3459 + 1.3987i+0.6214 + 0.5984i−0.6409 + 0.2027i
w2110101−0.2283 − 0.5036i−0.2415 + 0.9207i+1.0670 + 0.7825i−1.1236 + 0.2383i
w2210110−0.6963 − 0.1782i−0.3459 − 1.3987i+0.6214 − 0.5984i−0.6262 + 0.6234i
w2310111−0.6364 − 0.4437i−0.2415 − 0.9207i+1.0670 − 0.7825i−1.0921 + 0.7399i
w2411000−0.3541 + 1.4168i+1.2734 + 0.3186i−0.2042 + 0.5736i−0.2082 − 0.1996i
w2511001−0.2627 + 0.9170i+0.9258 + 0.9059i−0.2154 + 1.0277i−0.6964 − 1.2272i
w2611010−1.3162 + 0.3270i+1.2734 − 0.3186i−0.2042 − 0.5736i−0.2041 − 0.6147i
w2711011−0.9382 + 0.8637i+0.9258 − 0.9059i−0.2154 − 1.0277i−0.2297 − 1.0778i
w2811100−0.3541 − 1.4168i−1.2734 + 0.3186i−0.6214 + 0.5984i−0.6409 − 0.2027i
w2911101−0.2627 − 0.9170i−0.9258 + 0.9059i−1.0670 + 0.7825i−1.1236 − 0.2383i
w3011110−1.3162 − 0.3270i−1.2734 − 0.3186i−0.6214 − 0.5984i−0.6262 − 0.6234i
w3111111−0.9382 − 0.8637i−0.9258 − 0.9059i−1.0670 − 0.7825i−1.0921 − 0.7399i
B3) 64-QAM NUC
R = 1/2R = 5/8R = 3/4R = 13/16
w/MCS(or R = 5/8,(or R = 1/2, 3/4(or R = 1/2,(or R = 1/2,
indexbit label3/4 or 13/16or 13/165/8 or 13/165/8 or 3/4
w0000000+0.4732 + 0.2920i+0.4730 + 0.3019i+1.0501 − 0.1676i+1.0414 − 0.1712i
w1000001+1.2487 + 0.8348i−0.4730 + 0.3019i+1.4380 − 0.2294i+0.7230 − 0.1517i
w2000010+0.4732 − 0.2920i+1.0895 + 0.2172i+0.1398 − 0.1309i+1.0997 − 0.5419i
w3000011+1.2487 − 0.8348i−1.0895 + 0.2172i+0.1680 − 1.0338i+0.7484 − 0.4663i
w4000100+1.0283 + 0.2071i+0.1419 + 0.1122i+1.0725 − 0.5328i−1.0414 − 0.1712i
w5000101+0.8760 + 0.5811i−0.1419 + 0.1122i+0.0771 − 0.9315i−0.7230 − 0.1517i
w6000110+1.0283 − 0.2071i+0.7863 + 0.1337i+0.1361 − 0.4023i−1.0997 − 0.5419i
w7000111+0.8760 − 0.5811i−0.7863 + 0.1337i+0.1373 − 0.7043i−0.7484 − 0.4663i
w8001000−0.4732 + 0.2920i+0.4730 − 0.3019i+1.0501 + 0.1676i+1.0414 + 0.1712i
w9001001−1.2487 + 0.8348i−0.4730 − 0.3019i+1.4380 + 0.2294i+0.7230 + 0.1517i
w10001010−0.4732 − 0.2920i+1.0895 − 0.2172i+0.1398 + 0.1309i+1.0997 + 0.5419i
w11001011−1.2487 − 0.8348i−1.0895 − 0.2172i+0.1680 + 1.0338i+0.7484 + 0.4663i
w12001100−1.0283 + 0.2071i+0.1419 − 0.1122i+1.0725 + 0.5328i−1.0414 + 0.1712i
w13001101−0.8760 + 0.5811i−0.1419 − 0.1122i+0.0771 + 0.9315i−0.7230 + 0.1517i
w14001110−1.0283 − 0.2071i+0.7863 − 0.1337i+0.1361 + 0.4023i−1.0997 + 0.5419i
w15001111−0.8760 − 0.5811i−0.7863 − 0.1337i+0.1373 + 0.7043i−0.7484 + 0.4663i
w16010000+0.2920 + 1.4732i+1.2124 + 0.8333i+0.7233 − 0.1496i+0.1414 − 0.1379i
w17010001+0.8348 + 1.2487i−1.2124 + 0.8333i+0.6220 − 1.1896i+0.4272 − 0.1421i
w18010010+0.2920 − 1.4732i+0.8988 + 0.5768i+0.4246 − 0.1370i+0.1440 − 0.4167i
w19010011+0.8348 − 1.2487i−0.8988 + 0.5768i+0.2326 − 1.3986i+0.4369 − 0.4317i
w20010100+0.2071 + 1.0283i+0.3733 + 0.1498i+0.7267 − 0.4592i−0.1414 − 0.1379i
w21010101+0.5811 + 0.8760i−0.3733 + 0.1498i+0.6956 − 0.8095i−0.4272 − 0.1421i
w22010110+0.2071 − 1.0283i+0.6394 + 0.3211i+0.4198 − 0.4151i−0.1440 − 0.4167i
w23010111+0.5811 − 0.8760i−0.6394 + 0.3211i+0.4114 − 0.7109i−0.4369 − 0.4317i
w24011000−0.2920 + 1.4732i+1.2124 − 0.8333i+0.7233 + 0.1496i+0.1414 + 0.1379i
w25011001−0.8348 + 1.2487i−1.2124 − 0.8333i+0.6220 + 1.1896i+0.4272 + 0.1421i
w26011010−0.2920 − 1.4732i+0.8988 − 0.5768i+0.4246 + 0.1370i+0.1440 + 0.4167i
w27011011−0.8348 − 1.2487i−0.8988 − 0.5768i+0.2326 + 1.3986i+0.4369 + 0.4317i
w28011100−0.2071 + 1.0283i+0.3733 − 0.1498i+0.7267 + 0.4592i−0.1414 + 0.1379i
w29011101−0.5811 + 0.8760i−0.3733 − 0.1498i+0.6956 + 0.8095i−0.4272 + 0.1421i
w30011110−0.2071 − 1.0283i+0.6394 − 0.3211i+0.4198 + 0.4151i−0.1440 + 0.4167i
w31011111−0.5811 − 0.8760i−0.6394 − 0.3211i+0.4114 + 0.7109i−0.4369 + 0.4317i
w32100000+0.3138 + 0.1393i+0.2775 + 1.4188i−1.0501 − 0.1676i+1.4058 − 0.2115i
w33100001+0.3094 + 0.1671i−0.2775 + 1.4188i−1.4380 − 0.2294i+0.5981 − 1.1597i
w34100010+0.3138 − 0.1393i+0.2177 + 1.0243i−0.1398 − 0.1309i+1.0691 − 0.9443i
w35100011+0.3094 − 0.1671i−0.2177 + 1.0243i−0.1680 − 1.0338i+0.7360 − 0.8042i
w36100100+0.7004 + 0.1720i+0.1138 + 0.3999i−1.0725 − 0.5328i−1.4058 − 0.2115i
w37100101+0.6174 + 0.3741i−0.1138 + 0.3999i−0.0771 − 0.9315i−0.5981 − 1.1597i
w38100110+0.7004 − 0.1720i+0.1487 + 0.7260i−0.1361 − 0.4023i−1.0691 − 0.9443i
w39100111+0.6174 − 0.3741i−0.1487 + 0.7260i−0.1373 − 0.7043i−0.7360 − 0.8042i
w40101000−0.3138 + 0.1393i+0.2775 − 1.4188i−1.0501 + 0.1676i+1.4058 + 0.2115i
w41101001−0.3094 + 0.1671i−0.2775 − 1.4188i−1.4380 + 0.2294i+0.5981 + 1.1597i
w42101010−0.3138 − 0.1393i+0.2177 − 1.0243i−0.1398 + 0.1309i+1.0691 + 0.9443i
w43101011−0.3094 − 0.1671i−0.2177 − 1.0243i−0.1680 + 1.0338i+0.7360 + 0.8042i
w44101100−0.7004 + 0.1720i+0.1138 − 0.3999i−1.0725 + 0.5328i−1.4058 + 0.2115i
w45101101−0.6174 + 0.3741i−0.1138 − 0.3999i−0.0771 + 0.9315i−0.5981 + 1.1597i
w46101110−0.7004 − 0.1720i+0.1487 − 0.7260i−0.1361 + 0.4023i−1.0691 + 0.9443i
w47101111−0.6174 − 0.3741i−0.1487 − 0.7260i−0.1373 + 0.7043i−0.7360 + 0.8042i
w48110000+0.1393 + 0.3138i+0.7921 + 1.2096i−0.7233 − 0.1496i+0.1695 − 1.0298i
w49110001+0.1671 + 0.3094i−0.7921 + 1.2096i−0.6220 − 1.1896i+0.2236 − 1.3784i
w50110010+0.1393 − 0.3138i+0.6056 + 0.8481i−0.4246 − 0.1370i+0.1426 − 0.7102i
w51110011+0.1671 − 0.3094i−0.6056 + 0.8481i−0.2326 − 1.3986i+0.4351 − 0.7394i
w52110100+0.1720 + 0.7004i+0.2891 + 0.3110i−0.7267 − 0.4592i−0.1695 − 1.0298i
w53110101+0.3741 + 0.6174i−0.2891 + 0.3110i−0.6956 − 0.8095i−0.2236 − 1.3784i
w54110110+0.1720 − 0.7004i+0.4397 + 0.5853i−0.4198 − 0.4151i−0.1426 − 0.7102i
w55110111+0.3741 − 0.6174i−0.4397 + 0.5853i−0.4114 − 0.7109i−0.4351 − 0.7394i
w56111000−0.1393 + 0.3138i+0.7921 − 1.2096i−0.7233 + 0.1496i+0.1695 + 1.0298i
w57111001−0.1671 + 0.3094i−0.7921 − 1.2096i−0.6220 + 1.1896i+0.2236 + 1.3784i
w58111010−0.1393 − 0.3138i+0.6056 − 0.8481i−0.4246 + 0.1370i+0.1426 + 0.7102i
w59111011−0.1671 − 0.3094i−0.6056 − 0.8481i−0.2326 + 1.3986i+0.4351 + 0.7394i
w60111100−0.1720 + 0.7004i+0.2891 − 0.3110i−0.7267 + 0.4592i−0.1695 + 1.0298i
w61111101−0.3741 + 0.6174i−0.2891 − 0.3110i−0.6956 + 0.8095i−0.2236 + 1.3784i
w62111110−0.1720 − 0.7004i+0.4397 − 0.5853i−0.4198 + 0.4151i−0.1426 + 0.7102i
w63111111−0.3741 − 0.6174i−0.4397 − 0.5853i−0.4114 + 0.7109i−0.4351 + 0.7394i
B4) 128-QAM NUC
wConstellationwConstellation
indexbit labelpointindexbit labelpoint
for R = 1/2 (or R =+ 0 5/8, 3/4 or 13/16):
w00000000+0.7383 − 1.3947iw6401000000+1.5779 − 0.2230i
w10000000+0.2726 − 1.6070iw6501000001+1.2114 − 0.1662i
w20000001+0.7383 + 1.3947iw6601000010+1.5779 + 0.2230i
w30000001+0.2726 + 1.6070iw6701000011+1.2114 + 0.1662i
w40000010−0.7383 − 1.3947iw6801000100−1.5779 − 0.2230i
w50000010−0.2726 − 1.6070iw6901000101−1.2114 − 0.1662i
w60000011−0.7383 + 1.3947iw7001000110−1.5779 + 0.2230i
w70000011−0.2726 + 1.6070iw7101000111−1.2114 + 0.1662i
w80000100+1.0680 − 1.0753iw7201001000+1.4915 − 0.6927i
w90000100+1.0389 − 0.7336iw7301001001+1.1447 − 0.4719i
w100000101+1.0680 + 1.0753iw7401001010+1.4915 + 0.6927i
w110000101+1.0389 + 0.7336iw7501001011+1.1447 + 0.4719i
w120000110−1.0680 − 1.0753iw7601001100−1.4915 − 0.6927i
w130000110−1.0389 − 0.7336iw7701001101−1.1447 − 0.4719i
w140000111−1.0680 + 1.0753iw7801001110−1.4915 + 0.6927i
w150000111−1.0389 + 0.7336iw7901001111−1.1447 + 0.4719i
w160001000+0.5286 − 1.0997iw8001010000+0.7620 − 0.1121i
w170001000+0.1915 − 1.2689iw8101010001+0.9103 − 0.1272i
w180001001+0.5286 + 1.0997iw8201010010+0.7620 + 0.1121i
w190001001+0.1915 + 1.2689iw8301010011+0.9103 + 0.1272i
w200001010−0.5286 − 1.0997iw8401010100−0.7620 − 0.1121i
w210001010−0.1915 − 1.2689iw8501010101−0.9103 − 0.1272i
w220001011−0.5286 + 1.0997iw8601010110−0.7620 + 0.1121i
w230001011−0.1915 + 1.2689iw8701010111−0.9103 + 0.1272i
w240001100+0.6878 − 0.8578iw8801011000+0.7359 − 0.3230i
w250001100+0.7725 − 0.6723iw8901011001+0.8236 − 0.3936i
w260001101+0.6878 + 0.8578iw9001011010+0.7359 + 0.3230i
w270001101+0.7725 + 0.6723iw9101011011+0.8236 + 0.3936i
w280001110−0.6878 − 0.8578iw9201011100−0.7359 − 0.3230i
w290001110−0.7725 − 0.6723iw9301011101−0.8236 − 0.3936i
w300001111−0.6878 + 0.8578iw9401011110−0.7359 + 0.3230i
w310001111−0.7725 + 0.6723iw9501011111−0.8236 + 0.3936i
w320010000+0.1315 − 0.7332iw9601100000+0.1461 − 0.1146i
w330010000+0.1038 − 0.7670iw9701100001+0.1573 − 0.1142i
w340010001+0.1315 + 0.7332iw9801100010+0.1461 + 0.1146i
w350010001+0.1038 + 0.7670iw9901100011+0.1573 + 0.1142i
w360010010−0.1315 − 0.7332iw10001100100−0.1461 − 0.1146i
w370010010−0.1038 − 0.7670iw10101100101−0.1573 − 0.1142i
w380010011−0.1315 + 0.7332iw10201100110−0.1461 + 0.1146i
w390010011−0.1038 + 0.7670iw10301100111−0.1573 + 0.1142i
w400010100+0.1647 − 0.5388iw10401101000+0.1535 − 0.3082i
w410010100+0.1629 − 0.5296iw10501101001+0.1629 − 0.3084i
w420010101+0.1647 + 0.5388iw10601101010+0.1535 + 0.3082i
w430010101+0.1629 + 0.5296iw10701101011+0.1629 + 0.3084i
w440010110−0.1647 − 0.5388iw10801101100−0.1535 − 0.3082i
w450010110−0.1629 − 0.5296iw10901101101−0.1629 − 0.3084i
w460010111−0.1647 + 0.5388iw11001101110−0.1535 + 0.3082i
w470010111−0.1629 + 0.5296iw11101101111−0.1629 + 0.3084i
w480011000+0.3255 − 0.9067iw11201110000+0.4774 − 0.1074i
w490011000+0.1588 − 1.0122iw11301110001+0.4323 − 0.1096i
w500011001+0.3255 + 0.9067iw11401110010+0.4774 + 0.1074i
w510011001+0.1588 + 1.0122iw11501110011+0.4323 + 0.1096i
w520011010−0.3255 − 0.9067iw11601110100−0.4774 − 0.1074i
w530011010−0.1588 − 1.0122iw11701110101−0.4323 − 0.1096i
w540011011−0.3255 + 0.9067iw11801110110−0.4774 + 0.1074i
w550011011−0.1588 + 1.0122iw11901110111−0.4323 + 0.1096i
w560011100+0.4535 − 0.6452iw12001111000+0.4853 − 0.3237i
w570011100+0.4645 − 0.5898iw12101111001+0.4637 − 0.3425i
w580011101+0.4535 + 0.6452iw12201111010+0.4853 + 0.3237i
w590011101+0.4645 + 0.5898iw12301111011+0.4637 + 0.3425i
w600011110−0.4535 − 0.6452iw12401111100−0.4853 − 0.3237i
w610011110−0.4645 − 0.5898iw12501111101−0.4637 − 0.3425i
w620011111−0.4535 + 0.6452iw12601111110−0.4853 + 0.3237i
w630011111−0.4645 + 0.5898iw12701111111−0.4637 + 0.3425i
for R = 5/8, (or R = 1/2, 3/4 or 13/16)
w00000000+1.1438 + 0.4323iw6401000000+1.1438 − 0.4323i
w10000000+0.1045 + 0.4578iw6501000001+0.1045 − 0.4578i
w20000001−1.1438 + 0.4323iw6601000010−1.1438 − 0.4323i
w30000001−0.1045 + 0.4578iw6701000011−0.1045 − 0.4578i
w40000010+0.9006 + 0.4173iw6801000100+0.9006 − 0.4173i
w50000010+0.1067 + 0.3515iw6901000101+0.1067 − 0.3515i
w60000011−0.9006 + 0.4173iw7001000110−0.9006 − 0.4173i
w70000011−0.1067 + 0.3515iw7101000111−0.1067 − 0.3515i
w80000100+1.1598 + 0.1437iw7201001000+1.1598 − 0.1437i
w90000100+0.1075 + 0.0988iw7301001001+0.1075 − 0.0988i
w100000101−1.1598 + 0.1437iw7401001010−1.1598 − 0.1437i
w110000101−0.1075 + 0.0988iw7501001011−0.1075 − 0.0988i
w120000110+0.9102 + 0.1324iw7601001100+0.9102 − 0.1324i
w130000110+0.1136 + 0.1402iw7701001101+0.1136 − 0.1402i
w140000111−0.9102 + 0.1324iw7801001110−0.9102 − 0.1324i
w150000111−0.1336 + 0.1402iw7901001111−0.1336 − 0.1402i
w160001000+0.5578 + 0.4216iw8001010000+0.5578 − 0.4216i
w170001000+0.3411 + 0.4189iw8101010001+0.3411 − 0.4189i
w180001001−0.5578 + 0.4216iw8201010010−0.5578 − 0.4216i
w190001001−0.3411 + 0.4189iw8301010011−0.3411 − 0.4189i
w200001010+0.6797 + 0.3850iw8401010100+0.6797 − 0.3850i
w210001010+0.3088 + 0.3456iw8501010101+0.3088 − 0.3456i
w220001011−0.6797 + 0.3850iw8601010110−0.6797 − 0.3850i
w230001011−0.3088 + 0.3456iw8701010111−0.3088 − 0.3456i
w240001100+0.5755 + 0.1222iw8801011000+0.5755 − 0.1222i
w250001100+0.3700 + 0.1151iw8901011001+0.3700 − 0.1151i
w260001101−0.5755 + 0.1222iw9001011010−0.5755 − 0.1222i
w270001101−0.3700 + 0.1151iw9101011011−0.3700 − 0.1151i
w280001110+0.6787 + 0.1401iw9201011100+0.6787 − 0.1401i
w290001110+0.3294 + 0.1448iw9301011101+0.3294 − 0.1448i
w300001111−0.6787 + 0.1401iw9401011110−0.6787 − 0.1401i
w310001111−0.3294 + 0.1448iw9501011111−0.3294 − 0.1448i
w320010000+1.1837 + 0.8001iw9601100000+1.1837 − 0.8001i
w330010000+0.1121 + 0.6749iw9701100001+0.1121 − 0.6749i
w340010001−1.1837 + 0.8001iw9801100010−1.1837 − 0.8001i
w350010001−0.1121 + 0.6749iw9901100011−0.1121 − 0.6749i
w360010010+0.9008 + 0.6972iw10001100100+0.9008 − 0.6972i
w370010010+0.1179 + 0.8955iw10101100101+0.1179 − 0.8955i
w380010011−0.9008 + 0.6972iw10201100110−0.9008 − 0.6972i
w390010011−0.1179 + 0.8955iw10301100111−0.1179 − 0.8955i
w400010100+1.4855 + 0.1793iw10401101000+1.4855 − 0.1793i
w410010100+0.1933 + 1.4991iw10501101001+0.1933 − 1.4991i
w420010101−1.4855 + 0.1793iw10601101010−1.4855 − 0.1793i
w430010101−0.1933 + 1.4991iw10701101011−0.1933 − 1.4991i
w440010110+1.5681 + 0.5636iw10801101100+1.5681 − 0.5636i
w450010110+0.1440 + 1.1691iw10901101101+0.1440 − 1.1691i
w460010111−1.5681 + 0.5636iw11001101110−1.5681 − 0.5636i
w470010111−0.1440 + 1.1691iw11101101111−0.1440 − 1.1691i
w480011000+0.5354 + 0.6351iw11201110000+0.5354 − 0.6351i
w490011000+0.3342 + 0.6628iw11301110001+0.3342 − 0.6628i
w500011001−0.5354 + 0.6351iw11401110010−0.5354 − 0.6351i
w510011001−0.3342 + 0.6628iw11501110011−0.3342 − 0.6628i
w520011010+0.6549 + 0.7546iw11601110100+0.6549 − 0.7546i
w530011010+0.3585 + 0.8699iw11701110101+0.3585 − 0.8699i
w540011011−0.6549 + 0.7546iw11801110110−0.6549 − 0.7546i
w550011011−0.3585 + 0.8699iw11901110111−0.3585 − 0.8699i
w560011100+0.9727 + 1.2109iw12001111000+0.9727 − 1.2109i
w570011100+0.5835 + 1.4250iw12101111001+0.5835 − 1.4250i
w580011101−0.9727 + 1.2109iw12201111010−0.9727 − 1.2109i
w590011101−0.5835 + 1.4250iw12301111011−0.5835 − 1.4250i
w600011110+0.7102 + 1.0171iw12401111100+0.7102 − 1.0171i
w610011110+0.4344 + 1.1140iw12501111101+0.4344 − 1.1140i
w620011111−0.7102 + 1.0171iw12601111110−0.7102 − 1.0171i
w630011111−0.4344 + 1.1140iw12701111111−0.4344 − 1.1140i
R = 3/4 (or R = 1/2, 5/8 or 13/16):
w00000000+1.0837 + 0.3878iw6401000000+1.0605 + 0.1271i
w10000000+0.5568 + 0.5351iw6501000001+0.5216 + 0.0747i
w20000001+1.0837 − 0.3878iw6601000010+1.0605 − 0.1271i
w30000001+0.5568 − 0.5351iw6701000011+0.5216 − 0.0747i
w40000010+0.8372 + 0.4015iw6801000100+0.8209 + 0.1292i
w50000010+0.5992 + 0.3732iw6901000101+0.6018 + 0.1929i
w60000011+0.8372 − 0.4015iw7001000110+0.8209 − 0.1292i
w70000011+0.5992 − 0.3732iw7101000111+0.6018 − 0.1929i
w80000100+1.1795 + 0.6737iw7201001000+1.3525 + 0.1471i
w90000100+0.5823 + 0.7120iw7301001001+1.0702 + 1.0357i
w100000101+1.1795 − 0.6737iw7401001010+1.3525 − 0.1471i
w110000101+0.5823 − 0.7120iw7501001011+1.0702 − 1.0357i
w120000110+0.8934 + 0.6718iw7601001100+1.4799 + 0.4422i
w130000110+0.7091 + 0.8942iw7701001101+0.7653 + 1.1720i
w140000111+0.8934 − 0.6718iw7801001110+1.4799 − 0.4422i
w150000111+0.7091 − 0.8942iw7901001111+0.7653 − 1.1720i
w160001000+0.1125 + 0.5652iw8001010000+0.1054 + 0.0790i
w170001000+0.3356 + 0.5485iw8101010001+0.3169 + 0.0841i
w180001001+0.1125 − 0.5652iw8201010010+0.1054 − 0.0790i
w190001001+0.3356 − 0.5485iw8301010011+0.3169 − 0.0841i
w200001010+0.1063 + 0.3959iw8401010100+0.1042 + 0.2345i
w210001010+0.3354 + 0.3801iw8501010101+0.3223 + 0.2346i
w220001011+0.1063 − 0.3959iw8601010110+0.1042 − 0.2345i
w230001011+0.3354 − 0.3801iw8701010111+0.3223 − 0.2346i
w240001100+0.1174 + 0.7565iw8801011000+0.1687 + 1.4929i
w250001100+0.3498 + 0.7450iw8901011001+0.5173 + 1.4708i
w260001101+0.1174 − 0.7565iw9001011010+0.1687 − 1.4929i
w270001101+0.3498 − 0.7450iw9101011011+0.5173 − 1.4708i
w280001110+0.1285 + 0.9672iw9201011100+0.1455 + 1.2047i
w290001110+0.3973 + 0.9520iw9301011101+0.4442 + 1.1814i
w300001111+0.1285 − 0.9672iw9401011110+0.1455 − 1.2047i
w310001111+0.3973 − 0.9520iw9501011111+0.4442 − 1.1814i
w320010000−1.0837 + 0.3878iw9601100000−1.0605 + 0.1271i
w330010000−0.5568 + 0.5351iw9701100001−0.5216 + 0.0747i
w340010001−1.0837 − 0.3878iw9801100010−1.0605 − 0.1271i
w350010001−0.5568 − 0.5351iw9901100011−0.5216 − 0.0747i
w360010010−0.8372 + 0.4015iw10001100100−0.8209 + 0.1292i
w370010010−0.5992 + 0.3732iw10101100101−0.6018 + 0.1929i
w380010011−0.8372 − 0.4015iw10201100110−0.8209 − 0.1292i
w390010011−0.5992 − 0.3732iw10301100111−0.6018 − 0.1929i
w400010100−1.1795 + 0.6737iw10401101000−1.3525 + 0.1471i
w410010100−0.5823 + 0.7120iw10501101001−1.0702 + 1.0357i
w420010101−1.1795 − 0.6737iw10601101010−1.3525 − 0.1471i
w430010101−0.5823 − 0.7120iw10701101011−1.0702 − 1.0357i
w440010110−0.8934 + 0.6718iw10801101100−1.4799 + 0.4422i
w450010110−0.7091 + 0.8942iw10901101101−0.7653 + 1.1720i
w460010111−0.8934 − 0.6718iw11001101110−1.4799 − 0.4422i
w470010111−0.7091 − 0.8942iw11101101111−0.7653 − 1.1720i
w480011000−0.1125 + 0.5652iw11201110000−0.1054 + 0.0790i
w490011000−0.3356 + 0.5485iw11301110001−0.3169 + 0.0841i
w500011001−0.1125 − 0.5652iw11401110010−0.1054 − 0.0790i
w510011001−0.3356 − 0.5485iw11501110011−0.3169 − 0.0841i
w520011010−0.1063 + 0.3959iw11601110100−0.1042 + 0.2345i
w530011010−0.3354 + 0.3801iw11701110101−0.3223 + 0.2346i
w540011011−0.1063 − 0.3959iw11801110110−0.1042 − 0.2345i
w550011011−0.3354 − 0.3801iw11901110111−0.3223 − 0.2346i
w560011100−0.1174 + 0.7565iw12001111000−0.1687 + 1.4929i
w570011100−0.3498 + 0.7450iw12101111001−0.5173 + 1.4708i
w580011101−0.1174 − 0.7565iw12201111010−0.1687 − 1.4929i
w590011101−0.3498 − 0.7450iw12301111011−0.5173 − 1.4708i
w600011110−0.1285 + 0.9672iw12401111100−0.1455 + 1.2047i
w610011110−0.3973 + 0.9520iw12501111101−0.4442 + 1.1814i
w620011111−0.1285 − 0.9672iw12601111110−0.1455 − 1.2047i
w630011111−0.3973 − 0.9520iw12701111111−0.4442 − 1.1814i
for R = 13/16 (or R = 1/2, 5/8 or 3/4):
w00000000+1.0422 + 0.3376iw6401000000+1.1154 + 0.5839i
w10000000−1.0422 + 0.3376iw6501000001−1.1154 + 0.5839i
w20000001+1.0422 − 0.3376iw6601000010+1.1154 − 0.5839i
w30000001−1.0422 − 0.3376iw6701000011−1.1154 − 0.5839i
w40000010+0.1125 + 0.6269iw6801000100+0.1155 + 0.8217i
w50000010−0.1125 + 0.6269iw6901000101−0.1155 + 0.8217i
w60000011+0.1125 − 0.6269iw7001000110+0.1155 − 0.8217i
w70000011−0.1125 − 0.6269iw7101000111−0.1155 − 0.8217i
w80000100+1.0010 + 0.1105iw7201001000+1.2844 + 0.1345i
w90000100−1.0010 + 0.1105iw7301001001−1.2844 + 0.1345i
w100000101+1.0010 − 0.1105iw7401001010+1.2844 − 0.1345i
w110000101−1.0010 − 0.1105iw7501001011−1.2844 − 0.1345i
w120000110+0.0978 + 0.0913iw7601001100+0.1646 + 1.5274i
w130000110−0.0978 + 0.0913iw7701001101−0.1646 + 1.5274i
w140000111+0.0978 − 0.0913iw7801001110+0.1646 − 1.5274i
w150000111−0.0978 − 0.0913iw7901001111−0.1646 − 1.5274i
w160001000+0.7966 + 0.3496iw8001010000+0.8563 + 0.5705i
w170001000−0.7966 + 0.3496iw8101010001−0.8563 + 0.5705i
w180001001+0.7966 − 0.3496iw8201010010+0.8563 − 0.5705i
w190001001−0.7966 − 0.3496iw8301010011−0.8563 − 0.5705i
w200001010+0.1109 + 0.4454iw8401010100+0.1239 + 1.0311i
w210001010−0.1109 + 0.4454iw8501010101−0.1239 + 1.0311i
w220001011+0.1109 − 0.4454iw8601010110+0.1239 − 1.0311i
w230001011−0.1109 − 0.4454iw8701010111−0.1239 − 1.0311i
w240001100+0.7613 + 0.1187iw8801011000+1.4001 + 0.4092i
w250001100−0.7613 + 0.1187iw8901011001−1.4001 + 0.4092i
w260001101+0.7613 − 0.1187iw9001011010+1.4001 − 0.4092i
w270001101−0.7613 − 0.1187iw9101011011−1.4001 − 0.4092i
w280001110+0.1038 + 0.2705iw9201011100+0.1345 + 1.2611i
w290001110−0.1038 + 0.2705iw9301011101−0.1345 + 1.2611i
w300001111+0.1038 − 0.2705iw9401011110+0.1345 − 1.2611i
w310001111−0.1038 − 0.2705iw9501011111−0.1345 − 1.2611i
w320010000+0.5556 + 0.6306iw9601100000+0.5970 + 0.8482i
w330010000−0.5556 + 0.6306iw9701100001−0.5970 + 0.8482i
w340010001+0.5556 − 0.6306iw9801100010+0.5970 − 0.8482i
w350010001−0.5556 − 0.6306iw9901100011−0.5970 − 0.8482i
w360010010+0.3351 + 0.6308iw10001100100+0.3510 + 0.8405i
w370010010−0.3351 + 0.6308iw10101100101−0.3510 + 0.8405i
w380010011+0.3351 − 0.6308iw10201100110+0.3510 − 0.8405i
w390010011−0.3351 − 0.6308iw10301100111−0.3510 − 0.8405i
w400010100+0.4942 + 0.0780iw10401101000+1.1670 + 0.8997i
w410010100−0.4942 + 0.0780iw10501101001−1.1670 + 0.8997i
w420010101+0.4942 − 0.0780iw10601101010+1.1670 − 0.8997i
w430010101−0.4942 − 0.0780iw10701101011−1.1670 − 0.8997i
w440010110+0.2935 + 0.0906iw10801101100+0.4543 + 1.3933i
w450010110−0.2935 + 0.0906iw10901101101−0.4543 + 1.3933i
w460010111+0.2935 − 0.0906iw11001101110+0.4543 − 1.3933i
w470010111−0.2935 − 0.0906iw11101101111−0.4543 − 1.3933i
w480011000+0.5761 + 0.4286iw11201110000+0.8378 + 0.8041i
w490011000−0.5761 + 0.4286iw11301110001−0.8378 + 0.8041i
w500011001+0.5761 − 0.4286iw11401110010+0.8378 − 0.8041i
w510011001−0.5761 − 0.4286iw11501110011−0.8378 − 0.8041i
w520011010+0.3383 + 0.4404iw11601110100+0.3850 + 1.0724i
w530011010−0.3383 + 0.4404iw11701110101−0.3850 + 1.0724i
w540011011+0.3383 − 0.4404iw11801110110+0.3850 − 1.0724i
w550011011−0.3383 − 0.4404iw11901110111−0.3850 − 1.0724i
w560011100+0.5456 + 0.2367iw12001111000+0.9031 + 1.0698i
w570011100−0.5456 + 0.2367iw12101111001−0.9031 + 1.0698i
w580011101+0.5456 − 0.2367iw12201111010+0.9031 − 1.0698i
w590011101−0.5456 − 0.2367iw12301111011−0.9031 − 1.0698i
w600011110+0.3172 + 0.2666iw12401111100+0.6436 + 1.1770i
w610011110−0.3172 + 0.2666iw12501111101−0.6436 + 1.1770i
w620011111+0.3172 − 0.2666iw12601111110+0.6436 − 1.1770i
w630011111−0.3172 − 0.2666iw12701111111−0.6436 − 1.1770i
B5) 256-QAM NUC
wbitConstellationwbitConstellation
indexlabelpointindexlabelpoint
for R = 1/2 (or R = 5/8, 3/4 or 13/16):
w00000000−1.2901 + 1.0495iw6401000000−1.0382 + 0.8623i
w10000000−1.6350 + 0.1593iw6501000001−1.3225 + 0.1320i
w20000001−0.2844 + 0.1296iw6601000010−0.3734 + 0.2560i
w30000001−0.3237 + 0.0849iw6701000011−0.4582 + 0.1123i
w40000010−1.4625 + 0.7740iw6801000100−1.1794 + 0.6376i
w50000010−1.5776 + 0.4735iw6901000101−1.2742 + 0.3922i
w60000011−0.2853 + 0.1309iw7001000110−0.3799 + 0.2517i
w70000011−0.3228 + 0.0867iw7101000111−0.4545 + 0.1251i
w80000100+1.2901 + 1.0495iw7201001000+1.0382 + 0.8623i
w90000100+1.6350 + 0.1593iw7301001001+1.3225 + 0.1320i
w100000101+0.2844 + 0.1296iw7401001010+0.3734 + 0.2560i
w110000101+0.3237 + 0.0849iw7501001011+0.4582 + 0.1123i
w120000110+1.4625 + 0.7740iw7601001100+1.1794 + 0.6376i
w130000110+1.5776 + 0.4735iw7701001101+1.2742 + 0.3922i
w140000111+0.2853 + 0.1309iw7801001110+0.3799 + 0.2517i
w150000111+0.3228 + 0.0867iw7901001111+0.4545 + 0.1251i
w160001000−0.7273 + 0.6160iw8001010000−0.8504 + 0.7217i
w170001000−0.9430 + 0.1100iw8101010001−1.0854 + 0.1139i
w180001001−0.5902 + 0.4857iw8201010010−0.4868 + 0.3947i
w190001001−0.7502 + 0.1138iw8301010011−0.6473 + 0.1138i
w200001010−0.8177 + 0.4841iw8401010100−0.9638 + 0.5407i
w210001010−0.9069 + 0.2829iw8501010101−1.0441 + 0.3296i
w220001011−0.6355 + 0.4185iw8601010110−0.5231 + 0.3644i
w230001011−0.7325 + 0.2088iw8701010111−0.6339 + 0.1702i
w240001100+0.7273 + 0.6160iw8801011000+0.8504 + 0.7217i
w250001100+0.9430 + 0.1100iw8901011001+1.0854 + 0.1139i
w260001101+0.5902 + 0.4857iw9001011010+0.4968 + 0.3947i
w270001101+0.7502 + 0.1138iw9101011011+0.6473 + 0.1138i
w280001110+0.8177 + 0.4841iw9201011100+0.9638 + 0.5407i
w290001110+0.9069 + 0.2829iw9301011101+1.0441 + 0.3296i
w300001111+0.6355 + 0.4185iw9401011110+0.5231 + 0.3644i
w310001111+0.7325 + 0.2068iw9501011111+0.6339 + 0.1702i
w320010000−1.0646 + 1.2876iw9601100000−0.8555 + 1.0542i
w330010000−0.1658 + 1.6747iw9701100001−0.1322 + 1.3631i
w340010001−0.1053 + 0.1494iw9801100010−0.1938 + 0.3621i
w350010001−0.0872 + 0.1390iw9901100011−0.0928 + 0.3970i
w360010010−0.7949 + 1.4772iw10001100100−0.6363 + 1.2064i
w370010010−0.4907 + 1.6084iw10101100101−0.3929 + 1.3102i
w380010011−0.1052 + 0.1495iw10201100110−0.1909 + 0.3627i
w390010011−0.0871 + 0.1392iw10301100111−0.0937 + 0.3973i
w400010100+1.0646 + 1.2876iw10401101000+0.8555 + 1.0542i
w410010100+0.1658 + 1.6747iw10501101001+0.1322 + 1.3631i
w420010101+0.1053 + 0.1494iw10601101010+0.1938 + 0.3621i
w430010101+0.0872 + 0.1390iw10701101011+0.0928 + 0.3970i
w440010110+0.7949 + 1.4772iw10801101100+0.6363 + 1.2064i
w450010110+0.4907 + 1.6084iw10901101101+0.3929 + 1.3102i
w460010111+0.1052 + 0.1495iw11001101110+0.1909 + 0.3627i
w470010111+0.0871 + 0.1392iw11101101111+0.0937 + 0.3973i
w480011000−0.5707 + 0.7662iw11201110000−0.6961 + 0.8850i
w490011000−0.1088 + 0.9530iw11301110001−0.1124 + 1.1327i
w500011001−0.4294 + 0.6363iw11401110010−0.3224 + 0.5236i
w510011001−0.1091 + 0.7656iw11501110011−0.1054 + 0.5979i
w520011010−0.4490 + 0.8461iw11601110100−0.5229 + 1.0037i
w530011010−0.2464 + 0.9270iw11701110101−0.3160 + 1.0913i
w540011011−0.3744 + 0.6744iw11801110110−0.3016 + 0.5347i
w550011011−0.1699 + 0.7537iw11901110111−0.1230 + 0.5949i
w560011100+0.5707 + 0.7662iw12001111000+0.6961 + 0.8850i
w570011100+0.1088 + 0.9530iw12101111001+0.1124 + 1.1327i
w580011101+0.4294 + 0.6363iw12201111010+0.3224 + 0.5236i
w590011101+0.1091 + 0.7656iw12301111011+0.1054 + 0.5979i
w600011110+0.4490 + 0.8461iw12401111100+0.5229 + 1.0037i
w610011110−0.2464 + 0.9270iw12501111101+0.3160 + 1.0913i
w620011111+0.3744 + 0.6744iw12601111110+0.3016 + 0.5347i
w630011111+0.1699 + 0.7537iw12701111111+0.1230 + 0.5949i
for R = 5/8 (or R = 1/2, 3/4 or 13/16):
w00000000−1.2639 + 1.0084iw6401000000−0.2459 + 0.2059i
w10000000−0.7380 + 0.6059iw6501000001−0.6025 + 0.5077i
w20000001−1.0466 + 1.2415iw6601000010−0.0949 + 0.2552i
w30000001−0.6190 + 0.7456iw6701000011−0.5005 + 0.6310i
w40000010−1.2639 − 1.0084iw6801000100−0.2459 − 0.2059i
w50000010−0.7380 − 0.6069iw6901000101−0.6025 − 0.5077i
w60000011−1.0466 − 1.2415iw7001000110−0.0949 − 0.2552i
w70000011−0.6190 − 0.7456iw7101000111−0.5005 − 0.6310i
w80000100−1.4263 + 0.7399iw7201001000−0.2508 + 0.2016i
w90000100−0.8292 − 0.4496iw7301001001−0.6756 + 0.3836i
w100000101−0.7829 − 1.4275iw7401001010−0.0912 + 0.2556i
w110000101−0.4707 − 0.8613iw7501001011−0.3899 + 0.7222i
w120000110−1.4263 − 0.7399iw7601001100−0.2508 − 0.2016i
w130000110−0.8292 − 0.4496iw7701001101−0.6756 − 0.3836i
w140000111−0.7829 − 1.4275iw7801001110−0.0912 − 0.2556i
w150000111−0.4707 − 0.8613iw7901001111−0.3899 − 0.7222i
w160001000−1.0529 + 0.8398iw8001010000−0.3507 + 0.3002i
w170001000−0.8839 + 0.7116iw8101010001−0.4734 + 0.4072i
w180001001−0.8751 + 1.0349iw8201010010−0.2035 + 0.4115i
w190001001−0.7390 + 0.8761iw8301010011−0.3688 + 0.5265i
w200001010−1.0529 − 0.8398iw8401010100−0.3507 − 0.3002i
w210001010−0.8839 − 0.7116iw8501010101−0.4734 − 0.4072i
w220001011−0.8751 − 1.0349iw8601010110−0.2085 − 0.4116i
w230001011−0.7380 − 0.8761iw8701010111−0.3688 − 0.5265i
w240001100−1.1857 + 0.6167iw8801011000−0.3739 + 0.2698i
w250001100−0.9935 + 0.5250iw8901011001−0.5263 + 0.3281i
w260001101−0.6570 + 1.1922iw9001011010−0.1890 + 0.4220i
w270001101−0.5568 + 1.0106iw9101011011−0.3094 + 0.5791i
w280001110−1.1857 − 0.6167iw9201011100−0.3739 − 0.2698i
w290001110−0.9935 − 0.5250iw9301011101−0.5263 − 0.3281i
w300001111−0.6570 − 1.1922iw9401011110−0.1890 − 0.4220i
w310001111−0.5568 − 1.0106iw9501011111−0.3094 − 0.5791i
w320010000+1.2639 + 1.0084iw9601100000+0.2459 + 0.2059i
w330010000+0.7380 + 0.6059iw9701100001+0.6025 + 0.5077i
w340010001+1.0466 + 1.2415iw9801100010+0.0949 + 0.2552i
w350010001+0.6190 + 0.7456iw9901100011+0.5005 + 0.6310i
w360010010+1.2639 − 1.0084iw10001100100+0.2459 − 0.2059i
w370010010+0.7380 − 0.6059iw10101100101+0.6025 − 0.5077i
w380010011+1.0466 − 1.2415iw10201100110+0.0949 − 0.2552i
w390010011+0.6190 − 0.7456iw10301100111+0.5005 − 0.6310i
w400010100+1.4263 + 0.7399iw10401101000+0.2508 + 0.2016i
w410010100+0.8292 + 0.4496iw10501101001+0.6756 + 0.3836i
w420010101+0.7829 + 1.4275iw10601101010+0.0912 + 0.2566i
w430010101+0.4707 + 0.8613iw10701101011+0.3899 + 0.7222i
w440010110+1.4263 − 0.7399iw10801101100+0.2508 − 0.2016i
w450010110+0.8292 − 0.4496iw10901101101+0.6756 − 0.3836i
w460010111+0.7829 − 1.4275iw11001101110+0.0912 − 0.2556i
w470010111+0.4707 − 0.8613iw11101101111+0.3899 − 0.7222i
w480011000+1.0529 + 0.8398iw11201110000+0.3507 + 0.3002i
w490011000+0.8839 + 0.7116iw11301110001+0.4734 + 0.4072i
w500011001+0.8751 + 1.0349iw11401110010+0.2035 + 0.4116i
w510011001+0.7380 + 0.8761iw11501110011+0.3688 + 0.5265i
w520011010+1.0529 − 0.8398iw11601110100+0.3507 − 0.3002i
w530011010+0.8839 − 0.7116iw11701110101+0.4734 − 0.4072i
w540011011+0.8751 − 1.0349iw11801110110+0.2085 − 0.4116i
w550011011+0.7380 − 0.8761iw11901110111+0.3688 − 0.5265i
w560011100+1.1857 + 0.6167iw12001111000+0.3739 + 0.2698i
w570011100+0.9935 + 0.5250iw12101111001+0.5263 + 0.3281i
w580011101+0.6570 + 1.1922iw12201111010+0.1890 + 0.4220i
w590011101+0.5568 + 1.0106iw12301111011+0.3094 + 0.5791i
w600011110+1.1857 − 0.6167iw12401111100+0.3739 − 0.2698i
w610011110+0.9935 − 0.5250iw12501111101+0.5263 − 0.6281i
w620011111+0.6570 − 1.1922iw12601111110+0.1890 − 0.4220i
w630011111+0.5568 − 1.0106iw12701111111+0.3094 − 0.5791i
for R = 3/4 (or R = 1/2, 5/8 or 13/16):
w00000000−0.5207 + 1.2132iw6401000000−0.4992 + 1.0060i
w10000000−0.3108 + 1.2359iw6501000001−0.3097 + 1.0437i
w20000001−1.1610 + 1.1297iw6601000010−1.2435 + 0.8749i
w30000001−0.1051 + 1.2649iw6701000011−0.0961 + 1.0730i
w40000010−0.6193 + 0.6523iw6801000100−0.5761 + 0.8259i
w50000010−0.4633 + 0.6225iw6901000101−0.4319 + 0.7814i
w60000011−1.2194 + 0.5861iw7001000110−1.4344 + 0.6815i
w70000011−0.0684 + 0.5460iw7101000111−0.0548 + 0.6842i
w80000100+0.5207 + 1.2132iw7201001000+0.4992 + 1.0060i
w90000100+0.3108 + 1.2359iw7301001001+0.3097 + 1.0437i
w100000101+1.1610 + 1.1297iw7401001010+1.2435 + 0.8749i
w110000101+0.1051 + 1.2649iw7501001011+0.0961 + 1.0730i
w120000110+0.6193 + 0.6523iw7601001100+0.5761 + 0.8259i
w130000110+0.4633 + 0.6225iw7701001101+0.4319 + 0.7814i
w140000111+1.2194 + 0.5861iw7801001110+1.4344 + 0.6815i
w150000111+0.0684 + 0.5460iw7901001111+0.0548 + 0.6842i
w160001000−0.6089 + 1.4273iw8001010000−0.6956 + 1.0381i
w170001000−0.3588 + 1.4645iw8101010001−0.2552 + 0.9082i
w180001001−0.8292 + 1.2973iw8201010010−0.8938 + 1.0757i
w190001001−0.1197 + 1.4960iw8301010011−0.0867 + 0.8997i
w200001010−0.7956 + 0.6768iw8401010100−0.7562 + 0.8504i
w210001010−0.3209 + 0.5978iw8501010101−0.2908 + 0.7608i
w220001011−1.0079 + 0.6851iw8601010110−0.9633 + 0.8762i
w230001011−0.1960 + 0.5676iw8701010111−0.1482 + 0.7338i
w240001100+0.6089 + 1.4273iw8801011000+0.6956 + 1.0381i
w250001100+0.3588 + 1.4645iw8901011001+0.2552 + 0.9082i
w260001101+0.8292 + 1.2973iw9001011010+0.8938 + 1.0757i
w270001101+0.1197 + 1.4960iw9101011011+0.0867 + 0.8997i
w280001110+0.7956 + 0.6768iw9201011100+0.7562 + 0.8504i
w290001110+0.3209 + 0.5978iw9301011101+0.2903 + 0.7608i
w300001111+1.0079 + 0.6851iw9401011110+0.9633 + 0.8762i
w310001111+0.1960 + 0.5676iw9501011111+0.1482 + 0.7338i
w320010000−0.5207 − 1.2132iw9601100000−0.4992 − 1.0060i
w330010000−0.3103 − 1.2359iw9701100001−0.3097 − 1.0437i
w340010001−1.1610 − 1.1297iw9801100010−1.2435 − 0.8749i
w350010001−0.1051 − 1.2649iw9901100011−0.0961 − 1.0730i
w360010010−0.6193 − 0.6523iw10001100100−0.5761 − 0.8259i
w370010010−0.4633 − 0.6225iw10101100101−0.4319 − 0.7814i
w380010011−1.2194 − 0.5861iw10201100110−1.4344 − 0.6815i
w390010011−0.0684 − 0.5460iw10301100111−0.0548 − 0.6842i
w400010100+0.5207 − 1.2132iw10401101000+0.4992 − 1.0060i
w410010100+0.3103 − 1.2359iw10501101001+0.3097 − 1.0437i
w420010101+1.1610 − 1.1297iw10601101010+1.2435 − 0.8749i
w430010101+0.1051 − 1.2649iw10701101011+0.0961 − 1.0730i
w440010110+0.6193 − 0.6623iw10801101100+0.5761 − 0.8259i
w450010110+0.4633 − 0.6225iw10901101101+0.4319 − 0.7814i
w460010111+1.2194 − 0.5861iw11001101110+1.4344 − 0.6815i
w470010111+0.0684 − 0.5460iw11101101111+0.0548 − 0.6842i
w480011000−0.6089 − 1.4273iw11201110000−0.6956 − 1.0381i
w490011000−0.3588 − 1.4645iw11301110001−0.2552 − 0.9082i
w500011001−0.8292 − 1.2973iw11401110010−0.8938 − 1.0757i
w510011001−0.1197 − 1.4960iw11501110011−0.0867 − 0.8997i
w520011010−0.7956 − 0.6768iw11601110100−0.7562 − 0.8504i
w530011010−0.3209 − 0.5978iw11701110101−0.2903 − 0.7608i
w540011011−1.0079 − 0.6851iw11801110110−0.9633 − 0.8762i
w550011011−0.1960 − 0.5676iw11901110111−0.1482 − 0.7338i
w560011100+0.6089 − 1.4273iw12001111000+0.6956 − 1.0381i
w570011100+0.3588 − 1.4645iw12101111001+0.2552 − 0.9082i
w580011101+0.8292 − 1.2973iw12201111010+0.8938 − 1.0757i
w590011101+0.1197 − 1.4960iw12301111011+0.0867 − 0.8997i
w600011110+0.7956 − 0.6768iw12401111100+0.7562 − 0.8504i
w610011110+0.3209 − 0.5978iw12501111101+0.2908 − 0.7608i
w620011111+1.0079 − 0.6851iw12601111110+0.9633 − 0.8762i
w630011111+0.1960 − 0.5676iw12701111111+0.1482 − 0.7338i
for R = 13/16 (or R = 1/2, 5/8 or 3/4):
w00000000−0.4976 + 1.2018iw6401000000−0.5648 + 1.4015i
w10000000+0.4976 + 1.2018iw6501000001+0.5648 + 1.4015i
w20000001−0.4976 − 1.2018iw6601000010−0.5648 − 1.4015i
w30000001+0.4976 − 1.2018iw6701000011+0.5648 − 1.4015i
w40000010−0.4821 + 1.0103iw6801000100−0.6826 + 1.0558i
w50000010+0.4821 + 1.0103iw6901000101+0.6826 + 1.0558i
w60000011−0.4821 − 1.0103iw7001000110−0.6826 − 1.0558i
w70000011+0.4821 − 1.0103iw7101000111+0.6826 − 1.0558i
w80000100−1.1616 + 1.0595iw7201001000−0.7696 + 1.2863i
w90000100+1.1616 + 1.0595iw7301001001+0.7696 + 1.2863i
w100000101−1.1616 − 1.0595iw7401001010−0.7696 − 1.2863i
w110000101+1.1616 − 1.0595iw7501001011+0.7696 − 1.2863i
w120000110−1.2384 + 0.8218iw7601001100−0.8965 + 1.0947i
w130000110+1.2384 + 0.8218iw7701001101+0.8965 + 1.0947i
w140000111−1.2384 − 0.8218iw7801001110−0.8965 − 1.0947i
w150000111+1.2384 − 0.8218iw7901001111+0.8965 − 1.0947i
w160001000−0.6618 + 0.0721iw8001010000−0.8148 + 0.0743i
w170001000+0.6618 + 0.0721iw8101010001+0.8148 + 0.0743i
w180001001−0.6618 − 0.0721iw8201010010−0.8148 − 0.0743i
w190001001+0.6618 − 0.0721iw8301010011+0.8148 − 0.0743i
w200001010−0.6653 + 0.2161iw8401010100−0.8285 + 0.2219i
w210001010+0.6653 + 0.2161iw8501010101+0.8285 + 0.2219i
w220001011−0.6653 − 0.2161iw8601010110−0.8285 − 0.2219i
w230001011+0.6653 − 0.2161iw8701010111+0.8285 − 0.2219i
w240001100−1.4070 + 0.1153iw8801011000−0.9784 + 0.0686i
w250001100+1.4070 + 0.1153iw8901011001+0.9784 + 0.0686i
w260001101−1.4070 − 0.1153iw9001011010−0.9784 − 0.0686i
w270001101+1.4070 − 0.1153iw9101011011+0.9784 − 0.0686i
w280001110−1.1945 + 0.1045iw9201011100−1.0093 + 0.2102i
w290001110+1.1945 + 0.1045iw9301011101+1.0093 + 0.2102i
w300001111−1.1945 − 0.1045iw9401011110−1.0093 − 0.2102i
w310001111+1.1945 − 0.1045iw9501011111+1.0093 − 0.2102i
w320010000−0.2993 + 1.2594iw9601100000−0.3403 + 1.4686i
w330010000+0.2993 + 1.2504iw9701100001+0.3403 + 1.4686i
w340010001−0.2993 − 1.2594iw9801100010−0.3403 − 1.4686i
w350010001+0.2993 − 1.2594iw9901100011+0.3403 − 1.4686i
w360010010−0.2996 + 1.0772iw10001100100−0.2690 + 0.9234i
w370010010+0.2906 + 1.0772iw10101100101+0.2690 + 0.9234i
w380010011−0.2906 − 1.0772iw10201100110−0.2690 − 0.9234i
w390010011+0.2906 − 1.0772iw10301100111+0.2690 − 0.9234i
w400010100−0.0985 + 1.2520iw10401101000−0.1114 + 1.4628i
w410010100+0.0985 + 1.2520iw10501101001+0.1114 + 1.4628i
w420010101−0.0985 − 1.2520iw10601101010−0.1114 − 1.4628i
w430010101+0.0985 − 1.2520iw10701101011+0.1114 − 1.4628i
w440010110−0.0938 + 1.0710iw10801101100−0.0905 + 0.9054i
w450010110+0.0938 + 1.0710iw10901101101+0.0905 + 0.9054i
w460010111−0.0938 − 1.0710iw11001101110−0.0905 − 0.9054i
w470010111+0.0938 − 1.0710iw11101101111+0.0905 − 0.9054i
w480011000−0.5134 + 0.0686iw11201110000−0.3668 + 0.0653i
w490011000+0.5134 + 0.0686iw11301110001+0.3668 + 0.0653i
w500011001−0.5134 − 0.0686iw11401110010−0.3668 − 0.0653i
w510011001+0.5134 − 0.0686iw11501110011+0.3668 − 0.0653i
w520011010−0.5133 + 0.2063iw11601110100−0.3660 + 0.1965i
w530011010+0.5133 + 0.2063iw11701110101+0.3660 + 0.1965i
w540011011−0.5133 − 0.2063iw11801110110−0.3660 − 0.1965i
w550011011+0.5133 − 0.2063iw11901110111+0.3660 − 0.1965i
w560011100−0.0735 + 0.0614iw12001111000−0.2204 + 0.0628i
w570011100+0.0735 + 0.0614iw12101111001+0.2204 + 0.0628i
w580011101−0.0735 − 0.0614iw12201111010−0.2204 − 0.0628i
w590011101+0.0735 − 0.0614iw12301111011+0.2204 − 0.0628i
w600011110−0.0734 + 0.1846iw12401111100−0.2198 + 0.1888i
w610011110+0.0734 + 0.1846iw12501111101+0.2198 + 0.1888i
w620011111−0.0734 − 0.1846iw12601111110−0.2198 − 0.1888i
w630011111+0.0734 − 0.1846iw12701111111+0.2198 − 0.1888i
wbitConstellationwbitConstellation
indexlabelpointindexlabelpoint
for R = 1/2 (or R = 5/8, 3/4 or 13/16):
w12810000000−1.2901 − 1.0495iw19211000000−1.0382 − 0.8623i
w12910000001−1.6350 − 0.1593iw19311000001−1.3225 − 0.1320i
w13010000010−0.2844 − 0.1296iw19411000010−0.3734 − 0.2560i
w13110000011−0.3237 − 0.0849iw19511000011−0.4582 − 0.1123i
w13210000100−1.4625 − 0.7740iw19611000100−1.1794 − 0.6376i
w13310000101−1.5776 − 0.4735iw19711000101−1.2742 − 0.3922i
w13410000110−0.2853 − 0.1309iw19811000110−0.3799 − 0.2517i
w13510000111−0.3228 − 0.0867iw19911000111−0.4545 − 0.1251i
w13610001000+1.2901 − 1.0495iw20011001000+1.0882 − 0.8623i
W13710001001+1.6350 − 0.1593iw20111001001+1.3225 − 0.1320i
w13810001010+0.2844 − 0.1296iw20211001010+0.3734 − 0.2560i
w13910001011+0.3237 − 0.0849iw20311001011+0.4582 − 0.1123i
w14010001100+1.4625 − 0.7740iw20411001100+1.1794 − 0.6376i
w14110001101+1.5776 − 0.4735iw20511001101+1.2742 − 0.3922i
w14210001110+0.2853 − 0.1309iw20611001110+0.3799 − 0.2517i
w14310001111+0.3228 − 0.0867iw20711001111+0.4545 − 0.1251i
w14410010000−0.7273 − 0.6160iw20811010000−0.8504 − 0.7217i
w14510010001−0.9430 − 0.1100iw20911010001−1.0854 − 0.1139i
w14610010010−0.5902 − 0.4857iw21011010010−0.4968 − 0.3947i
w14710010011−0.7502 − 0.1138iw21111010011−0.6473 − 0.1138i
w14810010100−0.8177 − 0.4841iw21211010100−0.9638 − 0.5407i
w14910010101−0.9069 − 0.2829iw21311010101−1.0441 − 0.3296i
w15010010110−0.6355 − 0.4185iw21411010110−0.5231 − 0.3644i
w15110010111−0.7325 − 0.2088iw21511010111−0.6339 − 0.1702i
w15210011000+0.7273 − 0.6160iw21611011000+0.8504 − 0.7217i
w15310011001+0.9430 − 0.1100iw21711011001+1.0854 − 0.1139i
w15410011010+0.5902 − 0.4857iw21811011010+0.4968 − 0.3947i
w15510011011+0.7502 − 0.1138iw21911011011+0.6473 − 0.1138i
w15610011100+0.8177 − 0.4841iw22011011100+0.9638 − 0.5407i
w15710011101+0.9069 − 0.2829iw22111011101+1.0441 − 0.3296i
w15810011110+0.6355 − 0.4185iw22211011110+0.5231 − 0.3644i
w15910011111+0.7325 − 0.2088iw22311011111+0.6339 − 0.1702i
w16010100000−1.0646 − 1.2876iw22411100000−0.8555 − 1.0542i
w16110100001−0.1658 − 1.6747iw22511100001−0.1322 − 1.3631i
w16210100010−0.1053 − 0.1494iw22611100010−0.1938 − 0.3621i
w16310100011−0.0872 − 0.1390iw22711100011−0.0928 − 0.3970i
w16410100100−0.7949 − 1.4772iw22811100100−0.6363 − 1.2064i
w16510100101−0.4907 − 1.6064iw22911100101−0.3929 − 1.3102i
w16610100110−0.1052 − 0.1495iw23011100110−0.1909 − 0.3627i
w16710100111−0.0871 − 0.1392iw23111100111−0.0937 − 0.3973i
w16810101000+1.0646 − 1.2876iw23211101000+0.8555 − 1.0542i
w16910101001+0.1658 − 1.6747iw23311101001+0.1322 − 1.3631i
w17010101010+0.1053 − 0.1494iw23411101010+0.1938 − 0.3621i
w17110101011+0.0872 − 0.1390iw23511101011+0.0928 − 0.3970i
w17210101100+0.7949 − 1.4772iw23611101100+0.6363 − 1.2064i
w17310101101−0.4907 − 1.6084iw23711101101+0.3929 − 1.3102i
w17410101110+0.1052 − 0.1495iw23811101110+0.1909 − 0.3627i
w17510101111+0.0871 − 0.1392iw23911101111+0.0937 − 0.3973i
w17610110000−0.5707 − 0.7662iw24011110000−0.6961 − 0.8850i
w17710110001−0.1088 − 0.9530iw24111110001−0.1124 − 1.1327i
w17810110010−0.4294 − 0.6363iw24211110010−0.3224 − 0.5236i
w17910110011−0.1091 − 0.7656iw24311110011−0.1054 − 0.5979i
w18010110100−0.4490 − 0.8461iw24411110100−0.5229 − 1.0037i
w18110110101−0.2464 − 0.9270iw24511110101−0.3160 − 1.0913i
w18210110110−0.3744 − 0.6744iw24611110110−0.3016 − 0.5347i
w18310110111−0.1699 − 0.7537iw24711110111−0.1230 − 0.5949i
w18410111000+0.5707 − 0.7662iw24811111000+0.6961 − 0.8850i
w18510111001+0.1088 − 0.9530iw24911111001+0.1124 − 1.1327i
w18610111010+0.4294 − 0.6363iw25011111010+0.3224 − 0.5236i
w18710111011+0.1091 − 0.7656iw25111111011+0.1054 − 0.5979i
w18810111100+0.4490 − 0.8461iw25211111100+0.5229 − 1.0037i
w18910111101+0.2464 − 0.9270iw25311111101+0.3160 − 1.0913i
w19010111110+0.3744 − 0.6744iw25411111110+0.3016 − 0.5347i
w19110111111+0.1699 − 0.7537iw25511111111+0.1230 − 0.5949i
for R = 5/8 (or R = 1/2, 3/4 or 13/16):
w12810000000−1.5843 + 0.1512iw19211000000−0.2552 + 0.0725i
w12910000001−0.9275 + 0.0940iw19311000001−0.7681 + 0.0832i
w13010000010−0.1639 + 1.6237iw19411000010−0.0726 + 0.0865i
w13110000011−0.1000 + 0.9905iw19511000011−0.0867 + 0.8378i
w13210000100−1.5843 − 0.1512iw19611000101−0.2552 − 0.0725i
w13310000101−0.9275 − 0.0940iw19711000101−0.7681 − 0.0832i
w13410000110−0.1639 − 1.6237iw19811000110−0.0726 − 0.0865i
w13510000111−0.1000 − 0.9905iw19911000111−0.0867 − 0.8378i
w13610001000−1.5329 + 0.4508iw20011001000−0.2567 + 0.0753i
W13710001001−0.8993 + 0.2781iw20111001001−0.7371 + 0.2323i
w13810001010−0.4843 + 1.5571iw20211001010−0.0722 + 0.0866i
w13910001011−0.2959 + 0.9454iw20311001011−0.2417 + 0.8000i
w14010001100−1.5329 − 0.4505iw20411001100−0.2567 − 0.0753i
w14110001101−0.8933 − 0.2781iw20511001101−0.7371 − 0.2323i
w14210001110−0.4843 − 1.5571iw20611001110−0.0722 − 0.0866i
w14310001111−0.2959 − 0.9454iw20711001111−0.2417 − 0.8000i
w14410010000−1.3147 + 0.1263iw20811010000−0.4495 + 0.0766i
w14510010001−1.1029 + 0.1084iw20911010001−0.6140 + 0.0811i
w14610010010−0.1381 + 1.3595iw21011010010−0.0717 + 0.5169i
w14710010011−0.1179 + 1.1562iw21111010011−0.0837 + 0.6868i
w14810010100−1.3147 − 0.1263iw21211010100−0.4495 − 0.0766i
w14910010101−1.1029 − 0.1084iw21311010101−0.6140 − 0.0811i
w15010010110−0.1381 − 1.3595iw21411010110−0.0717 − 0.5169i
w15110010111−0.1179 − 1.1562iw21511010111−0.0837 − 0.6868i
w15210011000−1.2724 + 0.3763iw21611011000−0.4423 + 0.1097i
w15310011001−1.0662 + 0.3220iw21711011001−0.5925 + 0.1765i
w15410011010−0.4077 + 1.3024iw21811011010−0.0883 + 0.5092i
w15510011011−0.3470 + 1.1060iw21911011011−0.1746 + 0.6612i
w15610011100−1.2724 − 0.3763iw22011011100−0.4423 − 0.1097i
w15710011101−1.0662 − 0.3220iw22111011101−0.5925 − 0.1765i
w15810011110−0.4077 − 1.3024iw22211011110−0.0883 − 0.5092i
w15910011111−0.3470 − 1.1060iw22311011111−0.1746 − 0.6612i
w16010100000+1.5843 + 0.1512iw22411100000+0.2552 + 0.0725i
w16110100001+0.9275 + 0.0940iw22511100001+0.7681 + 0.0832i
w16210100010+0.1639 + 1.6237iw22611100010+0.0726 + 0.0865i
w16310100011+0.1000 + 0.9905iw22711100011+0.0867 + 0.8378i
w16410100100+1.5843 − 0.1512iw22811100100+0.2552 − 0.0725i
w16510100101+0.9275 − 0.0940iw22911100101+0.7681 − 0.0832i
w16610100110+0.1639 − 1.6237iw23011100110+0.0726 − 0.0865i
w16710100111+0.1000 − 0.9905iw23111100111+0.0867 − 0.8378i
w16810101000+1.5329 + 0.4508iw23211101000+0.2567 + 0.0753i
w16910101001+0.8933 + 0.2781iw23311101001+0.7371 + 0.2323i
w17010101010+0.4843 + 1.5571iw23411101010+0.0722 + 0.0866i
w17110101011+0.2959 + 0.9454iw23511101011+0.2417 + 0.8000i
w17210101100+1.5329 − 0.4508iw23611101100+0.2567 − 0.0753i
w17310101101+0.8933 − 0.2781iw23711101101+0.7371 − 0.2323i
w17410101110+0.4843 − 1.5571iw23811101110+0.0722 − 0.0866i
w17510101111+0.2959 − 0.9454iw23911101111+0.2417 − 0.8000i
w17610110000+1.3147 + 0.1263iw24011110000+0.4495 + 0.0766i
w17710110001+1.1029 + 0.1084iw24111110001+0.6140 + 0.0811i
w17810110010+0.1381 + 1.3595iw24211110010+0.0717 + 0.5169i
w17910110011+0.1179 + 1.1562iw24311110011+0.0837 + 0.6868i
w18010110100+1.3147 − 0.1263iw24411110100+0.4495 − 0.0766i
w18110110101+1.1029 − 0.1084iw24511110101+0.6140 − 0.0811i
w18210110110+0.1381 − 1.3595iw24611110110+0.0717 − 0.5169i
w18310110111+0.1179 − 1.1562iw24711110111+0.0837 − 0.6868i
w18410111000+1.2724 + 0.3763iw24811111000+0.4423 + 0.1097i
w18510111001+1.0662 + 0.3220iw24911111001+0.5925 + 0.1765i
w18610111010+0.4077 + 1.3024iw25011111010+0.0883 + 0.5092i
w18710111011+0.3470 + 1.1060iw25111111011+0.1746 + 0.6612i
w18810111100+1.2724 − 0.3763iw25211111100+0.4423 − 0.1097i
w18910111101+1.0662 − 0.3220iw25311111101+0.5925 − 0.1765i
w19010111110+0.4077 − 1.3024iw25411111110+0.0883 − 0.5092i
w19110111111+0.3470 − 1.1060iw25511111111+0.1746 − 0.6612i
for R = 3/4 (or R = 1/2, 5/8 or 13/16):
w12810000000−0.6538 + 0.0691iw19211000000−0.6518 + 0.2064i
w12910000001−0.5051 + 0.0654iw19311000001−0.5023 + 0.1969i
w13010000010−1.4515 + 0.1246iw19411000010−1.2169 + 0.1086i
w13110000011−0.0720 + 0.0589iw19511000011−0.0716 + 0.1743i
w13210000100−0.6396 + 0.4933iw19611000100−0.6490 + 0.3456i
w13310000101−0.4850 + 0.4726iw19711000101−0.4967 + 0.3308i
w13410000110−1.4339 + 0.3828iw19811000110−1.2175 + 0.3244i
w13510000111−0.0708 + 0.4166iw19911000111−0.0713 + 0.2961i
w13610001000+0.6538 + 0.0691iw20011001000+0.6518 + 0.2064i
W13710001001+0.5051 + 0.0654iw20111001001+0.5023 + 0.1959i
w13810001010+1.4515 + 0.1246iw20211001010+1.2169 + 0.1086i
w13910001011+0.0720 + 0.0589iw20311001011+0.0716 + 0.1743i
w14010001100+0.6396 + 0.4933iw20411001100+0.6490 + 0.3456i
w14110001101+0.4850 + 0.4726iw20511001101+0.4967 + 0.3308i
w14210001110+1.4339 + 0.3828iw20611001110+1.2175 + 0.3244i
w14310001111+0.0708 + 0.4156iw20711001111+0.0713 + 0.2951i
w14410010000−0.8080 + 0.0721iw20811010000−0.8177 + 0.2121i
w14510010001−0.3608 + 0.0619iw20911010001−0.3587 + 0.1857i
w14610010010−0.9770 + 0.0640iw21011010010−1.0126 + 0.1946i
w14710010011−0.2162 + 0.0599iw21111010011−0.2150 + 0.1782i
w14810010100−0.8066 + 0.5082iw21211010100−0.8186 + 0.3517i
w14910010101−0.3436 + 0.4483iw21311010101−0.3540 + 0.3139i
w15010010110−0.9839 + 0.5111iw21411010110−1.0159 + 0.3531i
w15110010111−0.2091 + 0.4280iw21511010111−0.2130 + 0.3012i
w15210011000+0.8080 + 0.0721iw21611011000+0.8177 + 0.2121i
w15310011001+0.3603 + 0.0619iw21711011001+0.3587 + 0.1857i
w15410011010+0.9770 + 0.0640iw21811011010+1.0126 + 0.1946i
w15510011011+0.2162 + 0.0599iw21911011011+0.2150 + 0.1782i
w15610011100+0.8066 + 0.5082iw22011011100+0.8186 + 0.3517i
w15710011101+0.3436 + 0.4483iw22111011101+0.3540 + 0.3139i
w15810011110+0.9839 + 0.5111iw22211011110+1.0159 + 0.3531i
w15910011111+0.2091 + 0.4280iw22311011111+0.2130 + 0.3012i
w16010100000−0.6538 − 0.0691iw22411100000−0.6518 − 0.2064i
w16110100001−0.5051 − 0.0654iw22511100001−0.5023 − 0.1959i
w16210100010−1.4515 − 0.1246iw22611100010−1.2169 − 0.1086i
w16310100011−0.0720 − 0.0589iw22711100011−0.0716 − 0.1743i
w16410100100−0.6396 − 0.4933iw22811100100−0.6490 − 0.3456i
w16510100101−0.4850 − 0.4726iw22911100101−0.4967 − 0.3308i
w16610100110−1.4339 − 0.3828iw23011100110−1.2175 − 0.3244i
w16710100111−0.0708 − 0.4166iw23111100111−0.0713 − 0.2951i
w16810101000+0.6538 − 0.0691iw23211101000+0.6518 − 0.2064i
w16910101001+0.5051 − 0.0654iw23311101001+0.5623 − 0.1959i
w17010101010+1.4515 − 0.1246iw23411101010+1.2169 − 0.1086i
w17110101011+0.0720 − 0.0589iw23511101011+0.0716 − 0.1743i
w17210101100+0.6396 − 0.4933iw23611101100+0.6490 − 0.3456i
w17310101101+0.4850 − 0.4726iw23711101101+0.4967 − 0.3308i
w17410101110+1.4339 − 0.3828iw23811101110+1.2175 − 0.3244i
w17510101111+0.0708 − 0.4166iw23911101111+0.0713 − 0.2951i
w17610110000−0.8080 − 0.0721iw24011110000−0.8177 − 0.2121i
w17710110001−0.3608 − 0.0619iw24111110001−0.3587 − 0.1857i
w17810110010−0.9770 − 0.0640iw24211110010−1.0126 − 0.1946i
w17910110011−0.2162 − 0.0599iw24311110011−0.2150 − 0.1782i
w18010110100−0.8066 − 0.5082iw24411110100−0.8486 − 0.3517i
w18110110101−0.3436 − 0.4483iw24511110101−0.3540 − 0.3139i
w18210110110−0.9839 − 0.5111iw24611110110−1.0159 − 0.3531i
w18310110111−0.2091 − 0.4280iw24711110111−0.2130 − 0.3012i
w18410111000+0.8080 − 0.0721iw24811111000+0.8177 − 0.2121i
w18510111001+0.3603 − 0.0619iw24911111001+0.3587 − 0.1857i
w18610111010+0.9770 − 0.0640iw25011111010+1.0126 − 0.1946i
w18710111011+0.2162 − 0.0599iw25111111011+0.2150 − 0.1782i
w18810111100+0.8066 − 0.5082iw25211111100+0.8186 − 0.3517i
w18910111101+0.3436 − 0.4483iw25311111101+0.3540 − 0.3139i
w19010111110+0.9839 − 0.5111iw25411111110+1.0159 − 0.3531i
w19110111111+0.2091 − 0.4280iw25511111111+0.2130 − 0.3012i
for R = 13/16 (or R = 1/2, 5/8 or 3/4):
w12810000000−0.6404 + 0.6801iw19211000000−0.8128 + 0.7021i
w12910000001+0.6404 + 0.6801iw19311000001+0.8128 + 0.7021i
w13010000010−0.6404 − 0.6801iw19410000010−0.8128 − 0.7021i
w13110000011+0.6404 − 0.6801iw19511000011+0.8128 − 0.7021i
w13210000100−0.5954 + 0.8500iw19611000100−0.7699 + 0.8797i
w13310000101+0.5954 + 0.8500iw19711000101+0.7699 + 0.8797i
w13410000110−0.5954 − 0.8500iw19811000110−0.7699 − 0.8797i
w13510000111+0.5954 − 0.8500iw19911000111+0.7699 − 0.8797i
w13610001000−1.1989 + 0.5582iw20011001000−1.0129 + 0.6976i
W13710001001+1.1989 + 0.5582iw20111001001+1.0129 + 0.6976i
w13810001010−1.1989 − 0.5582iw20211001010−1.0129 − 0.6976i
w13910001011+1.1989 − 0.5582iw20311001011+1.0129 − 0.6976i
w14010001100−1.4012 + 0.6249iw20411001100−0.9657 + 0.8860i
w14110001101+1.4012 + 0.6249iw20511001101+0.9657 + 0.8660i
w14210001110−1.4012 − 0.6249iw20611001110−0.9657 − 0.8860i
w14310001111+1.4012 − 0.6249iw20711001111+0.9657 − 0.8860i
w14410010000−0.6524 + 0.5156iw20811010000−0.8099 + 0.5313i
w14510010001+0.6524 + 0.5156iw20911010001+0.8099 + 0.5313i
w14610010010−0.6524 − 0.5156iw21011010010−0.8099 − 0.5313i
w14710010011+0.6524 − 0.5156iw21111010011+0.8099 − 0.5313i
w14810010100−0.6640 + 0.3620iw21211010100−0.8291 + 0.3705i
w14910010101+0.6640 + 0.3620iw21311010101+0.8291 + 0.3705i
w15010010110−0.6640 − 0.3620iw21411010110−0.8291 − 0.3705i
w15110010111+0.6640 − 0.3620iw21511010111+0.8291 − 0.3705i
w15210011000−1.4123 + 0.3539iw21611011000−0.9768 + 0.5294i
w15310011001+1.4123 + 0.3539iw21711011001+0.9768 + 0.5294i
w15410011010−1.4123 − 0.3539iw21811011010−0.9768 − 0.5294i
w1551011011+1.4123 − 0.3539iw21911011011+0.9768 − 0.5294i
w15610011100−1.2076 + 0.3137iw22011011100−1.0171 + 0.3701i
w15710011101+1.2076 + 0.3137iw22111011101+1.0171 + 0.3701i
w15810011110−1.2076 − 0.3137iw22211011110−1.0171 − 0.3701i
w15910011111+1.2076 − 0.3137iw22311011111+1.0171 − 0.3701i
w16010100000−0.4846 + 0.6443iw22411100000−0.3381 + 0.6175i
w16110100001+0.4846 + 0.6443iw22511100001+0.3381 + 0.6175i
w16210100010−0.4846 − 0.6443iw22611100010−0.3381 − 0.6175i
w16310100011+0.4846 − 0.6443iw22711100011+0.3381 − 0.6175i
w16410100100−0.4495 + 0.7999iw22811100100−0.3079 + 0.7726i
w16510100101+0.4495 + 0.7999iw22911100101+0.3079 + 0.7726i
w16610100110−0.4495 − 0.7999iw23011100110−0.3079 − 0.7726i
w16710100111+0.4495 − 0.7999iw23111100111+0.3079 − 0.7726i
w16810101000−0.0693 + 0.5689iw23211101000−0.2034 + 0.5915i
w16910101001+0.0693 + 0.5689iw23311101001+0.2034 + 0.5915i
w17010101010−0.0693 − 0.5689iw23411101010−0.2034 − 0.5915i
w17110101011+0.0693 − 0.5689iw23511101011+0.2034 − 0.5915i
w17210101100−0.0563 + 0.7102iw23611101100−0.1695 + 0.7506i
w17310101101+0.0563 + 0.7102iw23711101101+0.1695 + 0.7506i
w17410101110−0.0563 − 0.7102iw23811101110−0.1695 − 0.7506i
w17510101111+0.0563 − 0.7102iw23911101111+0.1695 − 0.7506i
w17610110000−0.5011 + 0.4924iw24011110000−0.3558 + 0.4698i
w17710110001+0.5011 + 0.4924iw24111110001+0.3558 + 0.4698i
w17810110010−0.5011 − 0.4924iw24211110010−0.3558 − 0.4698i
w17910110011+0.5011 − 0.4924iw24311110011+0.3558 − 0.4698i
w18010110100−0.5105 + 0.3465iw24411110100−0.3634 + 0.3304i
w18110110101+0.5105 + 0.3465iw24511110101+0.3634 + 0.3304i
w18210110110−0.5105 − 0.3465iw24611110110−0.3634 + 0.3304i
w18310110111+0.5105 − 0.3465iw24711110111+0.3634 − 0.3304i
w18410111000−0.0720 + 0.4369iw24811111000−0.2145 + 0.4495i
w18510111001+0.0720 + 0.4369iw24911111001+0.2145 + 0.4495i
w18610111010−0.0720 − 0.4369iw25011111010−0.2145 − 0.4495i
w18710111011+0.0720 − 0.4369iw25111111011+0.2145 − 0.4495i
w18810111100−0.0730 + 0.3094iw25211111100−0.2184 + 0.3170i
w18910111101+0.0730 + 0.3094iw25311111101+0.2184 + 0.3170i
w19010111110−0.0730 − 0.3094iw25411111110−0.2184 − 0.3170i
w19110111111+0.0730 − 0.3094iw25511111111+0.2184 − 0.3170i

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Classifications

3 codes
IPC · International Patent Classification
Section H — Electricity
  • H04L1/00
  • H04L27/34
  • H04L5/00

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⤢ drag to zoomJan 2019Apr 2019Jul 2019Oct 2019Jan 2020Apr 2020Jul 2020Oct 2020USPTOApplicantNon-final rejectionResponse after non-finalNotice of allowance
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Janice N Tieu
art unit 2633 · TC 2600
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