Coding and decoding scheme using symbol soft values

Abstract

The present disclosure relates to a coding and decoding scheme using symbol soft values. A first communication device (100) sends a set of modulation symbols. The set of modulation symbols has been obtained based on a set of coded bits, and the set of coded bits is obtained by linearly transforming a set of uncoded bits according to a coding matrix G, wherein the coding matrix G is the Kronecker product of two binary matrices G1 and G2. G1 is the nth Kronecker power of the matrix #imgabs0#, and G2 is a K×K full rank binary matrix, wherein K is the modulation order of the modulation symbol constellation and K>1, and wherein M0 is a multiple of K. A second communication device (300) receives the set of modulation symbols and obtains a set of decoded bits based on the set of received modulation symbols and a set of symbol soft values.

Description

Technical Field

[0001] The present disclosure relates to polarizing encoding and decoding schemes using symbol soft values ​​to improve coding performance. Background Art

[0002] Polar codes are linear block error correction codes that have been shown to achieve the channel capacity of binary-input discrete memoryless channels (B-DMC) with low coding and decoding complexity. Due to these advantages, polar codes are used to transmit uplink and downlink control signals of enhanced mobile broadband (eMBB) control channels in 3GPP New Radio (NR) systems. However, if high-order modulation (e.g., 16QAM) is used, the channel is no longer B-DMC, so polar codes may not achieve the channel capacity. Summary of the invention

[0003] The purpose of the disclosed examples is to provide a solution that alleviates or solves the disadvantages and problems of conventional solutions.

[0004] The above and other objects are achieved by the subject-matter of the independent claims. Further advantageous examples of the present disclosure can be found in the dependent claims.

[0005] According to a first aspect of the present disclosure, the above and other objects are achieved by a first communication device used in a wireless communication system, wherein the first communication device is configured to:

[0006] Obtaining a set of uncoded bits including M0 bits, wherein the set of uncoded bits includes information bits;

[0007] A set of coded bits is obtained by linearly transforming the set of uncoded bits according to a coding matrix G, wherein the coding matrix G is the Kronecker product of two binary matrices G1 and G2, wherein G1 is a matrix The nth Kronecker power of , and G2 is a K×K full rank binary matrix, where K is the modulation order of the modulation symbol constellation and K>1, and where M0 is a multiple of K;

[0008] obtaining a set of modulation symbols by modulating the set of coded bits according to the modulation symbol constellation; and

[0009] The set of modulation symbols is sent to a second communications device.

[0010] The modulation order of the modulation symbol constellation can be understood as the number of bits carried in a modulation symbol. Kmodulation symbols, the modulation order is K.

[0011] Obtaining a set of coded bits can be understood as using polar codes on a set of uncoded bits. Therefore, polar codes are used for coding.

[0012] An advantage of the first communication device according to the first aspect is that a polar-like code is guaranteed in each bit segment of length K. Therefore, the symbol soft value of each bit segment of length K can be used for decoding at the receiver.

[0013] In an implementation manner of the first communication device according to the first aspect,

[0014]

[0015] An advantage of this implementation is that it supports a length of M0 uncoded bits and guarantees that the number of coded bits is M0.

[0016] In an implementation of the first communication device according to the first aspect, when G2 is a matrix The log2 Kth Kronecker power is used when K is a power of 2.

[0017] In this case, G is the matrix log2 M0th Kronecker power. Therefore, one advantage of this implementation is that for G to be a matrix is a special case of the log2 M0th Kronecker power of , which guarantees a polar-like code in each bit segment of length K.

[0018] In an implementation manner of the first communication device according to the first aspect, obtaining the set of modulation symbols includes:

[0019] obtaining a subset of the set of coded bits, wherein the subset of the set of coded bits consists of a complete segment of the set of coded bits; and

[0020] The set of modulation symbols is obtained by modulating a subset of the set of coded bits.

[0021] An advantage of this implementation is that it ensures that each entire bit segment is either modulated or not modulated, thus avoiding modulating only a portion of a bit segment.

[0022] In an implementation manner of the first communication device according to the first aspect, obtaining the set of modulation symbols includes:

[0023] obtaining an extended set of coded bits, wherein the extended set of coded bits comprises the set of coded bits and one or more segments of the set of coded bits; and

[0024] The set of modulation symbols is obtained by modulating the set of spread coded bits.

[0025] An advantage of this implementation is that it ensures that each entire bit segment is either modulated or not modulated, thus avoiding modulating only a portion of a bit segment.

[0026] In an implementation manner of the first communication device according to the first aspect, obtaining the set of modulation symbols includes:

[0027] interleaving the set of coded bits by interleaving complete segments of the set of coded bits; and

[0028] The set of modulation symbols is obtained by modulating the interleaved set of coded bits.

[0029] An advantage of this implementation is that it ensures that each entire bit segment is modulated as one modulation symbol, thus avoiding modulation of only a portion of a bit segment.

[0030] In an implementation manner of the first communication device according to the first aspect, the coded bit segment is obtained according to the following equation:

[0031]

[0032] where k=1, 2, 3, ... is the index of a bit in the set of coded bits, and i b =1, 2, ...K.

[0033] One advantage of this implementation is that it provides a feasible bit segmentation solution.

[0034] According to a second aspect of the present disclosure, the above and other objects are achieved by a second communication device used in a wireless communication system, wherein the second communication device is configured to:

[0035] receiving a set of modulation symbols from a first communications device, wherein the received set of modulation symbols is associated with a set of coded bits and a modulation symbol constellation;

[0036] Obtaining a set of symbol soft values ​​based on the set of received modulation symbols and symbols of the modulation symbol constellation; and

[0037] A set of decoded bits associated with the set of coded bits is obtained based on the set of received modulation symbols and the set of symbol soft values.

[0038] An advantage of the second communication device according to the second aspect is that decoding of LLRs is based on symbol soft values ​​rather than bits, thereby providing improved performance in terms of error rates such as reduced BLER.

[0039] In an implementation of the second communication device according to the second aspect, the set of coded bits is obtained by linearly transforming a set of uncoded bits according to a coding matrix G, wherein the coding matrix G is the Kronecker product of two binary matrices G1 and G2, wherein G1 is a matrix , and G2 is a K×K full rank binary matrix, where K is the modulation order of the modulation symbol constellation and K>1, and where M0 is a multiple of K.

[0040] One advantage of this implementation is that it guarantees a polar-like code in each bit segment of length K. Therefore, the symbol soft value of each bit segment of length K can be used for decoding at the receiver.

[0041] In an implementation manner of the second communication device according to the second aspect,

[0042]

[0043] An advantage of this implementation is that it supports uncoded bits of length M0 and guarantees that the number of coded bits is M0.

[0044] In an implementation of a second communication device according to the second aspect, when the characteristics of the channel are unknown to the second communication device, each symbol soft value in the set of symbol soft values ​​is obtained based on the inner product between the received modulation symbol in the set of received modulation symbols and the symbol of the modulation symbol constellation.

[0045] The channel described herein refers to the channel over which the set of modulation symbols are received. Therefore, this is the case when the characteristics of the channel are unknown to the second communication device. For example, there is no reference signal or pilot signal for channel estimation or demodulation.

[0046] An advantage of this implementation is that the symbol soft values ​​are defined for the case where the channel is unknown, and the symbol soft values ​​are related to the correlation between the received symbols and the modulation symbols in the constellation.

[0047] In an implementation manner of the second communication device according to the second aspect, the inner product between the received modulation symbols in the set of received modulation symbols and the symbols of the modulation symbol constellation is obtained according to the following equation:

[0048] |YX H | 2 or YX H

[0049] wherein Y is the received modulation symbol of the set of received modulation symbols, X is the symbol of the modulation symbol constellation, and H is the conjugate transpose operator.

[0050] One advantage of this implementation is that H | 2 is related to the probability that the transmitted signal is X if the received signal is Y, and YX H It is related to the probability that if the received signal is Y, the transmitted signal is X and the angle between X and Y. H It can be used in situations where the channels of different modulation symbols sent are similar. |YX H | 2 Can be used in all situations.

[0051] In an implementation of a second communication device according to the second aspect, when the characteristics of the channel are known to the second communication device, each symbol soft value in the set of symbol soft values ​​is obtained based on the difference between a received modulation symbol in the set of received modulation symbols and a symbol of the modulation symbol constellation.

[0052] The channel referred to herein refers to the channel over which the set of modulation symbols is received. Thus, this is the case when the second communication device knows the characteristics of the channel.

[0053] An advantage of this implementation is that the symbol soft values ​​are defined for the case where the channel is known, the symbol soft values ​​being related to the differences between received symbols and modulation symbols in the constellation.

[0054] In an implementation of the second communication device according to the second aspect, the difference between the received modulation symbol in the set of received modulation symbols and the symbol of the modulation symbol constellation is obtained according to the following equation:

[0055] ρ|YX| 2

[0056] wherein Y is the received modulation symbol in the set of received modulation symbols, X is the symbol of the modulation symbol constellation, and p is the signal-to-noise ratio of the received modulation symbol in the set of received modulation symbols.

[0057] One advantage of this implementation is that it provides symbol soft values ​​for the case where the channel is known. 2 is related to the difference between X and Y, where |YX| 2 Also known as the Euclidean distance between X and Y, or the Frobenius norm of the difference between X and Y.

[0058] In an implementation manner of the second communication device according to the second aspect, obtaining the set of decoded bits includes:

[0059] The set of decoded bits is obtained according to the soft values ​​of the decoded bit segments, wherein the soft value of each decoded bit segment is determined according to the soft value of at least one intermediate bit segment, and wherein the soft value of each intermediate bit segment is determined according to the soft values ​​of two basic bit segments, wherein the sum of the two basic bit segments in the Galois field of two elements is equal to the intermediate bit segment, and wherein the soft values ​​of the two bit segments are obtained according to the set of symbol soft values.

[0060] An advantage of this implementation is that the decoder can calculate the soft values ​​for the decoded bit segments with low complexity.

[0061] In an implementation manner of the second communication device according to the second aspect, obtaining the set of decoded bits includes:

[0062] The set of decoded bits is obtained based on the soft values ​​of the decoded bit segments, wherein the soft value of each decoded bit segment is determined based on the soft value of at least one intermediate bit segment, and wherein the soft value of each intermediate bit segment is determined based on the initial soft value of the intermediate bit segment, the soft value of a basic bit segment and at least one decoded bit, and wherein the initial soft value of the intermediate bit segment is obtained based on the set of symbol soft values.

[0063] An advantage of this implementation is that the decoder is able to calculate the soft values ​​for decoded bit segments with low complexity by using this implementation.

[0064] According to a third aspect of the present disclosure, the above and other objects are achieved by a method for a first communication device, the method comprising:

[0065] Obtaining a set of uncoded bits including M0 bits, wherein the set of uncoded bits includes information bits;

[0066] A set of coded bits is obtained by linearly transforming the set of uncoded bits according to a coding matrix G, wherein the coding matrix G is the Kronecker product of two binary matrices G1 and G2, wherein G1 is a matrix The nth Kronecker power of , and G2 is a K×K full rank binary matrix, where K is the modulation order of the modulation symbol constellation and K>1, and where M0 is a multiple of K;

[0067] obtaining a set of modulation symbols by modulating the set of coded bits according to the modulation symbol constellation; and

[0068] The set of modulation symbols is sent to a second communications device.

[0069] The third aspect provides that the method described can be extended to an implementation corresponding to the implementation of the first communication device provided in the first aspect. Therefore, an implementation of the method includes the features of the corresponding implementation of the first communication device.

[0070] The advantages of the method provided in the third aspect are the same as the advantages of the corresponding implementation of the first communication device provided in the first aspect.

[0071] According to a fourth aspect of the present disclosure, the above and other objects are achieved by a method for a second communication device, the method comprising:

[0072] receiving a set of modulation symbols from a first communications device, wherein the received set of modulation symbols is associated with a set of coded bits and a modulation symbol constellation;

[0073] Obtaining a set of symbol soft values ​​based on the set of received modulation symbols and symbols of the modulation symbol constellation; and

[0074] A set of decoded bits associated with the set of coded bits is obtained based on the set of received modulation symbols and the set of symbol soft values.

[0075] The method provided in the fourth aspect can be extended to an implementation manner corresponding to the implementation manner of the second communication device provided in the second aspect. Therefore, an implementation manner of the method includes the features of the corresponding implementation manner of the second communication device.

[0076] The advantages of the method provided in the fourth aspect are the same as the advantages of the corresponding implementation method of the second communication device provided in the second aspect.

[0077] The present disclosure also relates to a computer program, characterized by program code, which, when executed by at least one processor, causes the at least one processor to perform any method described in the examples of the present disclosure. In addition, the present disclosure also relates to a computer program product, including a computer-readable medium and the computer program, wherein the computer program is included in the computer-readable medium and includes one or more of the following groups: read-only memory (ROM), programmable ROM (PROM), erasable PROM (EPROM), flash memory, electrically EPROM (EEPROM) and hard disk drive.

[0078] Other applications and advantages of the disclosed examples will become apparent from the following detailed description. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] The accompanying drawings are intended to illustrate and explain different examples of the present disclosure, in which:

[0080] - Figure 1 An example of the present disclosure provides a first communication device;

[0081] - Figure 2 An example of the present disclosure provides a method for a first communication device;

[0082] - Figure 3 A second communication device provided by an example of the present disclosure is shown;

[0083] - Figure 4 An example of the present disclosure provides a method for a second communication device;

[0084] - Figure 5 An example of the present disclosure provides a wireless communication system;

[0085] - Figure 6 The encoding and decoding schemes provided by the examples of the present disclosure are shown in more detail;

[0086] - Figure 7 The details of the polarization decoder of the second communication device provided by one example of the present disclosure are shown;

[0087] - Figure 8 A butterfly-based decoder provided by an example of the present disclosure is shown;

[0088] - Fig. 9 Performance results of one example of the present disclosure are shown. DETAILED DESCRIPTION

[0089] A transmitter using polar codes usually includes at least three blocks: a polarization encoder block, a bit segmentation block, and a modulation block.

[0090] The polar encoder block includes a mapper for mapping N information bits and M0-N frozen bits and parity bits (if any, generated based on the information bits and a predefined parity function) to a bit vector B of size 1×M0, where the vector length is M0. Thereafter, the polar code is applied as a linear mapping from B to a vector of coded bits C of size 1×M0 (i.e., C=BG in GF(2)). G is a matrix with size M0×M0, where the size is given by As a matrix The m0th Kronecker power is obtained.

[0091] The bit segmentation block divides the coded bits into M / K bit segments, and in each bit segment there are K bits. K is the number of bits transmitted by one modulation symbol.

[0092] The modulation block maps every K bits to a modulation symbol. If the modulation symbol contains more than one complex number, the modulation is called multi-dimensional modulation. Otherwise, the modulation is called single-dimensional modulation. The bit segmentation block and the modulation block can also be considered as a combined block to generate modulation symbols based on the coded bits.

[0093] A polar code receiver usually consists of two blocks: a demodulation block and a polar decoding block.

[0094] The demodulation block demodulates each received modulation symbol to estimate the log-likelihood ratio (LLR) of each of the K modulation bits based on the received modulation symbol. If the channel is known at the receiver, the received modulation symbol is the symbol after equalization of the received signal. Otherwise, the received modulation symbol is the received signal. The first step of demodulation is to calculate the symbol soft value of the demodulated symbol, which is defined as the symbol soft value for each constellation point (a total of 2) transmitted according to the received modulation symbol (i.e., as given in equation (1)). K The logarithmic probability of

[0095] LL(X)=ln Pr{X|Y} (1)

[0096] where X is the modulation symbol in the constellation and Y is the received modulation symbol.

[0097] In the second step, 2 of each received modulation symbol is converted to K The symbol soft value is converted to the bit soft value of each modulated bit, that is, the LLR value defined in equation (2)

[0098]

[0099] Where b is the modulation bit. Equation (4) introduces a method for obtaining LLR(b) from LL(X). Alternatively, an equivalent method can be used to obtain LLR(b) from X and Y.

[0100] The first step of the polar decoder is to estimate B bit by bit from the M0 LLR values ​​from the demodulation block by using successive cancellation (SC) polar decoding. The estimated bits of B are called decoded bits SC polarization decoding estimation The i-th bit in The principle is

[0101] if is a frozen bit, then

[0102] if is a parity bit, then its value is obtained based on the previously decoded bit and the parity function;

[0103] if is the information bit,

[0104]

[0105] in,

[0106] · is the probability of receiving Y, given that the current decoded bit is b, and the previous decoded bit is

[0107] Due to the recursive structure of the encoding matrix, SC polar decoding can be performed efficiently in a recursive manner using a data flow graph with a structure called a butterfly-based decoder. In a recursive manner, the following f and g functions are used:

[0108] f function: Calculates the LLR of the sum of two bits by the following equation:

[0109]

[0110] in

[0111] Input: LLRs of bits a and b,

[0112] Output: Bit LLRs.

[0113] g function: Update the LLR of one bit according to the LLR of one bit and the LLR of another bit, and their sum is known:

[0114]

[0115] in

[0116] Input: estimated bits and the LLRs of bits a and b,

[0117] Output: Updated LLR for bit a.

[0118] List decoding can be applied in this step to improve decoding performance. By list decoding, the vector B is estimated bit by bit to obtain Specifically, when estimating the i-th bit (1≤i≤M0), the decoding algorithm determines a list of estimates for the first i bits. Each entry in the list contains a feasible estimate of the first i bits and the corresponding probability of the estimate. Compared with unique decoding that only outputs the maximum possible value of each bit, list decoding has a higher chance of achieving a global optimal estimate. In addition, for complexity reasons, the maximum list size should be limited, for example, not larger than Lmax .L max The value of is predefined, such as L max =8.

[0119] In the second step, the polar decoder uses the demapper corresponding to the mapper at the transmitter to obtain Obtain estimated information bits.

[0120] It can be found that the input of the polar decoder is M0 LLR values ​​of the bit, but the received signal is M0 / K modulation symbols, and each corresponds to 2 K symbol soft values. How to make full use of these Decoding the soft values ​​of individual symbols becomes an important issue.

[0121] The traditional method is to calculate the probability of each bit being "0" or "1" by dividing the 2 of each received modulation symbol by K The symbol soft values ​​are converted into K LLR values.

[0122] The symbol soft value defined in equation (1) can be expressed as lnP(X f |Y) where Y is the received modulation and X f is the fth modulation symbol in the constellation and f∈[0, 1, ..., 2 K -1]. i-th b LLR value (i b ∈[0, 1, ..., K-1]) is calculated as

[0123]

[0124] in,

[0125] b f is the binary form of f, b f (i b ) is b f The i-th b bits,

[0126] The numerator and denominator of equation (4) are the probabilities that the current decoded bit is 1 and 0 respectively given that Y is received.

[0127] After this conversion, the LLR values ​​can be used directly in a conventional polar decoder.

[0128] However, in the following disclosure, it will be demonstrated that if, for certain modulation methods, the codewords are generated by a polar encoder, the conventional calculation of the LLR for each information bit using the coded bit soft information under the assumption that they are independent coded bits after demodulation results in erroneous LLR values ​​for the decoded bits. It is also demonstrated that the same problem still exists if list decoding of polar codes is applied.

[0129] Each information bit can be represented as a linear combination of coded bits in GF(2): In the polar encoder, the information bits are inserted into a binary vector B (size 1×M0) of length M0 together with the frozen bits and parity bits (if any). The coded bit vector C (size 1×M0) of the same length M0 is then obtained by linear mapping as follows

[0130] C=BG(mod2) (5)

[0131] in,

[0132] C is the vector of coded bits,

[0133] B is a vector consisting of information bits and frozen bits,

[0134] · (size M0×M0) is a matrix log2 M0th Kronecker power.

[0135] Since in GF(2) And for any full-rank square matrices E and D, In GF(2) we get Therefore, B = CG (mod 2). Therefore, each information bit in B can be represented as a linear combination of a coded bit C in GF (2) and a coefficient "0" or "1" in the G column.

[0136] The problem of calculating the LLR of information bits in a conventional polar decoder is: In equation (5), assuming that there are N information bits and M f frozen bits, the length of B is M0=N+M f , and is also equal to the length of the coded bit vector C. Consider the information bit b i As the i-th bit in B, the information bit is a linear combination of the M0 coded bits in C and the coefficients of the i-th column of G, which can be expressed as

[0137]

[0138] In GF(2), where

[0139] i∈{1, 2, ..., M0} is the bit index in vector B,

[0140] b i is the i-th bit in vector B,

[0141] k∈{1, 2, ..., M0} is the bit index in the coded bit vector C,

[0142] ·c k is the kth bit in the coded bit vector C,

[0143] ·g k，i is the value in the kth row and ith column of G,

[0144] · is to satisfy g i，k = 1, where for Z i Any z in u and z u+1 , z u <z u+1 .

[0145] b will be calculated in equation (6) i The LLR is defined in equation (2). According to equation (2) and equation (6), the information bit b i The LLR can be expressed as

[0146]

[0147] To calculate equation (7), the conventional polar decoder decomposes equation (7) into an expression consisting of the LLR values ​​of each coded bit. Specifically, the LLR indicating the sum of two statistically independent random binary variables U1 and U2 can be expressed as

[0148]

[0149] If we assume

[0150]

[0151] are statistically independent of each other, where

[0152] ·z u It's Z i Any index in

[0153] ·Z i \{z u} is Z i In addition to z u The set of all indices except i \{z u}={z∈Z i |z≠z u},

[0154] Then, b i The LLR of can be expressed as (for simplicity, U2 is used to represent the LLR given in equation (9) )

[0155]

[0156] In equation (10), the following assumptions are used: To express b i LLRs:

[0157] Assumption 1: and are statistically independent.

[0158] The problem with using equation (10) in a conventional polar decoder is that assumption 1 may not always hold. To show what happens when assumption 1 does not hold, we compare the and the LLR (b i ). By inserting equation (2) into equation (10), we obtain

[0159]

[0160] Similarly, by replacing and get

[0161]

[0162] By comparing equation (11) and equation (12), we can find that may not be equal to LLR(b i ), because if and are not statistically independent, the may not be equal to

[0163] To demonstrate that U1 and U2 may not be statistically independent, in the next section it will be shown that this is the case for 16QAM modulation.

[0164] For 16QAM, and Not statistically independent at the receiver: In this section, we first prove the general conclusion of 16QAM, that is, two coded bits demodulated from the same 16QAM symbol are not statistically independent at the receiver. Then, based on this conclusion, we will give a corollary of 16QAM, namely and are not statistically independent at the receiver.

[0165] In 3GPP TS38.211, a 16QAM symbol can be generated by 4 bits. Without loss of generality, the 16QAM symbol generated by 4 bits [a1, a2, a3, a4] is considered to be

[0166]

[0167] Without loss of generality, the conditional probability To prove that the demodulated a1 and a2 are not statistically independent.

[0168] Assume the received symbol is Y, and The probability can be expressed as

[0169]

[0170] in and It can be further expressed as

[0171]

[0172]

[0173] in,

[0174] Sent when Y is received probability.

[0175] Substituting equation (15) and equation (16) into equation (14), we can obtain

[0176]

[0177] For any 4 bits In equation (15) It can be further expressed as

[0178]

[0179] where σ 2 is the power of the channel noise. Substituting equation (13) and equation (18) into equation (17), after some mathematical derivation (see Appendix 1), we obtain

[0180]

[0181] where Re{Y} is the real part of Y.

[0182] It is obvious from equation (19) that depending on This means the following conclusions:

[0183] Conclusion 1: For the 16QAM symbol generated by equation (13), a1 is not independent of a2.

[0184] In equation (19), if a1 is demodulated as this means Equivalent to And further equivalent to In addition, for the situation It can be observed from equation (19) that Therefore, the following conclusions are drawn:

[0185] Conclusion 2: For 16QAM, if a1 is demodulated as must exist

[0186] These conclusions can also be observed from the following numerical estimation, where it is assumed that the 16QAM symbols generated by equation (13) are sent over an AWGN channel and the following bit error rates (BER) are compared:

[0187] BER of a1,

[0188] · Under conditional demodulation of a2 = 1, the BER of a1 is,

[0189] BER of a1 under conditional demodulation with a2=0.

[0190] It can be found that the BER of a1 is significantly related to whether a2 is demodulated to "1" or "0" at the receiver. Therefore, a1 and a2 are statistically correlated, that is, Conclusion 1 is verified. It can be found that the BER curve of a1 is lower and steeper when a2=1 is conditionally demodulated than when a2=0 is conditionally demodulated, which means that when a1 is demodulated to hour Therefore, conclusion 2 is verified.

[0191] It has been proven that for 16QAM, the two bits a1 and a2 demodulated from the same 16QAM symbol are statistically independent. and are not statistically independent, in the sum It is assumed that a1=U1 and a2 is 1 bit, and the feasibility is proved in Appendix 2.

[0192] Consider the following two facts:

[0193] 1) As demonstrated above, a1 and a2 are not statistically independent,

[0194] 2) Since a2 is summed in U2, and a2 are not statistically independent, we can draw the following conclusion: a1 and U2 are not statistically independent. Since a1=U1, we can draw the following inference:

[0195] inference: and are not statistically independent.

[0196] Using equation (12) to calculate the 16QAM estimate of the LLR will lead to decoding errors: In Sections 2 and 3, it was proved that the value of equation (8) is may not be equal to the LLR(b i ), since bits demodulated from the same 16QAM symbol may not be statistically independent. In this section, examples and numerical estimations for 16QAM are provided to show that using equation (10) in a conventional decoder may further lead to decoding errors.

[0197] At the transmitter, equation (5) is used to generate the coded bits. Specifically, consider a polar code of length M0=8, where M info = 4 information bits and M f =4 frozen bits, where the 4 information bits are assumed to be [1, 1, 1, 1]. B and G in equation (5) are obtained as follows:

[0198] In this example, assume that the information bits inserted into b4, b6, b7, b8 of vector B are

[0199] B=[0,0,0,b4,0,b6,b7,b8]=[0,0,0,1,0,1,1,1] (20)

[0200] "0" in equation (20) is a frozen bit, and b4, b6, b7, and b8 are information bits.

[0201] The matrix G is constructed as

[0202] Then, the coded bits C can be calculated using equation (5) and obtained as

[0203] C=BG(mod2)=[0,1,1,0,1,0,0,1]

[0204] Then, according to equation (13), the first and second 4 bits in C are modulated into two 16QAM symbols respectively: and The channel is an AWGN channel. In this example, SNR = 0 dB is assumed to simplify the calculation. Assume that the received symbol vector Y is

[0205]

[0206] Compare the following two decoders, a bit LLR based decoder and a symbol soft value based decoder.

[0207] Using a bit LLR based decoder at the receiver: When a bit LLR based decoder (i.e., a conventional polar decoder) is used, the LLR for each information bit is calculated by equation (13). By using the received signal in equation (21), the LLR calculated by equation (11) is as follows

[0208]

[0209]

[0210]

[0211]

[0212] Then, the decoded information bits can be obtained That is, a decoding error occurs.

[0213] A decoder based on symbol soft values ​​is used at the receiver: The symbol soft values ​​are defined in equation (1). In this example, the modulation symbol of the tth received modulation symbol The symbolic soft value of can be written as

[0214]

[0215] in,

[0216] · is a modulation symbol generated by 4 bits [a1, a2, a3, a4], as shown in equation (12),

[0217] t∈{1,2} is the index of the received modulation symbol,

[0218] ·Y t is the tth received modulation symbol.

[0219] Since there is a one-to-one mapping between the modulation symbols and the 4 bits [a1, a2, a3, a4] as shown in (13), the The probability of a value that can be mapped to 4 bits [a1, a2, a3, a4] can be used to calculate the LLR (b i).

[0220] Specifically, it is assumed that a1=c1, a2=c2, a3=c3, a4=c4 are used to generate the first modulation symbol by equation (13), and it is assumed that a1=c5, a2=c6, a3=c7, a4=c8 are used for the second modulation symbol, where c1 to c8 are the 1st to 8th coded bits in C, respectively. (i.e. z u =1) as an example, in equation (12) It can be expressed as:

[0221]

[0222] This is calculated based on the symbol soft value. Similarly, we get and Finally, LLR(b i ) can be calculated based on the symbol soft value.

[0223] According to the symbol soft value calculation equation (23) The method is different from the traditional method given in equations (10) and (11).

[0224] Based on these symbol soft values, LLR (b i ),in Calculate as shown in equation (18). The final result is as follows:

[0225] LLR(b4)=-2.2,

[0226] LLR(b6)=-2.9372,

[0227] LLR(b7)=-0.92,

[0228] LLR(b8)=-0.8387.

[0229] Then, the decoded information bits can be obtained That is, the decoding is correct.

[0230] The above examples show that a decoder based on bit LLRs may cause decoding errors when a decoder based on symbol soft values ​​can perform correct decoding. In addition, BLER simulations show that a decoder based on symbol soft values ​​is statistically less prone to decoding errors than a decoder based on bit LLRs, i.e., the BLER is reduced by about 20% at SNR=0 dB.

[0231] In the above examples, list decoding is not discussed. If list decoding is applied, the decoding process based on each entry in the list is the same as in the above examples. Therefore, list decoding has the same problems and the same solutions can be applied.

[0232] Polar codes can achieve the channel capacity of a binary input discrete memoryless channel (B-DMC). However, if high-order modulation (e.g., 16QAM) is used, the channel is no longer B-DMC, so polar codes may not achieve the channel capacity. By using the proposed encoder and decoder scheme disclosed in this article, higher throughput can be achieved compared to a bit-based decoder because the channel is DMC with symbol input.

[0233] The same problem can be found for any channel coding if the information bit can be expressed as the sum of at least two correlated bits. For example, in a low-density parity-check (LDPC) code, if there is a parity check function including one information bit and two other coded bits, and the two coded bits are correlated with each other due to the modulation (e.g., 16QAM) in the example in the IDF, the same problem can be found.

[0234] When a non-binary turbo encoder is used, a non-binary decoder is also considered for turbo codes, namely duobinary turbo convolutional codes. In duobinary turbo convolutional codes, the input to the encoder is quaternary or has a higher order.

[0235] Compared to the dual binary turbo convolutional encoder, the polar encoder is a binary encoder and is not based on convolution. At the decoder, SC polar decoding can be efficiently performed in a recursive manner by a butterfly-based decoder, which is different from the iteration-based dual binary turbo convolutional decoder. Due to the different structures of the encoder and decoder, the functions in the dual binary turbo convolutional code cannot be used for polar codes. Therefore, a polar decoder based on symbol soft values ​​and a corresponding encoder are needed.

[0236] For the above reasons, according to an example of the present disclosure, a first communication device 100 and a second communication device 300 are disclosed. In the example given herein, the first communication device 100 is used as a transmitter and the second communication device 300 is used as a receiver, but it is not limited thereto.

[0237] Figure 1 FIG. 1 shows a first communication device 100 provided by an example of the present disclosure. Figure 1In the example shown, the first communication device 100 includes a processor 102, a transceiver 104, and a memory 106. The processor 102 is coupled to the transceiver 104 and the memory 106 via a communication device 108 known in the art. The first communication device 100 may also include an antenna or an antenna array 110 coupled to the transceiver 104, which means that the first communication device 100 can be used for wireless communication in a wireless communication system. In the present disclosure, the first communication device 100 is used to perform certain actions, which should be understood to mean that the first communication device 100 includes suitable means for performing the actions, such as the processor 102 and the transceiver 104.

[0238] The processor 102 of the first communication device 100 may be referred to as one or more general-purpose central processing units (CPUs), one or more digital signal processors (DSPs), one or more application-specific integrated circuits (ASICs), one or more field programmable gate arrays (FPGAs), one or more programmable logic devices, one or more discrete gates, one or more transistor logic devices, one or more discrete hardware components, and one or more chipsets.

[0239] The memory 106 of the first communication device 100 may be a read-only memory, a random access memory, or a non-volatile random access memory (NVRAM).

[0240] The transceiver 104 of the first communication device 100 may be a transceiver circuit, a power controller, an antenna, or an interface for communicating with other modules or devices.

[0241] In an example, the transceiver 104 of the first communication device 100 may be a separate chipset or integrated in one chipset with the processor 102. In some examples, the processor 102, transceiver 104 and memory 106 of the first communication device 100 are integrated in one chipset.

[0242] According to an example of the present disclosure, the first communication device 100 is used to obtain a group of uncoded bits including M0 bits, wherein the group of uncoded bits includes information bits. The first communication device 100 is also used to obtain a group of coded bits by linearly transforming the group of uncoded bits according to a coding matrix G. The coding matrix G is the Kronecker product of two binary matrices G1 and G2, wherein G1 is a matrix The first communication device 100 is further configured to obtain a set of modulation symbols by modulating the set of coded bits according to the modulation symbol constellation. The first communication device 100 is further configured to send the set of modulation symbols to the second communication device 300.

[0243] In general, the Kronecker product of a first matrix A and a second matrix B of size M×N will produce a third matrix C, where the elements in the (M(d1-1)+d2)th row and (N(d3-1)+d4)th column of C are equal to the product of the elements in the d1th row and d2th column of A and the elements in the d3th row and d4th column of B. In addition, the matrix The nth Kronecker power of is The result of performing n-1 Kronecker products with itself.

[0244] Figure 2 It is shown that in, for example, Figure 1 Flowchart of a corresponding method 200 executed in the first communication device 100 shown. The method 200 includes obtaining (202) a set of uncoded bits including M0 bits, wherein the set of uncoded bits includes information bits. The method 200 also includes: obtaining (204) a set of coded bits by linearly transforming the set of uncoded bits according to a coding matrix G, wherein the coding matrix G is the Kronecker product of two binary matrices G1 and G2, wherein G1 is a matrix The method 200 further comprises: obtaining (206) a set of modulation symbols by modulating the set of coded bits according to the modulation symbol constellation. The method 200 further comprises: sending (208) the set of modulation symbols to the second communication device 300.

[0245] In an example of the present disclosure, the encoding matrix G may be equal to the Kronecker product of the two binary matrices G1 and G2.

[0246] In the examples of the present disclosure, the integer n is given by the following formula:

[0247]

[0248] In other examples of the present disclosure, when G2 is a matrix The log2 Kth Kronecker power is used when K is a power of 2.

[0249] Figure 3 FIG. 2 shows a second communication device 300 provided by an example of the present disclosure. Figure 3 In the example shown, the second communication device 300 includes a processor 302, a transceiver 304, and a memory 306. The processor 302 is coupled to the transceiver 304 and the memory 306 via a communication device 308 known in the art. The second communication device 300 can be used for wireless communication in a wireless communication system and for wired communication in a wired communication system, respectively. The wireless communication capability is provided by an antenna or antenna array 310 coupled to the transceiver 304, and the wired communication capability is provided by a wired communication interface 312 coupled to the transceiver 304. In the present disclosure, the second communication device 300 is used to perform certain actions, which should be understood to mean that the second communication device 300 includes suitable means for performing the actions, such as the processor 302 and the transceiver 304.

[0250] The processor 302 of the second communication device 300 may be referred to as one or more general purpose CPUs, one or more DSPs, one or more ASICs, one or more FPGAs, one or more programmable logic devices, one or more discrete gates, one or more transistor logic devices, one or more discrete hardware components, and one or more chipsets.

[0251] The memory 306 of the second communication device 300 may be a read-only memory, a random access memory, or an NVRAM.

[0252] The transceiver 304 of the second communication device 300 may be a transceiver circuit, a power controller, an antenna, or an interface for communicating with other modules or devices.

[0253] In an example, the transceiver 304 of the second communication device 300 may be a separate chipset or integrated in one chipset with the processor 302. In some examples, the processor 302, the transceiver 304, and the memory 306 of the second communication device 300 are integrated in one chipset.

[0254] According to an example of the present disclosure, the second communication device 300 is used to:

[0255] A set of modulation symbols is received from the first communication device 100. The set of received modulation symbols is associated with a set of coded bits and a modulation symbol constellation. The second communication device 300 is further configured to obtain a set of symbol soft values ​​based on the set of received modulation symbols and symbols of the modulation symbol constellation. The second communication device 300 is further configured to obtain a set of decoded bits associated with the set of coded bits based on the set of received modulation symbols and the set of symbol soft values.

[0256] Figure 4 It is shown that in e.g. Figure 3 Flowchart of a corresponding method 400 performed in the second communication device 300 shown. The method 400 includes: receiving (402) a set of modulation symbols from the first communication device 100. The set of received modulation symbols is associated with a set of coded bits and a modulation symbol constellation. The method 400 also includes: obtaining (404) a set of symbol soft values ​​based on the set of received modulation symbols and the symbols of the modulation symbol constellation. The method 400 also includes: obtaining (406) a set of decoded bits associated with the set of coded bits based on the set of received modulation symbols and the set of symbol soft values.

[0257] In an example of the present disclosure, the second communication device 300 obtains the set of coded bits by linearly transforming a set of uncoded bits according to a coding matrix G. The coding matrix G is the Kronecker product of two binary matrices G1 and G2, where G1 is a matrix The nth Kronecker power of G2 is a K×K full rank binary matrix. K is the modulation order of the modulation symbol constellation and K>1, and M0 is a multiple of K.

[0258] In other embodiments of the present disclosure, the integer n is given by the following formula:

[0259]

[0260] Figure 5 1 shows a communication system 500 provided by an example of the present disclosure. The wireless communication system 500 includes a first communication device 100 and a second communication device 300, which are configured to operate in the wireless communication system 500. For simplicity, Figure 5 The communication system 500 shown includes only one first communication device 100 and one second communication device 300. However, the wireless communication system 500 may include any number of first communication devices 100 and any number of second communication devices 300 without departing from the scope of the present disclosure.

[0261] In the communication system 500, the first communication device 100 is used as a transmitter and the second communication device 300 is used as a receiver. In other examples, the opposite situation may also be true. Figure 5 As shown, the first communication device 100 sends a group of modulation symbols to the second communication device 300 through the wireless channel 510. When receiving a group of modulation symbols from the first communication device 100, the second communication device 300 obtains a group of symbol soft values, and further obtains a group of decoded bits associated with the group of received modulation symbols and the group of symbol soft values. Figure 5 It should also be noted that the first communication device 100 is shown as a network access node, such as a base station, and the second communication device 300 is shown as a client device, such as a user equipment. However, examples of the present disclosure are not limited thereto.

[0262] For the polar code encoding and decoding scheme described in the examples of the present disclosure, at least two objectives are achieved. The first objective is to provide an efficient method for polar codes to calculate the correct LLR value for each information bit in the decoder of the second communication device 300 using the output signal of the demodulator of the transmitted modulation symbol. The second objective is to ensure that the proposed decoder can be efficiently executed in a recursive manner by using a data flow graph with a butterfly-based decoder structure, so that low decoding complexity can be achieved.

[0263] The concept of "bit segment" used in the present disclosure can be defined as a segment of consecutive bits (e.g., coded bits) in a bit stream. The definition of the soft value of a bit segment can be:

[0264]

[0265] where Pr(a=a0|Y) is the probability that a=a0 given that Y is received. If the bit segment is used to generate the modulation symbol X a , then it has

[0266] In an example of the present disclosure, the second communication device 300 has a universal polar decoder based on symbol soft values, and the following points can be proposed for the second communication device.

[0267] R1: The input of the decoder of the second communication device 300 is the symbol soft value. For a modulation symbol X and a received symbol Y (if the channel is known at the receiver, then it is the received symbol Y after equalization), in the case where the channel is unknown at the receiver, the symbol soft value is equal to |YX H | 2 or YX H or when the channel is known at the receiver, the symbol soft value is related to ρ|YX| 2 Related to, where ρ is the SNR.

[0268] R2: Calculate the LLR of the information bits in the decoder of the codeword generated by the polar encoder by using a set of corresponding modulation symbol soft values ​​for transmitting coded bits, where the linear combination of the coded bits produces the observed information bits in the first communication device 100. Specifically, assume that the i-th information bit b i is a set of coded bits c as defined in equation (6) z , z∈Z i A linear combination of ), b i The LLR can be calculated as

[0269]

[0270] in,

[0271] ·

[0272]

[0273] ·

[0274]

[0275] · is the previous estimated bit,

[0276] M0 is the length of the coded bits,

[0277] K is the modulation order,

[0278] C is the coded bit c i The vector of

[0279] ·C (t) is the tth bit segment in C, which is defined as C (t) =[c (t-1)K+1 , c (t-1)K+1 , ..., c tK ],

[0280] · is based on the coded bit segment C (t) The generated modulation symbols,

[0281] is the symbol soft value, which is Y at the tth received symbol t The modulation symbols sent in the case of The logarithmic probability of

[0282] ·G (：，1：i-1) is a submatrix that includes the first column to the (i-1)th column (including all rows) of G.

[0283] In order to implement the decoder in equation (25) with low complexity, the following novel f function and g function may be recursively applied at the second communication device 300, which are different from the f and g functions used in the above-mentioned conventional decoder.

[0284] R3: b in equation (25) i The LLR can be calculated according to the following novel f and g functions:

[0285] Definition of the f function: The soft value of the sum of two independent bit segments in GF(2) is calculated by the following equation:

[0286]

[0287] in

[0288] Input: soft values ​​of bit segments a and b,

[0289] Output: bit segment The soft value of

[0290] · Defined in equation (24).

[0291] Definition of g function: Update the soft value of a bit segment a according to the soft value of the bit segment a and the soft value of another bit segment b, and the sum of the two bit segments c in GF(2) is known:

[0292]

[0293] Input: bit segment The estimated sum of, and the soft values ​​of bit segments a and b,

[0294] Output: soft value of bit segment a,

[0295] · Defined in equation (24).

[0296] In order to apply the recursive method at the second communication device 300, the first communication device 100 needs to ensure that the recursive structure of the coding matrix of the coded bit segment corresponds to each transmitted modulation symbol. Specifically, the following points can be proposed for the second communication device 300.

[0297] T1: The encoding matrix G is Where M0 is the number of coded bits, and K is the modulation order, G2 is a full rank binary matrix of size K×K.

[0298] T2: If rate matching is applied, the entire bit segment (of length K) should be kept, removed or repeated in the rate matching bits. This is explained in more detail in the following disclosure.

[0299] T3: If interleaving is applied after encoding, the interleaving should be at the bit segment level rather than the bit level, i.e., only the order of each entire bit segment (length K) is changed. This is also explained in more detail in the following disclosure.

[0300] T4: If Then K is a power of 2.

[0301] In the examples of the present disclosure, interleaving can be considered as part of rate matching. In this case, rate matching includes at least two steps: the first step, selecting or removing or adding some bits for repetition; the second step, interleaving. In this case, the above T2 point is designed for the first step, and the T3 point is used for the second step.

[0302] refer to Figure 6 , other examples of the present disclosure are shown in the figure, which will be described and explained herein. The terms, expressions, system designs, etc. described according to 3GPP NR may be used, but are not limited thereto.

[0303] The second communication device 300 includes a demodulation block 320 coupled to a polar decoder block 322. If interleaving and / or rate matching is performed at the first communication device 100, conventional rate matching deinterleaving and / or inverse operations may be applied at the second communication device 300 accordingly, but Figure 6 Not shown in FIG.

[0304] Demodulation block 320: The input of the demodulation block 320 is a set of received modulation symbols that have been sent by the first communication device 100 on the wireless channel 510. In the demodulation block 320, the probability of each symbol is calculated, which is equivalent to the symbol soft value of the symbol. The output of the demodulation block 320 provided to the polar decoder block 322 is the symbol soft value, rather than the bit LLR in the traditional scheme. The symbol soft value corresponds to the modulation symbol X in the constellation and the received modulation symbol Y. It represents or relates to the probability that the modulation symbol X was sent from the first communication device 100.

[0305] If the channel 510 is unknown at the second communication device 300, then the channel 510 can be determined based on XY H or |XY H | 2 To calculate the probability, the symbol soft value can be XY H or |XY H | 2 The reason is that the logarithm of the probability of sending X given a received symbol Y is proportional to |XY H | 2 If XY HIf |XY is used as a symbol soft value, the phase information of the channel 510 is also considered. When calculating the soft value of the sum of two bit segments (corresponding to two symbols), it is assumed that the phase information of the channel 510 of the two symbols is the same, that is, calculated by vector addition. Otherwise, |XY H | 2 , and the phase information of channel 510 is not considered, so there is no restriction on the channel phase, that is, the soft value of the sum is calculated by scalar addition. Or, |XY H | 2 Can be replaced by |XY H |. In addition, if the symbols X and Y are matrices (which means that there are multiple transmitting antennas at the first communication device 100), then the above |XY H | 2 Can be replaced by trace(XY H YX H ).

[0306] In other words, when the characteristics of the channel 510 are unknown to the second communication device 300, each symbol soft value in the set of symbol soft values ​​is obtained according to the inner product between the received modulation symbol in the set of received modulation symbols and the symbol of the modulation symbol constellation.

[0307] The inner product between a received modulation symbol in the set of received modulation symbols and a symbol of the modulation symbol constellation may be calculated according to |YX H | 2 or YX H Obtain, where Y is a received modulation symbol in the set of received modulation symbols, X is a symbol of the modulation symbol constellation, and H is a conjugate transpose operator.

[0308] On the other hand, if the channel 510 is known at the second communication device 300 and equalization is applied before demodulation, the symbol soft value may be ρ|YX| 2 , where ρ is the SNR of channel 510. The reason is that the logarithm of the probability of sending X given that Y is received is proportional to ρ|YX| 2 is proportional to. Optionally, ρ|YX| 2 Can be replaced by

[0309] In other words, when the characteristics of the channel 510 are known to the second communication device 300, each symbol soft value in the set of symbol soft values ​​is obtained based on the difference between the received modulation symbol in the set of received modulation symbols and the symbol of the modulation symbol constellation.

[0310] The difference between the received modulation symbol in the set of received modulation symbols and the symbol of the modulation symbol constellation may be calculated according to ρ|YX| 2 Obtain, where Y is the received modulation symbol in the set of received modulation symbols, X is the symbol of the modulation symbol constellation, and p is a signal-to-noise ratio (SNR) of the received modulation symbol in the set of received modulation symbols.

[0311] In addition, the relative value of the symbol soft value can also be used by the second communication device 300. For example, when X f As a reference (X f is a constellation point), for example, f = 0 or {0, 1, ... 2 K -1}, the relative value can be |XY H | 2 -|X f Y H | 2 , for the unknown channel at the second communication device 300, and may also be ρ|YX| 2 -ρ|YX f | 2 , for a known channel at the second communication device 300.

[0312] Assume that there are 2 K modulation symbols, each received modulation symbol will generate 2 K The corresponding symbol soft value.

[0313] Polarization decoder block 322: The polarization decoder block 322 of the second communication device 300 includes two sub-blocks, namely a decoding block 330 and a demapper block 332, which corresponds to two steps, namely:

[0314] 1. Generate a decoded bit vector by estimating the probability of B segment by segment That is, decoding block 330 .

[0315] 2. From The information bits are selected in the demapper block 332 .

[0316] The second step corresponding to the demapper block 332 of the polar decoder block 322 is the same as in a conventional polar decoder. Therefore, only the first step, and thus the decoding block 330, is focused on.

[0317] Figure 7 An exemplary scheme is shown which may be performed in the decoding block 330 and comprises three steps I-III.

[0318] exist Figure 7 In step I, the second communication device 300 obtains symbol soft values ​​for each modulation symbol, and these symbol soft values ​​are soft values ​​of corresponding coded bit segments.

[0319] exist Figure 7 In step II, the second communication device 300 uses the formula B=CG (i.e. ) calculates the probability of the qth decoded bit segment.

[0320] exist Figure 7 In step III, the second communication device 300 estimates the qth decoded bit segment as the bit segment with the highest probability. If the qth decoded bit segment is the last bit segment to be estimated, then Figure 7 As shown, the decoding is completed and the estimation of B is output. Otherwise, the second communication device 300 will calculate the probability of the next (ie, q=q+1) decoded bit segment, as shown in FIG. Figure 7 This is shown as the feedback line from step III to step II.

[0321] The idea of ​​the first step is to estimate each bit segment of B in turn according to the bit segment level successive cancellation (SC) polar decoding algorithm:

[0322]

[0323] where Y is received and the previously decoded bit segment is hour, The current decoded bit segment is The feasible value of the bit segment should ensure that the frozen bits are 0 and the parity bits are correct.

[0324] According to equation (29), the i-th bit b in B can be calculated by equation (25): i To further calculate equation (25), it can be expressed as shown in equation (11)

[0325]

[0326] Similar to equation (23), the probability in equation (27) It can be calculated as:

[0327]

[0328] in,

[0329] ·X t is the tth modulation symbol,

[0330] · It is based on bit segment C (t) The generated modulation symbols,

[0331] · is the symbol soft value defined in equation (22), where Y t is the tth received symbol,

[0332] ·G (：，1：Kq ) is a submatrix that includes the first column to the Kqth column (including all rows) of G,

[0333] · because (as demonstrated in Section 1.2.2.1) and (Probability conditions).

[0334] The remaining probabilities in equation (27) can be calculated using the same method as equation (20), and finally equation (25) can be obtained. Therefore, the LLR of each bit in B can be obtained based on the symbol soft value according to equation (27) and equation (28). This is very important and different from the traditional LLR-based polar decoder, as shown in equation (11). The SC decoder based on equations (26) to (28) is novel because the LLR of the coded bits is not required / calculated at the second communication device 300. By using equations (26) and equations (27), the above-mentioned problems can be avoided.

[0335] In addition, since list decoding is applied, when determining the qth decoded bit segment by equation (26), the decoder should follow Output to the list in descending order If the list length exceeds the maximum length L after estimating the qth bit segment max , then keep L max Finally, after decoding all the bit segments of B, the most likely estimate is output.

[0336] The computation of equations (26) to (28) can be performed efficiently in a recursive manner using a bit segment level data flow graph having a structure called a butterfly based decoder. In Appendix 3, it is demonstrated that the structure of the butterfly based decoder is similar to the conventional one with The structure of the polar decoder for each coded bit is the same.

[0337] Two functions, namely, f function and g function, can be used in a butterfly-based decoder, such as Figure 8 As shown. The f function is used to calculate the probability of the sum of two independent bit segments in GF(2), that is, the f function: for two independent bit segments a and b, if Then the probability of c satisfies

[0338]

[0339] If the probability in equation (29) is converted into a symbol soft value, the following f function of the symbol soft value can be obtained:

[0340]

[0341] It can be used to calculate equation (28). and

[0342] In other words, in the example of the present disclosure, the f function can be expressed as: obtaining the set of decoded bits includes obtaining the set of decoded bits according to the soft values ​​of the decoded bit segments. The soft value of each decoded bit segment is determined according to the soft value of at least one intermediate bit segment (e.g., c in equation (29) and equation (30)), and the soft value of each intermediate bit segment is determined according to the soft value values ​​of two basic bit segments (e.g., bit segments a and b in equation (29) and equation (30)). The sum of the two basic bit segments in the Galois Field (GF) of two elements is equal to the intermediate bit segment, and the soft values ​​of the two bit segments are obtained according to the set of symbol soft values.

[0343] The g function is used to calculate the probability of the sum of two bit segments in GF(2) when one of the bit segments has been estimated, that is, the g function: For two bit segments a and b, if And c is known to be c=c0, then the probability of a can be updated as

[0344]

[0345] If the probability in equation (31) is converted into a symbol soft value, the following g function of the symbol soft value can be obtained:

[0346]

[0347] It can be used to calculate equation (28) in a butterfly-based decoder. and

[0348] In other words, in the example of the present disclosure, the g function can be expressed as: obtaining the set of decoded bits includes obtaining the set of decoded bits according to the soft values ​​of the decoded bit segments. Determining the soft value of each decoded bit segment according to the soft value of at least one intermediate bit segment (e.g., a in equation (31) and equation (32)), and determining the soft value of each intermediate bit segment (e.g., the soft value on the left side of equation (32)) according to the following items ): the initial soft value of the middle bit segment (e.g., the soft value on the right side of equation (32) ), a basic bit segment (for example, in equation (31) and equation (32), the basic bit segment is the soft value of b), and at least one decoded bit (for example, the decoded bit in c0 of equation (31) and equation (32)). The initial soft value of the intermediate bit segment is obtained based on the set of symbol soft values.

[0349] Refer to Figure 6 On the other hand, the first communication device 100 includes a polarization encoder block 120 coupled to a bit segmentation block 122 , which in turn is coupled to a modulation block 124 .

[0350] Polar encoder block 120: Polar encoder block 120 includes two sub-blocks, namely mapper block 130 and linear transformation block 132. The first step opposite to demapper block 332 in polar decoder block 322 and the corresponding mapper block 130 are the same as in the conventional polar encoder and will not be described in detail. Mapper block 130 obtains N bits and outputs a bit vector B with M0 uncoded bits, which are provided to linear transformation block 132.

[0351] For the second step and the corresponding linear transformation block 132 (which is the inverse transformation of the decoding block 330 in the polar decoder block 322), the bit vector B is linearly transformed using the coding matrix G to obtain a bit vector C with M0 coded bits, i.e., C=BG. The conventional polar coding matrix can be used here Where M0 is the number of coded bits. The bit vector C is provided to the bit segmentation block 122.

[0352] Alternatively, a set of coding matrices can also be used here as an extension of the coding matrix used in the linear transformation block 132. Specifically, assuming that C (q) is the qth bit segment of C, and Defined as

[0353]

[0354] Where K is the modulation order.

[0355] Assumptions Is The bit vector composed of yes According to equation (5) and equation (33), B generates The encoding matrix can be expressed as

[0356]

[0357] It is a block coding matrix. Decoding is based on G blockstructure and is independent of With C (q) The transformation matrix between Therefore, any full-rank binary transformation matrix G2 is feasible for the proposed decoder. Therefore, the encoding matrix can be expanded to

[0358]

[0359] where G2 can be any full-rank binary matrix of size K×K.

[0360] According to equation (35), according to the block coding matrix G with a recursive structure in equation (33) block Generate coded bits, and G2 is the bit segment to C (q) Therefore, if each modulation symbol is based on each bit segment C (q) Generated, the recursive structure can be guaranteed, which requires that the encoded operation should not mix any two bit segments and

[0361] Bit segmentation block 122: Soft values ​​for each coded bit segment are required at the polar decoder. To obtain soft values ​​for the bit segments at the second communication device 300, the same bit segmentation will be used at the first communication device 100, and each bit segment will be used to generate a modulation symbol. Therefore, the bit segmentation is located in the bit segmentation block 122: The qth coded bit segment includes the [K(q-1)+1]th to [Kq]th bits in the vector C obtained from the linear transformation block 132.

[0362] The output of the bit segmentation block 122 is a parallel bit segment having K bits, each bit being provided to the modulation block 124 .

[0363] Modulation block 124: Modulation is the mapping of the bit segments provided by the bit segmentation block 122 to the modulation symbols in the modulation block 124. The difference from conventional modulation is that if The modulation order K here is a power of 2. This is because With C (j) The transformation matrix between It is required that log2 K is an integer, that is, K is a power of 2.

[0364] In implementations of the present disclosure, there may be one or more additional steps at the first communication device 100, and there may also be corresponding steps at the second communication device 300. Some examples are described herein.

[0365] Interleaving: Interleaving is usually to change the order of coded bits to make the transmission more robust. However, the second communication device 300 needs to obtain the soft value of each complete original (before interleaving) coded bit segment. Therefore, interleaving should be at the bit segment level rather than the bit level, that is, interleaving is to change the order of the entire bit segment.

[0366] Therefore, in an example of the present disclosure, the first communication device 100 interleaves the set of coded bits by interleaving complete segments of the set of coded bits; and obtains the set of modulation symbols by modulating the interleaved set of coded bits.

[0367] Rate matching: Rate matching is to change the length of the coded bits to meet the scheduled resources. Assuming that the number of coded bits required is M according to the scheduled resources and the modulation order, it may not be equal to M0. Specifically, if M<M0, M bits can be selected from the M0 coded bits at the transmitter. If M>M0, the repetition of the coded bits can be used to generate M bits at the first communication device 100. The requirement of rate matching is that the complete coded bit segment should be maintained, removed or repeated in the rate matching bit. The reason is that selecting, removing or repeating a half-bit segment will make it impossible for the second communication device 300 to obtain a soft value of the complete bit segment.

[0368] Therefore, in an example of the present disclosure, the first communication device 100 obtains the set of modulation symbols based on obtaining a subset of the set of coded bits. The subset of the set of coded bits includes a complete segment of the set of coded bits. The first communication device 100 also obtains the set of modulation symbols by modulating the subset of the set of coded bits.

[0369] In addition, in an example of the present disclosure, the first communication device 100 obtains the set of modulation symbols based on obtaining a set of extended coded bits. The set of extended coded bits includes the set of coded bits and one or more segments of the set of coded bits. The first communication device 100 also obtains the set of modulation symbols by modulating the set of extended coded bits.

[0370] In the present disclosure, the coded bit segment can be defined and obtained according to the following formula:

[0371]

[0372] where k=1, 2, 3, ... is the index of a bit in the set of coded bits, and i b =1, 2,...K.

[0373] In addition, as described above, there are two main situations at the second communication device 300 that have an impact on the decoding process, namely, the situation when the second communication device 300 knows the characteristics of the channel 510 and the situation when the second communication device 300 does not know the characteristics of the channel 510 that have been discussed previously. Knowing the channel 510 may, for example, involve knowing the SNR, SNIR, phase rotation or other relevant channel characteristics. These channel characteristics can be estimated based on the reception of a reference or pilot signal. However, information about the channel characteristics may also be received from other communication devices, for example, in control signaling. First, the situation when the second communication device 300 does not know the characteristics of the channel 510 will be further described, and the situation when the second communication device 300 knows the characteristics of the channel 510 will be further described thereafter.

[0374] The following aspects are that the characteristics of the channel 510 are unknown to the second communication device 300 .

[0375] Modulation: In this case, multi-dimensional modulation may be used due to the presence of an unknown channel at the second communication device 300. Each multi-dimensional modulation symbol contains a plurality of elements, ie, as a vector x.

[0376] Demodulation: The symbol vector received on the time-frequency (TF) resource for mapping the tth modulation symbol is y t The demodulation block 320 may adopt two options.

[0377] Option 1: The demodulated output is where x f is the fth symbol in the constellation. To reduce complexity, the demodulator can be Some value of x f Output Alternatively, the output can be based on Calculated values, for example, Or relative value. In this embodiment, use As an example.

[0378] Option 2: The demodulated output is where x f is the fth symbol vector in the constellation. To reduce complexity, the demodulator can be Some value of x f Output some The second option can only be applied when the channels of some modulation symbols can be considered to be the same or similar to each other. Therefore, in NR, the base station / network access node may need to send a control signal to the UE to indicate the time and / or frequency resource size that can be considered to use the same beam / precoder or be considered to be the same channel. Otherwise, the resource size can be pre-configured or determined by the receiver.

[0379] Polarimetric decoder: A list polarimetric decoder based on symbol soft values ​​is used to estimate B: The LLR for each bit in B can be estimated by equation (25) or by a recursive polarimetric decoder. For the recursive polarimetric decoder, according to Appendix 3, it can be Figure 8 A butterfly based decoder is shown used to estimate B. In an example of the present disclosure, the butterfly based decoder may be part of the decoder block 330 of the second communication device 300 .

[0380] The butterfly-based decoder obtains 2 of each received modulation symbol from the demodulation block 320. K symbol soft values. Estimating B in a butterfly-based decoder involves Figure 8 shown stages, and each stage includes Operations. The uth operation in the vth stage is expressed as in Operation and The input is the operation The output of . There is no operation at stage 0. For other stages:

[0381] ·if If is an even number, then the operation is the function f,

[0382] ·if If is an odd number, then the operation is the g function.

[0383] The f and g functions have been discussed above, and the simplified operation is as follows:

[0384]

[0385]

[0386] For decision making, due to list decoding, Figure 8 The decision block in needs to output the probabilities of all feasible decodable bit segments, which are represented by path metric (PM) values.

[0387]

[0388] In all After the decision is completed, the output Its bit segment is passed through Generated by multiplying the bit segment with the maximum PM value in the decision operation.

[0389] Alternatively, G1 may be multiplied by the binary index of the input soft value, thus changing the index of the input soft value.

[0390] According to Appendix 3 below, Figure 8 The butterfly-based structure of the recursive decoder with symbol soft-value input proposed in is the same as the conventional SC polar decoder. Since the complexity of the conventional SC polar decoder is O(M0 logM0), the proposed recursive decoder also has a complexity of order O(M0 log M0).

[0391] In this example of the present disclosure, the channel 510 is known at the second communication device 300. The channel 510 may be known, for example, based on a pair of data symbols transmitted from the first communication device 100 to the Figure 5 The detection of the pilot symbol or reference symbol of the second communication device 300 shown is estimated. In this case, equalization is required before demodulation. Therefore, the set of received modulation symbols used in the demodulation block is a set of modulation symbols after equalization. The following aspects are specifically for this situation.

[0392] Modulation: At the first communication device 100, the only difference compared to the embodiment when the channel is unknown is that a modulation symbol can be a complex value or a vector of complex values.

[0393] Demodulation: At the second communication device 300, when the channel is unknown, the demodulation block is different from the example. After equalization, the symbol used to map the tth modulation symbol on the TF resource is y t The demodulated output is ρ|y t -x f | 2 , where x f is the fth symbol in the constellation, and ρ is the SNR at the receiver. To reduce complexity, demodulation can be performed with large ρ|y t -x f | 2 Some value of x f Output ρ|y t -x f | 2 Alternatively, the output can be based on ρ|y t -x f | 2 The calculated value, for example, exp(ρ|y t -x f | 2 ) or relative value. ρ can also be expressed as where σ 2 is the noise power after equalization.

[0394] Polarization decoder: At the second communication device 300, when the channel is unknown, the f function in the polarization decoder is different from the example due to the different demodulated output. The f function is as follows:

[0395]

[0396] Performance Results

[0397] The proposed polar decoder according to the examples of the present disclosure is compared with a conventional polar decoder using link-level estimation of the block error rate (BLER) when multi-dimensional modulation is applied at the receiver and the channel is unknown. The simulation parameters are given in Table 1.

[0398] Table 1: Simulation parameters

[0399]

[0400] Fig. 9 The estimation results are shown in FIG. 1 , where the x-axis shows the SNR (dB) and y The θ axis shows the block error rate (BLER). Fig. 9 It can be seen that compared with the traditional decoder ( Fig. 9 Compared with the dashed line in Fig. 9 The solid line in the figure can achieve a 2.3dB SNR gain.

[0401] Appendix 1

[0402] Proof of equation (19):

[0403] First, define the normalization factor

[0404]

[0405] Substituting equations (18) and (A1) into equation (17), we can obtain

[0406]

[0407]

[0408] where Re{} and Im{} are the real part and the imaginary part respectively. According to equation (12), we have

[0409]

[0410]

[0411] It can be found that Only related to a1 and a2, is only related to a3 and a4. Therefore, for any a1, And for any a3 and a4, same.

[0412] Therefore, (A2) can be simplified to

[0413]

[0414] Substitute (A3) into (A5) and replace {0, 1} with Can get

[0415]

[0416] Then, equation (19) is obtained.

[0417] Appendix 2

[0418] Proof: When When a2 is summed middle

[0419] because The indices of a1 and a2 in the coded bit vector C are z u and z u +1. In addition, due to z u ∈Z i , according to equation (6) Z i The definition of It can be proved as follows

[0420] As in (5), consider Obviously, if k is an odd number and g k，i =1, then g k+1，i = 1. Since every 4 coded bits are modulated into a 16QAM symbol and a1 is the first bit modulated in the 16QAM symbol, the index of a1 in C must be an odd number, i.e. z u is an odd number. and z u is an odd number, we can get

[0421] According to Z in (6) i The definition of a2(i.e. z u +1) belongs to Z i Therefore, in the sum a2 is involved.

[0422] Appendix 3

[0423] Proof: The structure of the butterfly-based decoder for the symbol soft-value based decoder is similar to that with The coded bits are the same as in a conventional polar decoder.

[0424] Proof: Due to and C=BG, we can get

[0425]

[0426] Among them B (q) is the qth bit segment in B, I K×K is the identity matrix. It can be observed that C can be obtained by using the encoding matrix right Encode to get, where yes The qth bit segment of G. block is a block matrix with block size K×K, and the value of each block is I K×K and The product of the factors in . Therefore, for The bit segment in G block The structure and The conventional polar encoder with coded bits Therefore, at the receiver, the The same butterfly-based decoder structure of a conventional polar decoder for coded bits can be used for the proposed symbol soft value based decoder.

[0427] Client devices in the present disclosure include, but are not limited to, smart phones, cellular phones, cordless phones, session initiation protocol (SIP) phones, wireless local loop (WLL) stations, personal digital assistants (PDAs), handheld devices with wireless communication capabilities, computing devices or other processing devices connected to wireless modems, UEs, vehicle-mounted devices, wearable devices, integrated access and backhaul (IAB) nodes (e.g., mobile cars or devices installed in cars), drones, device-to-device (D2D) devices, wireless cameras, mobile stations, access terminals, subscriber units, wireless communication devices, wireless local access network (WLAN) stations, wireless-enabled tablets, laptop embedded devices, universal serial bus (USB) dongles, wireless customer-premises equipment (CPE) and / or chipsets. In the Internet of Things (IOT) scenario, a client device may refer to a machine or another device or chipset that performs communication with another wireless device and / or a network device.

[0428] UE may also be referred to as a mobile phone, cellular phone, tablet computer or laptop computer with wireless capabilities. The UE herein may be, for example, a portable, pocket-storable, handheld, computer-composed or vehicle-mounted mobile device capable of transmitting voice and / or data with another entity (e.g., another receiver or server) via a wireless access network. UE may be a station (STA), i.e., any device including a media access control (MAC) and physical layer (PHY) interface compliant with IEEE 802.11 connected to a wireless medium (WM). UE may also be used to communicate in 3GPP-related Long Term Evolution (LTE) and Advanced LTE, in WiMAX and its evolution, and in fifth-generation wireless technologies such as NR.

[0429] The network access nodes in the present disclosure include but are not limited to: Node B in a wideband code division multiple access (WCDMA) system, an evolutionary Node B (eNB) or evolved NodeB (eNodeB) in an LTE system, a relay node or access point, or a vehicle-mounted device, wearable device or gNB in ​​a fifth generation (5G) network.

[0430] In addition, the network access node in this article can be expressed as a wireless network access node, an access network access node, an access point or a base station, such as a radio base station (RBS), which can be called a transmitter, "gNB", "gNodeB", "eNB", "eNodeB", "NodeB" or "B node" in some networks, depending on the technology and terminology used. Depending on the transmission power and cell size, wireless network access nodes can have different categories, such as macro base stations (eNodeB), home base stations (eNodeB) or micro base stations. A wireless network access node can be a station (STA), which is any device that includes an IEEE 802.11-compliant MAC and PHY interface to a wireless medium. The wireless network access node can also be a base station corresponding to a 5G wireless system.

[0431] In addition, any method according to the examples of the present disclosure may be implemented in a computer program having a coding module, and when a processing device runs the computer program, the processing device is caused to perform the method steps. The computer program is included in a computer-readable medium of a computer program product. The computer-readable medium may include substantially any memory, such as a read-only memory (ROM), a programmable read-only memory (PROM), an erasable PROM (EPROM), a flash memory, an electrically erasable EPROM (EEPROM), or a hard disk drive.

[0432] In addition, the technician recognizes that the examples of the first communication device 100 and the second communication device 300 include necessary communication capabilities in the form of functions, devices, units, elements, etc. for implementing the solution. Other examples of such devices, units, elements and functions are: processors, memories, buffers, control logic, encoders, decoders, rate matchers, de-rate matchers, mapping units, multipliers, decision units, selection units, switches, interleavers, deinterleavers, modulators, demodulators, inputs, outputs, antennas, amplifiers, receiver units, transmitter units, DSPs, maintenance signal distributors (MSD), trellis encoding and modulating (TCM) encoders, TCM decoders, power supply units, power feeders, communication interfaces, communication protocols, etc., which are appropriately arranged together to implement the above technical solutions.

[0433] In particular, the processors of the first communication device 100 and the second communication device 300 may include, for example, a central processing unit (CPU), a processing unit, a processing circuit, a processor, an application specific integrated circuit (ASIC), a microprocessor, or one or more instances of other processing logic that can interpret and execute instructions. The expression "processor" may therefore refer to a processing circuit including a plurality of processing circuits, such as any, some or all of the items listed above. The processing circuit may also perform data processing functions for inputting, outputting, and processing data, including data buffering and device control functions, such as call processing control, user interface control, etc.

[0434] Finally, it should be understood that the present disclosure is not limited to the examples described above, but also relates to and encompasses all embodiments within the scope of the attached independent claims.

Claims

1. A first communication device (100) for a communication system (500), characterized in that: The first communication device (100) is used for: Obtaining a set of uncoded bits including M0 bits, wherein the set of uncoded bits includes information bits; A set of coded bits is obtained by linearly transforming the set of uncoded bits according to a coding matrix G, wherein the coding matrix G is the Kronecker product of two binary matrices G1 and G2, wherein G1 is a matrix is the nth Kronecker power of , and G2 is a K×K full rank binary matrix, where K is the modulation order of the modulation symbol constellation and K>1, and where M0 is a multiple of K; obtaining a set of modulation symbols by modulating the set of coded bits according to the modulation symbol constellation; as well as Sending the set of modulation symbols to a second communication device (300) to obtain, by the second communication device (300), a set of symbol soft values ​​based on the set of received modulation symbols and symbols of the modulation symbol constellation, and obtaining a set of decoded bits associated with the set of coded bits based on the set of received modulation symbols and the set of symbol soft values; Wherein, obtaining the set of decoded bits by the second communication device (300) comprises: The set of decoded bits is obtained based on soft values ​​of decoded bit segments, wherein the soft value of each decoded bit segment is determined based on the soft value of at least one intermediate bit segment, and wherein: determining a soft value for each intermediate bit segment based on soft values ​​of two basic bit segments, wherein a sum of the two basic bit segments in a Galois field of two elements is equal to the intermediate bit segment, and wherein the soft values ​​of the two bit segments are obtained based on the set of symbol soft values; or The soft value of each intermediate bit segment is determined based on the initial soft value of the intermediate bit segment, the soft value of a basic bit segment and at least one decoded bit, and wherein the initial soft value of the intermediate bit segment is obtained based on the set of symbol soft values.

2. The first communication device (100) according to claim 1, characterized in that 3. The first communication device (100) according to claim 1, characterized in that When G2 is a matrix When is raised to the log2Kth Kronecker power, K is a power of 2.

4. The first communication device (100) according to any one of the preceding claims, characterized in that: Obtaining the set of modulation symbols includes: obtaining a subset of the set of coded bits, wherein the subset of the set of coded bits consists of a complete segment of the set of coded bits; and The set of modulation symbols is obtained by modulating a subset of the set of coded bits.

5. The first communication device (100) according to any one of claims 1 to 4, characterized in that: Obtaining the set of modulation symbols includes: obtaining an extended set of coded bits, wherein the extended set of coded bits comprises the set of coded bits and one or more segments of the set of coded bits; and The set of modulation symbols is obtained by modulating the set of spread coded bits.

6. The first communication device (100) according to any one of claims 1 to 4, characterized in that: Obtaining the set of modulation symbols includes: interleaving the set of coded bits by interleaving complete segments of the set of coded bits; and The set of modulation symbols is obtained by modulating the interleaved set of coded bits.

7. The first communication device (100) according to claim 4, characterized in that The coded bit segment is obtained according to the following equation: where k=1,2,3,... is the index of a bit in the set of coded bits, and i b =1,2,…K.

8. A second communication device (300) for a communication system (500), characterized in that: The second communication device (300) is used for: receiving a set of modulation symbols from a first communication device (100), wherein the received set of modulation symbols is associated with a set of coded bits and a modulation symbol constellation; Obtaining a set of symbol soft values ​​based on the set of received modulation symbols and symbols of the modulation symbol constellation; as well as obtaining a set of decoded bits associated with the set of coded bits based on the set of received modulation symbols and the set of symbol soft values; Wherein, obtaining the set of decoded bits comprises: The set of decoded bits is obtained based on soft values ​​of decoded bit segments, wherein the soft value of each decoded bit segment is determined based on the soft value of at least one intermediate bit segment, and wherein: determining a soft value for each intermediate bit segment based on soft values ​​of two basic bit segments, wherein a sum of the two basic bit segments in a Galois field of two elements is equal to the intermediate bit segment, and wherein the soft values ​​of the two bit segments are obtained based on the set of symbol soft values; or The soft value of each intermediate bit segment is determined based on the initial soft value of the intermediate bit segment, the soft value of a basic bit segment and at least one decoded bit, and wherein the initial soft value of the intermediate bit segment is obtained based on the set of symbol soft values.

9. The second communication device (300) according to claim 8, characterized in that: The set of coded bits is obtained by linearly transforming a set of uncoded bits according to a coding matrix G, wherein the coding matrix G is the Kronecker product of two binary matrices G1 and G2, wherein G1 is a matrix The nth Kronecker power of , and G2 is a K×K full rank binary matrix, where K is the modulation order of the modulation symbol constellation and K>1, and where M0 is a multiple of K.

10. The second communication device (300) according to claim 9, characterized in that:

11. The second communication device (300) according to any one of claims 8 to 10, characterized in that: When the characteristics of the channel (510) are unknown to the second communication device (300), each symbol soft value in the set of symbol soft values ​​is obtained based on an inner product between a received modulation symbol in the set of received modulation symbols and a symbol of the modulation symbol constellation.

12. The second communication device (300) according to claim 11, characterized in that: The inner product between a received modulation symbol in the set of received modulation symbols and a symbol of the modulation symbol constellation is obtained according to the following equation: |YX H | 2 or YX H wherein Y is the received modulation symbol of the set of received modulation symbols, X is the symbol of the modulation symbol constellation, and H is the conjugate transpose operator.

13. The second communication device (300) according to any one of claims 8 to 10, characterized in that: When the characteristics of the channel (510) are known to the second communication device (300), each symbol soft value in the set of symbol soft values ​​is obtained based on the difference between a received modulation symbol in the set of received modulation symbols and a symbol of the modulation symbol constellation.

14. The second communication device (300) according to claim 13, characterized in that: The difference between the received modulation symbol in the set of received modulation symbols and the symbol of the modulation symbol constellation is obtained according to the following equation: σ|YX| 2 wherein Y is the received modulation symbol in the set of received modulation symbols, X is the symbol of the modulation symbol constellation, and p is the signal-to-noise ratio of the received modulation symbol in the set of received modulation symbols.

15. A method (200) for a first communication device (100), characterized in that: The method (200) comprises: Obtaining (202) a set of uncoded bits comprising M0 bits, wherein the set of uncoded bits comprises information bits; A set of coded bits is obtained (204) by linearly transforming the set of uncoded bits according to a coding matrix G, wherein the coding matrix G is the Kronecker product of two binary matrices G1 and G2, wherein G1 is a matrix is the nth Kronecker power of , and G2 is a K×K full rank binary matrix, where K is the modulation order of the modulation symbol constellation and K>1, and where M0 is a multiple of K; obtaining (206) a set of modulation symbols by modulating the set of coded bits according to the modulation symbol constellation; and sending (208) the set of modulation symbols to a second communication device (300) to obtain, by the second communication device (300), a set of symbol soft values ​​based on the set of received modulation symbols and symbols of the modulation symbol constellation, and obtaining a set of decoded bits associated with the set of coded bits based on the set of received modulation symbols and the set of symbol soft values; Wherein, obtaining the set of decoded bits by the second communication device (300) comprises: The set of decoded bits is obtained based on soft values ​​of decoded bit segments, wherein the soft value of each decoded bit segment is determined based on the soft value of at least one intermediate bit segment, and wherein: determining a soft value for each intermediate bit segment based on soft values ​​of two basic bit segments, wherein a sum of the two basic bit segments in a Galois field of two elements is equal to the intermediate bit segment, and wherein the soft values ​​of the two bit segments are obtained based on the set of symbol soft values; or The soft value of each intermediate bit segment is determined based on the initial soft value of the intermediate bit segment, the soft value of a basic bit segment and at least one decoded bit, and wherein the initial soft value of the intermediate bit segment is obtained based on the set of symbol soft values.

16. A method (400) for a second communication device (300), characterized in that: The method (400) comprises: receiving (402) a set of modulation symbols from a first communication device (100), wherein the received set of modulation symbols is associated with a set of coded bits and a modulation symbol constellation; obtaining (404) a set of symbol soft values ​​based on the set of received modulation symbols and symbols of the modulation symbol constellation; and obtaining (406) a set of decoded bits associated with the set of coded bits based on the set of received modulation symbols and the set of symbol soft values; Wherein, obtaining the set of decoded bits comprises: The set of decoded bits is obtained based on soft values ​​of decoded bit segments, wherein the soft value of each decoded bit segment is determined based on the soft value of at least one intermediate bit segment, and wherein: determining a soft value for each intermediate bit segment based on soft values ​​of two basic bit segments, wherein a sum of the two basic bit segments in a Galois field of two elements is equal to the intermediate bit segment, and wherein the soft values ​​of the two bit segments are obtained based on the set of symbol soft values; or The soft value of each intermediate bit segment is determined based on the initial soft value of the intermediate bit segment, the soft value of a basic bit segment and at least one decoded bit, and wherein the initial soft value of the intermediate bit segment is obtained based on the set of symbol soft values.

17. A computer readable medium, characterized in that A computer program comprising a program code is included, which executes the method according to claim 15 or 16 when the computer program is run on a computer.

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