A rate-compatible polar code encoder and encoding method based on polarization spectrum

Abstract

The present invention discloses a code rate compatible polarization code encoder and encoding method based on polarization spectrum. The present invention comprises: a polarization code mother code parameter setting module for determining the code length, code rate and number of punctures of the polarization code mother code; a polarization code mother code construction module for constructing the polarization code mother code using the polarization spectrum, including an initial polarization spectrum module, a polarization spectrum generation module, and a polarization channel reliability estimation module; a generating matrix minimum column weight calculation module for calculating the weight of each column of the generating matrix and determining a partial puncture pattern; a code rate compatible polarization code encoding module for determining the final puncture pattern, including a polarization code final puncture module and an encoding module. The present invention determines the puncture position by using the column weight of the generating matrix, which can reduce the influence of puncture on the performance of the polarization code, estimates the reliability of the polarization sub-channel based on the polarization spectrum, and selects the sub-channel with low reliability for puncturing when the column weight of the generating matrix is ​​the same, thereby effectively reducing the performance loss caused by puncturing.

Description

Technical Field

[0001] The present invention belongs to the technical field of channel coding, and relates to a rate-compatible polar code encoder based on polarization spectrum and a coding method. Background Art

[0002] Polar code is a channel code with a deterministic coding method. It has been strictly proved in theory that it can reach the channel capacity of binary-input discrete memoryless channel (B-DMC) and has been selected as the coding scheme for control channels in 5G enhanced mobile broadband scenarios. Since polar code is based on the idea of ​​channel polarization for channel merging and channel splitting, the code length of polar code is usually fixed to a power of 2. In actual communication systems, it is necessary to design rate-compatible polar code to meet the coding requirements in different application scenarios. In order to design a variable rate polar code, a puncturing operation can be performed.

[0003] Without changing the polar code structure, a quasi-uniform puncturing method can be designed by using random puncturing or bit reversal and rearrangement operations. The quasi-uniform puncturing method evenly distributes the puncturing positions in the channel positions, which can reduce the performance loss caused by puncturing when decoding the polar code. However, when the number of punctures increases, punctures will be made at the sub-channel positions with high channel reliability, resulting in performance loss. Summary of the invention

[0004] An object of the present invention is to provide a rate-compatible polar code encoder and encoding method based on polarization spectrum in view of the problems existing in the prior art.

[0005] The code rate compatible polar code encoder based on polarization spectrum of the present invention comprises: a polarization code mother code parameter setting module, a polarization code mother code construction module, a generator matrix minimum column weight calculation module, and a code rate compatible polar code encoding module based on polarization spectrum.

[0006] The polarization code mother code parameter setting module is used to determine the code length, code rate and number of puncturing of the polarization code mother code.

[0007] The polarization code mother code construction module adopts polarization spectrum to construct polarization code mother code, including: initial polarization spectrum module, polarization spectrum generation module, polarization channel reliability estimation module; wherein:

[0008] The initial polarization spectrum module is used to obtain the polarization spectrum of the initial polarization code short code;

[0009] The polarization spectrum generation module is used to call the initial polarization spectrum of the short polarization code and recursively obtain the polarization spectrum of the long polarization code;

[0010] The polarization channel reliability estimation module is used to simplify the obtained polarization spectrum and estimate the reliability of the polarization sub-channel.

[0011] The generator matrix minimum column weight calculation module is used to calculate the weight of each column of the generator matrix, and determine a part of the puncturing pattern based on the polarization subchannel corresponding to the column weight of the generator matrix.

[0012] The rate-compatible polar code encoding module is used to determine the final puncturing pattern of the polar code mother code, including: a polar code final puncturing module based on the polarization spectrum, and an encoding module; wherein:

[0013] The polar code final puncturing module estimates the reliability of the polarization sub-channel by using the polarization spectrum, assists the polarization code according to the reliability of the polarization sub-channel, determines the final puncturing channel position, and then punctures the polarization code mother code;

[0014] The encoding module is used to encode the polarization code after puncturing.

[0015] Another object of the present invention is to provide a rate-compatible polar code encoding method based on polarization spectrum, which is as follows:

[0016] Step (1) inputs given polarization code parameter information (N', R, S) into a polarization code mother code parameter setting module, determines a code length N', a code rate R, and a number of puncturing S of the polarization code mother code, and stores the parameter information in an information storage unit of the polarization code mother code parameter setting module for subsequent reading.

[0017] Step (2) the polarization code mother code construction module reads the parameter information stored in the polarization code mother code parameter setting module, constructs the polarization code mother code using the polarization spectrum, and estimates the reliability of the polarization subchannel using the polarization spectrum; specifically:

[0018] (2-1) The polarization spectrum of the initial polarization code is input into the initial polarization spectrum module; after the initial polarization code is polarized in the channel, N polarization sub-channels are obtained. The first i-1 bits of the bit vector u corresponding to the i-th polarization sub-channel are fixed to 0, and the remaining positions are 0 or 1. Then the number of bit vectors of the i-th polarization sub-channel is 2 N-i+1 , the number of codeword vectors x is also 2 N-i+1 ; The matrix is ​​generated by the Kronecker product It means that the recursive relationship between the initial polar code with code length N and the polar code generation matrix with code length 2N is: in, Codeword vector x = uF N , the number distribution of the Hamming weights of the polarization subchannel codeword vector is the weight distribution of the polarization subchannel, that is, the weight spectrum i represents the polarization subchannel, d represents the codeword weight; the polarization spectrum does not include the codeword corresponding to the next polarization subchannel, and does not include the all-0 codeword, that is, in, i=1,2,…,N;

[0019] (2-2) The code length of the initial polarization code is set to N=4, and the polarization spectrum of the initial polarization code is obtained by the initial polarization spectrum module; then, the polarization spectrum of the polarization code with a decoding length of N=8 is recursively obtained, and then the polarization spectrum of the polarization code with a decoding length of N=16 is recursively obtained, and the process is repeated repeatedly until N=N′;

[0020] (2-3) The union-Bhattacharyya bound weight (UBW) is used to estimate the reliability of the polarimetric subchannel. The smaller the value of , the higher the reliability of the corresponding polarization subchannel. Z(W) is the Bhattacharyya parameter of the channel.

[0021] The Bhattacharyya parameter Z(W) of a binary erasure channel is the erasure probability ε; the Bhattacharyya parameter of a binary symmetric channel is δ represents the error probability of a binary symmetric channel; Bhattacharyya parameter of a Gaussian channel E s / N0 represents the symbol signal-to-noise ratio.

[0022] Step (3) The minimum column weight calculation module of the generator matrix determines a partial puncturing pattern; for the constructed generator matrix, the weight of each column is first calculated, and then the corresponding polarization sub-channel puncturing is selected in order from small to large according to the column weight.

[0023] Step (4) reads the channel reliability of the polar code mother code construction module and the polarization sub-channel corresponding to the column weight of the minimum column weight calculation module of the generation matrix based on the rate-compatible polar code encoding module of the polarization spectrum; specifically,

[0024] (4-1) The polar code final puncturing module uses the polarization spectrum to assist in determining the final puncturing pattern of the polar code mother code: When the polarization subchannels corresponding to the column weight of the generated matrix obtained in step (3) cannot be punctured completely, the remaining puncturing positions are selected based on the reliability of the polarization subchannel estimated by the UBW value; for columns with the same column weight, the corresponding polarization subchannel with the lowest reliability is selected as the final puncturing position;

[0025] (4-2) The encoding module encodes the punctured polarization code; determines the frozen bit position, including the polarization subchannel position corresponding to the punctured position and the polarization subchannel position with low reliability selected according to the UBW value; the remaining polarization subchannel positions are used as information bit positions, and the LLR values ​​at the punctured positions are set to 0 at the decoding end.

[0026] Furthermore, the recursive solution of the polarization spectrum in (2-2) is as follows:

[0027] (2-2-1) For the polarization spectrum of the N-code length polar code, The polarization spectrum of the second half of the polarization subchannel of the 2N-code-long polar code is obtained, where k is a positive integer, i=1, 2, ..., N, l=i+N, and p is the codeword weight of the 2N-code-long polar code;

[0028] (2-2-2) Using the formula The weight spectrum of the second half of the 2N-code length polar code is obtained, where Then, according to the MacWilliams identity, the weight spectrum of the dual code of the second half polarization subchannel is calculated, that is, the weight spectrum of the first half polarization subchannel;

[0029] (2-2-3) The polarization spectrum of the first half of the polarization subchannel is calculated using the weight spectrum of the first half of the polarization subchannel, thereby obtaining the polarization spectrum of the 2N code length polarization code;

[0030] (2-2-4) The obtained polarization spectrum is used as the polarization spectrum of the initial polarization spectrum module, and steps (2-2-1) to (2-2-3) are repeated to obtain a polarization spectrum with a longer code length, until a polarization spectrum with the same length as the polarization code mother code is calculated.

[0031] Furthermore, in step (3), the partial puncturing pattern means that when the polarization subchannels corresponding to the column weight cannot be fully punctured, the puncturing is terminated in the generator matrix minimum column weight calculation module to obtain the partial puncturing pattern.

[0032] Compared with the prior art, the present invention has the following beneficial effects: by using the column weight of the generating matrix to determine the puncturing position, the influence of puncturing on the performance of the polarization code can be reduced; the reliability of the polarization sub-channel is estimated based on the polarization spectrum; when the column weight of the generating matrix is ​​the same, the sub-channel with low reliability is selected for puncturing, which effectively reduces the performance loss caused by puncturing on the polarization sub-channel with higher channel reliability. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 A schematic diagram of an encoder of the present invention;

[0034] Figure 2 It is a schematic diagram of punching holes in the generator matrix of the present invention. DETAILED DESCRIPTION

[0035] The technical solution of the present invention is further specifically described below through embodiments and in conjunction with the accompanying drawings.

[0036] like Figure 1 A rate-compatible polarization code encoder based on polarization spectrum includes: a polarization code mother code parameter setting module, a polarization code mother code construction module, a generation matrix minimum column weight calculation module, and a rate-compatible polarization code encoding module based on polarization spectrum.

[0037] The polarization code mother code parameter setting module is used to determine the code length, code rate and number of puncturing of the polarization code mother code.

[0038] The polarization code mother code construction module adopts the polarization spectrum to construct the polarization code mother code, including: an initial polarization spectrum module, a polarization spectrum generation module, and a polarization channel reliability estimation module; wherein:

[0039] An initial polarization spectrum module, used to obtain the polarization spectrum of the initial polarization code short code;

[0040] A polarization spectrum generation module is used to call the initial polarization spectrum of the short polarization code and recursively obtain the polarization spectrum of the long polarization code;

[0041] The polarization channel reliability estimation module is used to simplify the obtained polarization spectrum and estimate the reliability of the polarization sub-channel.

[0042] The generator matrix minimum column weight calculation module is used to calculate the weight of each column of the generator matrix and determine a partial puncturing pattern based on the polarization subchannel corresponding to the column weight of the generator matrix.

[0043] The code rate compatible polar code encoding module is used to determine the final puncturing pattern of the polar code mother code, including: a polar code final puncturing module based on the polarization spectrum and an encoding module; wherein:

[0044] The polar code final puncturing module estimates the reliability of the polarization sub-channel using the polarization spectrum, assists the polarization code according to the reliability of the polarization sub-channel, determines the final puncturing channel position, and then punctures the polarization code mother code;

[0045] The encoding module is used to encode the polarization code after puncturing.

[0046] The encoding method using the above polarization spectrum-based rate-compatible polar code encoder is as follows:

[0047] Step (1) inputs given polarization code parameter information (N', R, S) into a polarization code mother code parameter setting module, determines a code length N', a code rate R, and a number of puncturing S of the polarization code mother code, and stores the parameter information in an information storage unit of the polarization code mother code parameter setting module for subsequent reading.

[0048] Step (2) The polarization code mother code construction module reads the parameter information stored in the polarization code mother code parameter setting module, constructs the polarization code mother code using the polarization spectrum, and estimates the reliability of the polarization sub-channel using the polarization spectrum. Specifically:

[0049] (2-1) The polarization spectrum of the initial polarization code is input into the initial polarization spectrum module; after the initial polarization code is polarized in the channel, N polarization sub-channels are obtained. The first i-1 bits of the bit vector u corresponding to the i-th polarization sub-channel are fixed to 0, and the remaining positions are 0 or 1. Then the number of bit vectors of the i-th polarization sub-channel is 2N-i+1 , the number of codeword vectors x is also 2 N-i+1 ; The matrix is ​​generated by the Kronecker product It means that the recursive relationship between the initial polar code with code length N and the polar code generation matrix with code length 2N is: in, Codeword vector x = uF N , the number distribution of the Hamming weights of the polarization subchannel codeword vector is the weight distribution of the polarization subchannel, that is, the weight spectrum i represents the polarization subchannel, d represents the codeword weight; the polarization spectrum does not include the codeword corresponding to the next polarization subchannel, and does not include the all-0 codeword, that is, in, i=1,2,…,N;

[0050] (2-2) Set the code length of the initial polarization code N=4, and obtain the polarization spectrum of the initial polarization code by the initial polarization spectrum module; then recursively calculate the polarization spectrum of the polarization code with a decoding length of N=8, and then recursively calculate the polarization spectrum of the polarization code with a decoding length of N=16, and repeat this cycle until N=N′. The recursive solution of the polarization spectrum is as follows:

[0051] (2-2-1) For the polarization spectrum of the N-code length polar code, The polarization spectrum of the second half of the polarization subchannel of the 2N-code-long polar code is obtained, where k is a positive integer, i=1, 2, ..., N, l=i+N, and p is the codeword weight of the 2N-code-long polar code;

[0052] (2-2-2) Using the formula The weight spectrum of the second half of the 2N-code length polar code is obtained, where Then, according to the MacWilliams identity, the weight spectrum of the dual code of the second half polarization subchannel is calculated, that is, the weight spectrum of the first half polarization subchannel;

[0053] (2-2-3) The polarization spectrum of the first half of the polarization subchannel is calculated using the weight spectrum of the first half of the polarization subchannel, thereby obtaining the polarization spectrum of the 2N code length polarization code;

[0054] (2-2-4) The obtained polarization spectrum is used as the polarization spectrum of the initial polarization spectrum module, and steps (2-2-1) to (2-2-3) are repeated to obtain a polarization spectrum with a longer code length, until a polarization spectrum with the same length as the polarization code mother code is calculated.

[0055] (2-3) Using the consistent Bhattacharyya parameter bound weight UBW to estimate the reliability of the polarimetric subchannel;

[0056] The smaller the value of , the higher the reliability of the corresponding polarization subchannel. Z(W) is the Bhattacharyya parameter of the channel.

[0057] The Bhattacharyya parameter Z(W) of a binary erasure channel is the erasure probability ε; the Bhattacharyya parameter of a binary symmetric channel is δ represents the error probability of a binary symmetric channel; Bhattacharyya parameter of a Gaussian channel E s / N0 represents the symbol signal-to-noise ratio.

[0058] Step (3) The minimum column weight calculation module of the generated matrix determines a partial puncturing pattern. The partial puncturing pattern means that when the polarization subchannel corresponding to the column weight cannot be fully punctured, the minimum column weight calculation module of the generated matrix ends puncturing to obtain a partial puncturing pattern. When encoding the input bits, the column weight of the generated matrix reflects the degree of influence on the input bits. The larger the column weight, the greater the influence on the input bits during encoding. Polar code generation matrix F N is a lower triangular matrix. For the constructed generator matrix, first calculate the weight of each column, and then select the corresponding polarization sub-channel puncturing in order from small to large according to the column weight. Figure 2 As shown, the polarization subchannel corresponding to the column with a column weight of 1 is first selected for puncturing, and the corresponding row is deleted.

[0059] Step (4) reads the channel reliability of the polar code mother code construction module and the polarization sub-channel corresponding to the column weight of the minimum column weight calculation module of the generation matrix based on the rate-compatible polar code encoding module of the polarization spectrum; specifically,

[0060] (4-1) The polar code final puncturing module uses the polarization spectrum to assist in determining the final puncturing pattern of the polar code mother code: When the polarization subchannels corresponding to the column weight of the generated matrix obtained in step (3) cannot be punctured completely, the remaining puncturing positions are selected based on the reliability of the polarization subchannel estimated by the UBW value; for columns with the same column weight, the corresponding polarization subchannel with the lowest reliability is selected as the final puncturing position;

[0061] (4-2) The encoding module encodes the punctured polarization code; determines the frozen bit position, including the polarization subchannel position corresponding to the punctured position and the polarization subchannel position with low reliability selected according to the UBW value; the remaining polarization subchannel positions are used as information bit positions, and the LLR values ​​at the punctured positions are set to 0 at the decoding end.

Claims

1. A rate-compatible polar code encoder based on polarization spectrum, characterized in that: include: Polarization code mother code parameter setting module, polarization code mother code construction module, generation matrix minimum column weight calculation module, polarization spectrum-based code rate compatible polarization code encoding module; The polarization code mother code parameter setting module is used to determine the code length, code rate and number of puncturing of the polarization code mother code; The polarization code mother code construction module adopts polarization spectrum to construct polarization code mother code, including: initial polarization spectrum module, polarization spectrum generation module, polarization channel reliability estimation module; wherein: The initial polarization spectrum module is used to obtain the polarization spectrum of the initial polarization code short code; The polarization spectrum generation module is used to call the initial polarization spectrum of the short polarization code and recursively obtain the polarization spectrum of the long polarization code; The polarization channel reliability estimation module is used to simplify the obtained polarization spectrum and estimate the reliability of the polarization sub-channel; The generator matrix minimum column weight calculation module is used to calculate the weight of each column of the generator matrix, and determine a partial puncturing pattern based on the polarization subchannel corresponding to the column weight of the generator matrix; The rate-compatible polar code encoding module is used to determine the final puncturing pattern of the polar code mother code, including: a polar code final puncturing module based on the polarization spectrum, and an encoding module; wherein: The polar code final puncturing module estimates the reliability of the polarization sub-channel by using the polarization spectrum, assists the polarization code according to the reliability of the polarization sub-channel, determines the final puncturing channel position, and then punctures the polarization code mother code; The encoding module is used to encode the polarization code after puncturing.

2. The encoding method of the rate-compatible polar code encoder based on polarization spectrum according to claim 1, characterized in that: Step (1) inputting given polarization code parameter information (N', R, S) into a polarization code mother code parameter setting module, determining a code length N', a code rate R, and a number of puncturing S of the polarization code mother code, and storing the parameter information in an information storage unit of the polarization code mother code parameter setting module for subsequent reading; Step (2) the polarization code mother code construction module reads the parameter information stored in the polarization code mother code parameter setting module, constructs the polarization code mother code using the polarization spectrum, and estimates the reliability of the polarization subchannel using the polarization spectrum; specifically: (2-1) The polarization spectrum of the initial polarization code is input into the initial polarization spectrum module; after the initial polarization code is polarized in the channel, N polarization sub-channels are obtained. The first i-1 bits of the bit vector u corresponding to the i-th polarization sub-channel are fixed to 0, and the remaining positions are 0 or 1. Then the number of bit vectors of the i-th polarization sub-channel is 2 N-i+1 , the number of codeword vectors x is also 2 N-i+1 ; The matrix is ​​generated by the Kronecker product It means that the recursive relationship between the initial polar code with code length N and the polar code generation matrix with code length 2N is: in, Codeword vector x = uF N , the number distribution of the Hamming weights of the polarization subchannel codeword vector is the weight distribution of the polarization subchannel, that is, the weight spectrum i represents the polarization subchannel, d represents the codeword weight; the polarization spectrum does not include the codeword corresponding to the next polarization subchannel, and does not include the all-0 codeword, that is, in, (2-2) The code length of the initial polarization code is set to N=4, and the polarization spectrum of the initial polarization code is obtained by the initial polarization spectrum module; then, the polarization spectrum of the polarization code with a decoding length of N=8 is recursively obtained, and then the polarization spectrum of the polarization code with a decoding length of N=16 is recursively obtained, and the process is repeated repeatedly until N=N′; (2-3) Using the consistent Bhattacharyya parameter bound weight UBW to estimate the reliability of the polarimetric subchannel; The smaller the value of is, the higher the reliability of the corresponding polarimetric subchannel is. Z(W) is the Bhattacharyya parameter of the channel. The Bhattacharyya parameter Z(W) of a binary erasure channel is the erasure probability ε; the Bhattacharyya parameter of a binary symmetric channel is δ represents the error probability of a binary symmetric channel; Bhattacharyya parameter of a Gaussian channel E s / N0 represents the symbol signal-to-noise ratio; Step (3) The minimum column weight calculation module of the generator matrix determines a partial puncturing pattern; for the constructed generator matrix, the weight of each column is first calculated, and then the corresponding polarization subchannel puncturing is selected in order from small to large according to the column weight; Step (4) reads the channel reliability of the polar code mother code construction module and the polarization sub-channel corresponding to the column weight of the minimum column weight calculation module of the generation matrix based on the rate-compatible polar code encoding module of the polarization spectrum; specifically, (4-1) The polar code final puncturing module uses the polarization spectrum to assist in determining the final puncturing pattern of the polar code mother code: When the polarization subchannels corresponding to the column weight of the generated matrix obtained in step (3) cannot be punctured completely, the remaining puncturing positions are selected based on the reliability of the polarization subchannel estimated by the UBW value; for columns with the same column weight, the corresponding polarization subchannel with the lowest reliability is selected as the final puncturing position; (4-2) The encoding module encodes the punctured polarization code; determines the frozen bit position, including the polarization subchannel position corresponding to the punctured position and the polarization subchannel position with low reliability selected according to the UBW value; the remaining polarization subchannel positions are used as information bit positions, and the LLR values ​​at the punctured positions are set to 0 at the decoding end.

3. The encoding method according to claim 2, characterized in that: The recursive solution of the polarization spectrum in (2-2) is as follows: (2-2-1) For the polarization spectrum of the N-code length polar code, The polarization spectrum of the second half of the polarization subchannel of the 2N-code-long polar code is obtained, where k is a positive integer, i=1, 2, ..., N, l=i+N, and p is the codeword weight of the 2N-code-long polar code; (2-2-2) Using the formula The weight spectrum of the second half of the 2N-code length polar code is obtained, where Then, according to the MacWilliams identity, the weight spectrum of the dual code of the second half polarization subchannel is calculated, that is, the weight spectrum of the first half polarization subchannel; (2-2-3) The polarization spectrum of the first half of the polarization subchannel is calculated using the weight spectrum of the first half of the polarization subchannel, thereby obtaining the polarization spectrum of the 2N code length polarization code; (2-2-4) The obtained polarization spectrum is used as the polarization spectrum of the initial polarization spectrum module, and steps (2-2-1) to (2-2-3) are repeated to obtain a polarization spectrum with a longer code length, until a polarization spectrum with the same length as the polarization code mother code is calculated.

4. The encoding method according to claim 2, characterized in that: In step (3), the partial puncturing pattern means that when the polarization sub-channels corresponding to the column weight cannot be fully punctured, the puncturing is terminated in the generator matrix minimum column weight calculation module to obtain the partial puncturing pattern.

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