Method and device for polar code encoding and decoding
The disclosure relates to generating a polar code and also to encoding and decoding data using a polar code. A method of generating a polar code includes obtaining a first matrix as an m-fold Kronecker product of a 2×2 binary lower triangular matrix where m=log 2(M/2), M<N, and N is the length of a polar code to be generated. A second matrix may be obtained, where the inverse of the second matrix is a lower triangular band matrix. A transformation matrix may be generated for the polar code by calculating a Kronecker product of the second matrix with the first matrix. An information set I identifying reliable bit channels for the polar code may be determined. A polar codeword of length N may be obtained using the polar code that is decodable by iteratively applying a sliding decoding window of length M to the polar codeword.
1. An encoding method performed by an encoder, the method comprising:
obtaining a first matrix as an m-fold Kronecker product of a 2×2 binary lower triangular matrix, where m=log 2(M/2), M<N, and N is the length of a polar code to be generated;
obtaining a second matrix of dimension 2S×2S, where S=N/M and an inverse of the second matrix is a lower triangular band matrix;
generating a transformation matrix for the polar code by calculating a Kronecker product of the second matrix with the first matrix;
determining an information set I identifying reliable bit channels for the polar code;
obtaining a polar codeword of length N using the polar code; and
transmitting a transmission signal comprising the polar codeword to a receiving device.
2. The method according to claim 1 , wherein the polar codeword is decodable by iteratively applying a sliding decoding window of length M to the polar codeword.
3. The method according to claim 2 , where a successive decoding process using a polar code of size M/2 is applied to the windowed polar codeword during each iteration of the successive decoding process.
4. The method according to claim 1 , wherein determining the information set comprises:
estimating bit-error probability and/or log-likelihood ratios of first and second kernels having i bit channels, corresponding to the first and second matrices.
5. The method according to claim 1 , wherein the second matrix is a full binary lower triangular matrix.
6. The method according to claim 1 , wherein the step of obtaining the polar codeword of length N using the polar code comprises:
inserting K message bits into an input vector u according to the reliable bit channels identified by the information set I; and
generating a polar codeword using the input vector u by calculating the product of the input vector and the transformation matrix.
7. The method according to claim 1 , wherein the step of obtaining the polar codeword of length N using the polar code comprises:
inserting K message bits into an input vector u according to the reliable bit channels identified by the information set I of the polar code of length N;
dividing the input vector u into 2S sub-input vectors of size M/2;
encoding the sub-input vectors using the first matrix; and
iteratively adding respective bits of one or more encoded sub-input vectors to an immediately preceding encoded sub-input vector.
8. An encoding apparatus, comprising one or more processors and a memory storing instructions, wherein when the one or more processors execute the instructions in the memory, the one or more processors are configured to:
obtain a first matrix as an m-fold Kronecker product of a 2×2 binary lower triangular matrix, where m log 2(M/2), M<N, and N is the length of a polar code to be generated;
obtain a second matrix of dimension 2S×2S, where S=N/M and an inverse of the second matrix is a lower triangular band matrix;
generate a transformation matrix for the polar code by calculating a Kronecker product of the second matrix with the first matrix;
determine an information set I identifying reliable bit channels for the polar code;
obtain a polar codeword of length N using the polar code; and
transmit a transmission signal comprising the polar codeword to a receiving device.
9. The apparatus according to claim 8 , wherein the polar codeword is decodable by iteratively applying a sliding decoding window of length M to the polar codeword.
10. The apparatus according to claim 9 , wherein a successive decoding process using a polar code of size M/2 is applicable to the windowed polar codeword during each iteration of the successive decoding process.
11. The apparatus according to claim 8 , wherein the one or more processors are further configured to:
estimate bit-error probability and/or log-likelihood ratios of first and second kernels having i bit channels, corresponding to the first and second matrices.
12. The apparatus according to claim 8 , wherein the second matrix is a full binary lower triangular matrix.
13. The apparatus according to claim 8 , wherein the one or more processors are further configured to:
insert K message bits into an input vector u according to the reliable bit channels identified by the information set I; and
generate a polar codeword using the input vector u by calculating the product of the input vector and the transformation matrix.
14. The apparatus according to claim 8 , wherein the one or more processors are further configured to:
insert K message bits into an input vector u according to the reliable bit channels identified by the information set I of the polar code of length N;
divide the input vector u into 2S sub-input vectors of size M/2;
encode the sub-input vectors using the first matrix; and
iteratively add respective bits of one or more encoded sub-input vectors to an immediately preceding encoded sub-input vector.