Abstract: A device is configured for encoding an input sequence comprising message bits into a codeword using a polar code. The device is configured to sequentially encode each of a plurality of blocks of the input sequence by applying a sliding window to the input sequence, wherein each block of the input sequence is encoded based on an XOR operation of the block and a previous block of the input sequence to obtain a codeword block of the codeword, and sequentially output each obtained codeword block of the codeword.

Abstract: A method and apparatus for generating a polar code; and also, encoding and decoding data using a polar code. The 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.

Abstract: 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=log2(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.

Abstract: 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.

Abstract: A device is configured for encoding an input sequence comprising message bits into a codeword using a polar code. The device is configured to sequentially encode each of a plurality of blocks of the input sequence by applying a sliding window to the input sequence, wherein each block of the input sequence is encoded based on an XOR operation of the block and a previous block of the input sequence to obtain a codeword block of the codeword, and sequentially output each obtained codeword block of the codeword.

Abstract: A method generates a frozen vector associated with a polar code codeword on the basis of a frozen matrix associated with a product code codeword, the frozen matrix being of size Nc×Nr. The method includes replicating a first matrix row of the frozen matrix Nc times to generate an expanded matrix row; replicating a first matrix column of the frozen matrix Nr times to generate an expanded matrix column; generating the frozen vector on the basis of the expanded matrix row and the expanded matrix column. The disclosure further provides a method for generating a frozen matrix associated with a product code codeword on the basis of a frozen vector associated with a polar code codeword, wherein the product code codeword comprises a matrix of size Nc×Nr, and the frozen vector comprises a vector of size N with a plurality of bits.

Abstract: 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=log2(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.

Abstract: A method generates a frozen vector associated with a polar code codeword on the basis of a frozen matrix associated with a product code codeword, the frozen matrix being of size Nc×Nr. The method includes replicating a first matrix row of the frozen matrix Nc times to generate an expanded matrix row; replicating a first matrix column of the frozen matrix Nr times to generate an expanded matrix column; generating the frozen vector on the basis of the expanded matrix row and the expanded matrix column. The disclosure further provides a method for generating a frozen matrix associated with a product code codeword on the basis of a frozen vector associated with a polar code codeword, wherein the product code codeword comprises a matrix of size Nc×Nr, and the frozen vector comprises a vector of size N with a plurality of bits.