A Scheme for Collective Encoding and Iterative Soft-Decision Decoding of Cyclic Codes of Prime Lengths: Applications to Reed–Solomon, BCH, and Quadratic Residue Codes
IEEE Transactions on Information Theory(2020)
摘要
A novel scheme is presented for encoding and iterative soft-decision decoding of cyclic codes of prime lengths. The encoding of a cyclic code of a prime length is performed on a collection of codewords which are mapped through Galois Fourier transform into a codeword in a low-density parity-check code with a binary parity-check matrix for transmission. Using this matrix, binary iterative soft-decision decoding algorithm is applied to jointly decode a collection of codewords from the cyclic code. The joint-decoding allows for information sharing among the received vectors corresponding to the codewords in the collection during the iterative decoding process. For decoding Reed-Solomon and BCH codes of prime lengths, the proposed decoding scheme not only requires much lower decoding complexity than other soft-decision decoding algorithms for these codes, but also yields superior performance. The proposed decoding scheme can also achieve a joint-decoding gain over the maximum likelihood decoding of individual codewords. The decoding scheme is also applied to quadratic residue codes.
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关键词
BCH code,collective encoding,cyclic code,Galois Fourier transform,joint iterative soft-decision decoding,LDPC code,parity-check matrix,prime code length,quadratic residue code,Reed–Solomon code
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