A Novel Coding Scheme for Encoding and Iterative Soft-Decision Decoding of Binary BCH Codes of Prime Lengths

A novel coding scheme is presented for encoding and iterative soft-decision decoding of binary BCH codes of prime lengths. The encoding of such a BCH code is performed on a collection of codewords which are mapped through Galois Fourier transform into a codeword of a nonbinary low-density parity-check (LDPC) code which has a binary parity-check matrix for transmission. Using this matrix, a binary iterative soft-decision decoding algorithm based on belief-propagation is applied to jointly decode a collection of codewords of the BCH code. The joint-decoding allows information sharing among the received vectors corresponding to the codewords in the collection during the iterative decoding process. For decoding a BCH code of prime length, the proposed decoding scheme not only requires low decoding complexity, but also yields superior performance. The proposed decoding scheme can achieve a joint-decoding gain over the maximum likelihood decoding of individual codewords.