Sum-product decoding of BCH codes

This paper proposes methods to improve soft-input and soft-output decoding performance of BCH codes by sum-product algorithm (SPA). A method to remove cycles of length four (RmFC) in the Tanner graph has been proposed. However, the RmFC can not realize good decoding performance for BCH codes which have more than one error correcting capability. To overcome this problem, this paper proposes two methods. One is to use a parity check matrix of the echelon canonical form as the starting check matrix of RmFC. The other is to use a parity check matrix that is concatenation (ConC) of multiple parity check matrices. For BCH(31,11,11) code, SPA with ConC realizes E_b/N₀ 3.8 dB better than the original SPA, and 3.1 dB better than the SPA with only RmFC at bit error rate 10^-5. The decoding complexity is 0.08 times of that of Chase-2 decoding.