Iterative Decoding of L-step Majority-Logic Decodable Codes Based on Belief Propagation

Iterative decoding of L-step Majority-Logic decodable (LSMLD) codes based on belief propagation (BP) is presented. The orthogonal Tanner graph of LSMLD codes is derived based on the L-step orthogonalized parity checks. The BP decoding algorithm based on the orthogonal Tanner graph (BP-O) is also designed. As the orthogonal Tanner graph is sparse and free of 4- cycles, LSMLD codes perform well under BP-O decoding. Simulation results show that BP-O decoding of LSMLD codes achieves a good soft-decision decoding gain over hard-decision decoding and the performance of LSMLD codes under BP-O decoding is equally well as that of LDPC codes with the same block length and rate under BP decoding.