Multiple-Vote Symbol-Flipping Decoder for Nonbinary LDPC Codes

A multiple-vote symbol-flipping (MV-SF) decoding algorithm for nonbinary low-density parity-check (NB-LDPC) codes is proposed in this paper. Our algorithm improves the generalized bit-flipping algorithm (GBFDA) by considering the multiplicity of the candidates at the check-node output, to perform a more accurate symbol-flipping decision at the variable node update. The MV-SF algorithm greatly improves the frame error rate performance of GBFDA and approaches the performance of the best state-of-the-art decoders [extended min-sum and min-max (Min-Max)] with lower complexity. For a (N = 837, K = 723) NB-LDPC code over GF(32), the decoder derived from the proposed algorithm can reach a throughput higher than 500 Mb/s and a coding gain of 0.44 dB compared with the most efficient GBFDA architecture with only twice the silicon area. Our architecture has 27% efficiency gain compared with the best Min-Max architecture found in the literature, with a performance loss of just 0.21 dB at frame error rate 10^-4.