Simplified Symbol Flipping Algorithms for Nonbinary Low-Density Parity-Check Codes

Based on the symbol-flipping algorithm with multiple-votes (MV-SF), this paper presents two simplified algorithms, symbol flipping with truncated and multiple votes (T-MV-SF) and symbol flipping with simplified and multiple votes (S-MV-SF), for nonbinary low-density parity-check(NB-LDPC) codes. Unlike previous symbol-flipping based algorithms (SFBAs), the T(S)-MV-SF uses the truncated voting information in each check and variable node update. The proposed algorithms also approximate the sorting function in each check update. Therefore, their complexity and memory consumption are remarkably reduced as compared with existing SFBAs. Furthermore, we introduce several parameters to compensate the information loss caused by the truncated voting information. After optimizing all the parameters, the proposed algorithms even have better performance than the MV-SF. As compared with the MV-SF, the maximum performance gain among all numerical examples is about 0.11 dB for the S-MV-SF on the (63, 37) code. The T-MV-SF has the largest reduction of the computational complexity on the (255, 175) code, which is about 80% of the complexity of the MV-SF. Moreover, the performance of the T-MV-SF is better than the MV-SF on the (255, 175) code. As a result, the proposed algorithms can effectively balance the error performance and complexity for decoding of NB-LDPCs.