Symbol-flipping decoding of nonbinary LDPC codes over BI-AWGN channels

This paper analyzes a weighted symbol-flipping (SF) algorithm for nonbinary low density parity-check (NB-LDPC) codes over binary input AWGN (BI-AWGN) channels. The weighted SF algorithm has two main parts: the symbol-flipping function and the new candidate symbol rule. First, it is demonstrated that a rule for choosing the new candidate symbol based on absolute values of observed channel outputs is equivalent to a rule based on Euclidean distances. Then, it is verified that the weighting factor of flipping function has negligible impact on algorithm performance. Motivated by this fact, a SF decoding algorithm is proposed whose flipping function requires only syndrome values and flips symbols in parallel. It is observed that SF decoding outperforms WSF for q-ary codes with large q.