we present two iterative reliability-based majority-logic decoding algorithms.The proposed algorithm has a lower complexity due to the following two modifications.First
at check nodes
syndrome messages instead of extrinsic messages are calculated and passed back to variable nodes.Second
at the variable nodes
the syndrome messages are directly involved in the voting process.The non-uniform quantization scheme and a new iterative process of reliability-message shifting are also presented in this paper.The received signal achieve a higher quantization resolution near the decision threshold.The shifting direction/step are jointly designed with the quantization parameter and the column weights.Simulation results show that
the presented algorithms can achieve excellent BER performance and fast decoding speed
even with very small quantization levels (3~4 bits resolution).