In this paper

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).