Comparisons Between Reliability-Based Iterative Min-Sum and Majority-Logic Decoding Algorithms for LDPC Codes

A modified reliability-based iterative majority-logic decoding (MRBI-MLGD) algorithm for two classes of structured LDPC codes is presented based on a recent work by Huang et al. Compared with the original one, the modified algorithm has better performance with slightly increased complexity. Then a reliability-based iterative min-sum decoding (RBI-MSD) algorithm is presented. For the presented RBI-MSD algorithm, reliability-based integer messages are processed and exchanged between variable nodes and check nodes. The main computations include only binary logical operations and integer additions. Different from the conventional min-sum algorithm, the variable nodes pass full messages rather than extrinsic messages to check nodes. This can reduce the memory loads and the computational complexity but with a little (or negligible) performance degradation. Simulation results show that, compared with the (M)RBI-MLGD algorithms, the presented RBI-MSD algorithm achieves better error performance, faster decoding convergence rate and fewer quantization bits with moderate increased computational complexity. Furthermore, the RBI-MSD algorithm is also applicable to decoding random LDPC codes, a distinct difference from the (M)RBI-MLGD algorithms. Finally, we point out that the scaling factors employed in the MRBI-MLGD algorithm and the RBI-MSD algorithm can be optimized using discretized density evolution.