Near Optimum Majority-Logic Based Decoding of Low-Density Parity-Check Codes

A reliability-based iterative majority-logic decoding algorithm for regular low-density parity-check (LDPC) codes was recently proposed by Huang et al. In this paper we present an improved version of that algorithm by introducing a different reliability measure for each check-sum of the parity-check matrix, and taking it into account in the computation of the extrinsic information that is used to update the reliability measure of each received bit in each iteration. Some simulations results are given, which show that the new algorithm, while requiring very little additional computational complexity, not only achieves a considerable error performance gain over the standard one, but also, importantly, outperforms the iterative decoding based on belief propagation (IDBP), especially for short and medium block length finite-geometry (FG) LDPC codes.