Statistical-Based Density Evolution Algorithm for Nonbinary Low-Density Parity-Check Codes

A statistical-based density evolution algorithm is proposed for nonbinary low-density parity-check (LDPC) codes. It is applicable to both regular and irregular codes under study. The algorithm proposed serves as a tool to analyze the performance limit for iterative decoding of nonbinary LDPC codes, which in turn guides code design. Specifically, it provides approximated evaluations of convergence thresholds for codes given specific degree distributions. It is shown that, for a class of quasi-cyclic (QC) structured extended irregular repeat-accumulate (SeIRA) nonbinary LDPC codes, degree distributions can be optimized via the algorithm proposed. Simulation results exhibit that the nonbinary LDPC codes designed outperform the optimized binary LDPC codes on the AWGN channel with similar code length and rate in terms of bits. Performance gap between the binary and nonbinary LDPC codes is larger in the scenario of higher order modulation.