List Message Passing Decoding of Non-binary Low-Density Parity-Check Codes

A decoding algorithm for \(q\)-ary low-density parity-check codes over the \(q\)-ary symmetric channel is introduced. The exchanged messages are lists of symbols from \(\Fq\). A density evolution analysis for maximum list sizes \(1\) and \(2\) is developed. Thresholds for selected regular low-density parity-check code ensembles are computed showing gains with respect to a similar algorithm in the literature. Finite-length simulation results confirm the asymptotic analysis.