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
$\mathbb{F}_{q}$
. 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.