Analysis of Binary and Ternary Message Passing Decoding for Generalized LDPC Codes
Emna Ben Yacoub, Gianluigi Liva · 2021
Binary and a ternary message passing decoding algorithms for generalized low-density parity-check codes are defined and analyzed. In all algorithms, the variable nodes exploit soft channel information. However, the exchanged messages between variable and check nodes are binary or ternary. Two types of local decoders are assumed at the check nodes, namely an optimum a-posteriori probability soft-input soft-output decoder, and a more practical bounded distance decoder. A density evolution analysis for irregular code ensembles is developed for all the introduced algorithms, which allows obtaining the scaling coefficients needed for the variable node operation. Finite-length simulation results confirm the validity of the asymptotic analysis.