Error-Correction Performance of Regular Ring-Linear LDPC Codes over Lee Channels

• DOI: 10.48550/arxiv.2312.14674
• Publication Date: 2023-01-01
• Authors: Jessica Bariffi; Hannes Bartz; Gianluigi Liva; Joachim Rosenthal
• Keywords: Belief Propagation

Most low-density parity-check (LDPC) code constructions are considered over finite fields. In this work, we focus on regular LDPC codes integer residue rings and analyze their performance with respect to the Lee metric. Their error-correction is studied two channel models, in The first model a discrete memoryless channel, whereas second an error vector drawn uniformly at random from all vectors of fixed weight. It known that laws coincide asymptotic regime, meaning marginal distributions match. For both derive upper bounds block probability terms coding union bound as well sphere packing make use distribution channels. We estimate decoding ensembles channels using determining expected weight ring. By means density evolution finite-length simulations, selected under belief propagation low-complexity symbol message passing algorithm compare performances.