Spatially-Coupled MacKay-Neal Codes and Hsu-Anastasopoulos Codes

TL;DR

This paper provides empirical evidence that spatially-coupled MacKay-Neal and Hsu-Anastasopoulos codes with bounded weight matrices can achieve capacity on the binary erasure channel, with thresholds near the Shannon limit.

Contribution

It introduces a spatial coupling scheme for MN and HA codes and demonstrates through density evolution that these codes approach capacity with BP decoding.

Findings

Spatially-coupled MN and HA codes achieve thresholds close to the Shannon limit.

Bounded weight matrices do not hinder capacity achievement in spatially-coupled codes.

Density evolution confirms near-capacity performance of the proposed codes.

Abstract

Kudekar et al. recently proved that for transmission over the binary erasure channel (BEC), spatial coupling of LDPC codes increases the BP threshold of the coupled ensemble to the MAP threshold of the underlying LDPC codes. One major drawback of the capacity-achieving spatially-coupled LDPC codes is that one needs to increase the column and row weight of parity-check matrices of the underlying LDPC codes. It is proved, that Hsu-Anastasopoulos (HA) codes and MacKay-Neal (MN) codes achieve the capacity of memoryless binary-input symmetric-output channels under MAP decoding with bounded column and row weight of the parity-check matrices. The HA codes and the MN codes are dual codes each other. The aim of this paper is to present an empirical evidence that spatially-coupled MN (resp. HA) codes with bounded column and row weight achieve the capacity of the BEC. To this end, we introduce a spatial coupling scheme of MN (resp. HA) codes. By density evolution analysis, we will show that the resulting spatially-coupled MN (resp. HA) codes have the BP threshold close to the Shannon limit.