Nonbinary Spatially-Coupled LDPC Codes on the Binary Erasure Channel

TL;DR

This paper investigates the performance of nonbinary spatially-coupled LDPC codes over the binary erasure channel, demonstrating threshold saturation effects similar to binary codes and providing bounds on MAP thresholds.

Contribution

It introduces an efficient method to bound the MAP threshold for nonbinary LDPC codes and shows that threshold saturation occurs for nonbinary SC-LDPC codes.

Findings

MAP performance improves with larger alphabet size

Threshold saturation occurs for nonbinary SC-LDPC codes

BP threshold approaches MAP threshold with large termination length

Abstract

We analyze the asymptotic performance of nonbinary spatially-coupled low-density parity-check (SC-LDPC) codes built on the general linear group, when the transmission takes place over the binary erasure channel. We propose an efficient method to derive an upper bound to the maximum a posteriori probability (MAP) threshold for nonbinary LDPC codes, and observe that the MAP performance of regular LDPC codes improves with the alphabet size. We then consider nonbinary SC-LDPC codes. We show that the same threshold saturation effect experienced by binary SC-LDPC codes occurs for the nonbinary codes, hence we conjecture that the BP threshold for large termination length approaches the MAP threshold of the underlying regular ensemble.