Typical performance of low-density parity-check codes over general symmetric channels

TL;DR

This paper investigates the typical performance of LDPC codes over general symmetric channels using statistical mechanics, demonstrating that their fundamental properties, including potential Shannon limit saturation, extend beyond specific channels.

Contribution

It provides a theoretical framework for analyzing LDPC codes over general symmetric channels and confirms known properties for these codes in broader contexts.

Findings

LDPC codes can potentially saturate Shannon's limit over general symmetric channels

Theoretical framework applies to various symmetric channels including Gaussian and Laplace

Properties of LDPC codes are preserved across different symmetric noise models

Abstract

Typical performance of low-density parity-check (LDPC) codes over a general binary-input output-symmetric memoryless channel is investigated using methods of statistical mechanics. Theoretical framework for dealing with general symmetric channels is provided, based on which Gallager and MacKay-Neal codes are studied as examples of LDPC codes. It has been shown that the basic properties of these codes known for particular channels, including the property to potentially saturate Shannon's limit, hold for general symmetric channels. The binary-input additive-white-Gaussian-noise channel and the binary-input Laplace channel are considered as specific channel noise models.