Statistical mechanics of LDPC codes on channels with memory

TL;DR

This paper develops an analytical approach to evaluate the performance of LDPC codes on channels with memory, modeled as finite-state Markov channels, revealing their behavior akin to spin-glass systems on small-world lattices.

Contribution

It introduces a novel analytical method for assessing LDPC codes on channels with memory, connecting coding theory with spin-glass models.

Findings

Critical noise levels for binary-symmetric channels identified

Performance thresholds vary with channel symmetry

Method applicable to different channel types

Abstract

We present an analytic method of assessing the typical performance of low-density parity-check codes on finite-state Markov channels. We show that this problem is similar to a spin-glass model on a `small-world' lattice. We apply our methodology to binary-symmetric and binary-asymmetric channels and we provide the critical noise levels for different degrees of channel symmetry.