Analytical Solution of Covariance Evolution for Irregular LDPC Codes

TL;DR

This paper provides the first analytical solution to the covariance evolution equations for irregular LDPC codes, enabling more precise estimation of their error performance.

Contribution

It introduces an analytical solution to the covariance evolution system, which was previously unsolved, for irregular LDPC code ensembles.

Findings

Analytical expressions for covariance evolution derived.

Improved accuracy in error probability estimation for irregular LDPC codes.

Facilitates better code design and analysis.

Abstract

A scaling law developed by Amraoui et al. is a powerful technique to estimate the block error probability of finite length low-density parity-check (LDPC) codes. Solving a system of differential equations called covariance evolution is a method to obtain the scaling parameter. However, the covariance evolution has not been analytically solved. In this paper, we present the analytical solution of the covariance evolution for irregular LDPC code ensembles.