A Fast Convergence Density Evolution Algorithm for Optimal Rate LDPC Codes in BEC

TL;DR

This paper introduces a new fast converging Density Evolution algorithm to efficiently design optimal rate LDPC codes for the binary erasure channel, improving convergence speed and code performance analysis.

Contribution

A novel fast convergent Density Evolution algorithm for designing optimal rate LDPC codes over BEC, enhancing analysis efficiency and code optimization.

Findings

The new DE algorithm converges faster than previous methods.

It successfully designs LDPC codes with optimal rate for given parameters.

Improved analysis speed aids in better code performance evaluation.

Abstract

We derive a new fast convergent Density Evolution algorithm for finding optimal rate Low-Density Parity-Check (LDPC) codes used over the binary erasure channel (BEC). The fast convergence property comes from the modified Density Evolution (DE), a numerical method for analyzing the behavior of iterative decoding convergence of a LDPC code. We have used the method of [16] for designing of a LDPC code with optimal rate. This has been done for a given parity check node degree distribution, erasure probability and specified DE constraint. The fast behavior of DE and found optimal rate with this method compare with the previous DE constraint.