Optimal Rate Irregular LDPC Codes in Binary Erasure Channel

TL;DR

This paper presents a method to design optimal rate irregular LDPC codes for the Binary Erasure Channel using a semi-definite programming approach, achieving near-capacity performance without relaxations.

Contribution

It introduces a practical semi-definite programming method for designing capacity-approaching irregular LDPC codes without relaxations or approximations.

Findings

Codes with rates close to capacity are constructed.

Simulation results demonstrate the maximum achievable rate behavior.

Degree distributions are optimized for near-capacity performance.

Abstract

In this paper, we design the optimal rate capacity approaching irregular Low-Density Parity-Check code ensemble over Binary Erasure Channel, by using practical Semi-Definite Programming approach. Our method does not use any relaxation or any approximate solution unlike previous works. Our simulation results include two parts; first, we present some codes and their degree distribution functions that their rates are close to the capacity. Second, the maximum achievable rate behavior of codes in our method is illustrated through some figures.