Optimal Rate for Irregular LDPC Codes in Binary Erasure Channel

TL;DR

This paper presents a simple, fast, and accurate method for designing capacity-approaching irregular LDPC codes over the BEC, ensuring optimal rate without approximations.

Contribution

A new practical method for constructing optimal variable node degree distributions for irregular LDPC codes over BEC, outperforming previous approximation-based approaches.

Findings

Method is simple, fast, and accurate.

Constructs degree distributions close to channel capacity.

Time complexity is polynomial, suitable for practical use.

Abstract

In this paper, we introduce a new practical and general method for solving the main problem of designing the capacity approaching, optimal rate, irregular low-density parity-check (LDPC) code ensemble over binary erasure channel (BEC). Compared to some new researches, which are based on application of asymptotic analysis tools out of optimization process, the proposed method is much simpler, faster, accurate and practical. Because of not using any relaxation or any approximate solution like previous works, the found answer with this method is optimal. We can construct optimal variable node degree distribution for any given binary erasure rate, {\epsilon}, and any check node degree distribution. The presented method is implemented and works well in practice. The time complexity of this method is of polynomial order. As a result, we obtain some degree distribution which their rates are close to the capacity.