Optimal Rate and Maximum Erasure Probability LDPC Codes in Binary Erasure Channel

TL;DR

This paper introduces a simple, fast, and accurate method for designing capacity-approaching irregular LDPC codes over the BEC, finding optimal degree distributions without relaxations.

Contribution

It presents a novel, exact method for optimizing LDPC code degree distributions over BEC, outperforming previous approximate approaches.

Findings

Achieves near-capacity code rates with maximum erasure probability

Method works efficiently with polynomial time complexity

Provides degree distributions close to the channel capacity

Abstract

In this paper, we present a novel way for solving the main problem of designing the capacity approaching irregular low-density parity-check (LDPC) code ensemble over binary erasure channel (BEC). The proposed method is much simpler, faster, accurate and practical than other methods. Our method does not use any relaxation or any approximate solution like previous works. Our method works and finds optimal answer for any given check node degree distribution. The proposed method was implemented and it works well in practice with polynomial time complexity. As a result, we represent some degree distributions that their rates are close to the capacity with maximum erasure probability and maximum code rate.