Degree-degree Correlated Low-density Parity-check Codes Over a Binary Erasure Channel

TL;DR

This paper investigates how degree-degree correlations in LDPC codes influence their performance over a BEC, proposing new construction methods and showing that negative correlations can enhance erasure tolerance and error protection.

Contribution

It introduces two methods for constructing degree-degree correlated LDPC ensembles and derives density evolution equations for their analysis over BEC.

Findings

Negative degree-degree correlation improves maximum erasure probability.

Increasing negative correlation enhances unequal error protection.

Correlations significantly impact LDPC code performance.

Abstract

Most existing works on analyzing the performance of a random ensemble of low-density parity-check (LDPC) codes assume that the degree distributions of the two ends of a randomly selected edge are independent. In the paper, we take one step further and consider ensembles of LDPC codes with degree-degree correlations. For this, we propose two methods to construct an ensemble of degree-degree correlated LDPC codes. We then derive a system of density evolution equations for such degree-degree correlated LDPC codes over a binary erasure channel (BEC). By conducting extensive numerical experiments, we show how the degree-degree correlation affects the performance of LDPC codes. Our numerical results show that LDPC codes with negative degree-degree correlation could improve the maximum tolerable erasure probability. Moreover, increasing the negative degree-degree correlation could lead to better unequal error protection (UEP) design.