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.

翻译：针对低密度奇偶校验（LDPC）码随机系综的性能分析，现有研究大多假设随机选取边两端节点的度分布相互独立。本文在此基础上进一步考虑具有度-度相关性的LDPC码系综。为此，我们提出两种构造度-度相关LDPC码系综的方法，并推导出此类码在二进制擦除信道（BEC）上的密度演化方程组。通过大量数值实验，我们揭示了度-度相关性对LDPC码性能的影响机制。数值结果表明，具有负度-度相关性的LDPC码能够提升最大可容忍擦除概率。此外，增强负度-度相关性可优化非等差错保护（UEP）设计。