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：在分析随机群集低密度奇偶校验（LDPC）码的表现情况时，现有的大多数工作都假定随机选择的一条边的两个端点的度分布是独立的。本文进一步考虑了具有度-度相关性的LDPC码群集。为此，我们提出了两种方法构建一类度-度相关的LDPC码群集，并导出了这种度-度相关LDPC码在二元擦除信道上的密度演化方程组。通过大量的数值实验，我们展示了度-度相关性如何影响LDPC码的表现效果。数值结果表明，具有负度-度相关性的LDPC码可以提高最大可承受擦除概率。此外，增加负度-度相关性可能会导致更好的不平等误差保护设计。