大多數現存研究在分析一個隨機組成的低密度奇偶檢查碼(LDPC code) 的性能時，假設隨機選取的邊的兩端點度數分布是獨立的。在這篇論文中，我們進一步考慮具有度-度相關性的低密度奇偶檢查碼(LDPC code) 的組成。為此，我們提出了兩種方法來構建度-度相關的低密度奇偶檢查碼(LDPC code) 集合，並且推導了這種度-度相關低密度奇偶檢查碼(LDPC code) 在二元擦除通道（BEC）上的機率密度演化方程組。通過進行廣泛的數值實驗，我們展示了度-度相關如何影響低密度奇偶檢查碼(LDPC code) 的性能。我們的數值結果表示，具有負度-度相關的低密度奇偶檢查碼(LDPC code) 可以提高最大可容忍擦除機率。此外，增加負度-度相關性可以促進更好的不等錯誤保護(UEP) 設計。在我們擴展的最後一部分中，我們將度-度相關的低密度奇偶檢查碼(LDPC code) 推廣到多邊緣類型的低密度奇偶檢查碼(multi-edge type LDPC code)。此外，我們利用多邊緣類型的低密度奇偶檢查碼(multi-edge type LDPC code)來構建卷積低密度奇偶檢查碼(convolutional LDPC code)。

Most existing work on analyzing the performance of a random ensemble of low-density parity-check (LDPC) codes assumes that the degree distributions of the two ends of a randomly selected edge are independent. In this paper, we go one step further by considering ensembles of LDPC codes with degree-degree correlations. We propose two methods to construct such an ensemble of degree-degree correlated LDPC codes and derive a system of density evolution equations for these codes over a binary erasure channel (BEC). By conducting extensive numerical experiments, we demonstrate how the degree-degree correlation affects the performance of LDPC codes. Our numerical results suggest that LDPC codes with negative degree-degree correlation could enhance the maximum tolerable erasure probability. Moreover, increasing the negative degree-degree correlation could facilitate better unequal error protection (UEP) design. In the final part of our extension efforts, we extend degree-degree correlated LDPC codes to multi-edge type LDPC codes and leverage these to construct convolutional LDPC codes.

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