Degree-degree Correlated Low-density Parity-check Codes and Their Extensions

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.