  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.
