Asymptotic analysis of LDPC codes with depth-2 connectivity distributions over BEC

This paper deals with the randomness of depth-2 connectivity of LDPC ensembles. We study how the randomness of LDPC graphs affect asymptotic performance over binary erasure channel (BEC). First, a new attribute, degree-spectrum distribution, is defined to specify the connectivity of more detailed ensembles than those defined by degree distribution. With this, specified ensembles become subsets of conventional ensemble, and we develop a new density evolution method. Some extreme cases of specified ensembles are given, and we prove that the random specified ensemble is better than other regularized types.