Asymptotic Analysis of Weight Distribution for Detailedly Represented Irregular LDPC Code Ensembles

摘要

Burshtein and Miller provided an asymptotic estimation of the exponent of the average weight dis-tribution for conventional irregular LDPC ensembles defined by Richardson et al., which are based on bipartite graphs. This estimation is derived by the asymptotic estimation of the exponent of a coefficient in multinomials with non-negative coefficients. In this paper, we employ Burshtein's method to provide an asymptotic estimation of the exponent of the average weight distribution for detailedly represented irregular LDPC ensembles. Moreover, we present numerical examples which show the relation between the exponent of the average weight distribution for conventional and detailedly represented ensemble, and provide an example of code ensemble which has larger typical minimum distance than given conventional ensemble has.