Tight Bounds of Minimum Distance Distributions of Irregular LDPC Code Ensembles

Upper bounds of minimum distance distributions of Gallger codes and irregular LDPC codes were derived by Callage and Di, respectively. Di's bounds are tight for irregular LDPC codes which have variable nodes of degree two, however, it is not tight for irregular LDPC codes which do not. In this paper, we derive tight lower and upper bounds of minimum distance distributions of irregular LDPC code ensembles without variable nodes of degree two.