Detailed evolution of degree distributions in residual graphs with joint degree distributions

Abstract

Luby et al. derived evolution of degree distributions in residual graphs for irregular LDPC code ensembles. Evolution of degree distributions in residual graphs is an important characteristic which is used for finite-length analysis of the expected block and bit error probabilities over the binary erasure channel. In this paper, we derive detailed evolution of degree distributions in residual graphs for irregular LDPC code ensembles with joint degree distributions.