Minimum Distance Distribution of Irregular Generalized LDPC Code Ensembles

TL;DR

This paper analyzes the minimum distance distribution of irregular generalized LDPC code ensembles, identifying conditions for linear growth of minimum distance and extending prior results to hybrid check node types.

Contribution

It provides a detailed analysis of irregular GLDPC ensembles, including cases with regular and unstructured Tanner graphs, and extends existing results to hybrid check node configurations.

Findings

Ensembles with regular variable nodes have minimum distance growing linearly with high probability.

The work extends previous LDPC and GLDPC results to hybrid check node ensembles.

Identifies conditions under which minimum distance scales with block length.

Abstract

In this paper, the minimum distance distribution of irregular generalized LDPC (GLDPC) code ensembles is investigated. Two classes of GLDPC code ensembles are analyzed; in one case, the Tanner graph is regular from the variable node perspective, and in the other case the Tanner graph is completely unstructured and irregular. In particular, for the former ensemble class we determine exactly which ensembles have minimum distance growing linearly with the block length with probability approaching unity with increasing block length. This work extends previous results concerning LDPC and regular GLDPC codes to the case where a hybrid mixture of check node types is used.