Weight Distribution for Non-binary Cluster LDPC Code Ensemble

TL;DR

This paper derives the average weight distributions and exponential growth rates for irregular non-binary cluster LDPC codes, demonstrating the existence of ensembles with positive normalized typical minimum distances.

Contribution

It provides the first derivation of average weight distributions and growth rates for irregular non-binary cluster LDPC codes, highlighting their minimum distance properties.

Findings

Existence of ensembles with positive normalized minimum distances

Derived average weight distributions for irregular non-binary cluster LDPC codes

Established exponential growth rates of weight distributions

Abstract

In this paper, we derive the average weight distributions for the irregular non-binary cluster low-density parity-check (LDPC) code ensembles. Moreover, we give the exponential growth rate of the average weight distribution in the limit of large code length. We show that there exist $(2,d_c)$-regular non-binary cluster LDPC code ensembles whose normalized typical minimum distances are strictly positive.