Effective distribution of codewords for Low Density Parity Check Cycle codes in the presence of disorder

TL;DR

This paper analyzes how disorder affects the distribution of codewords in Low Density Parity Check cycle codes by using zeta-function representations and ensemble averaging, revealing an exponential decay in nontrivial codeword likelihood.

Contribution

It introduces a method to quantify the impact of graph disorder on codeword distribution using zeta functions and ensemble averaging, providing insights into code performance under randomness.

Findings

Exponential decay of nontrivial codeword likelihood with increasing graph size

Quantitative estimate of disorder effects on codeword distribution

Application insights for cybersecurity involving randomized codes

Abstract

We review the zeta-function representation of codewords allowed by a parity-check code based on a bipartite graph, and then investigate the effect of disorder on the effective distribution of codewords. The randomness (or disorder) is implemented by sampling the graph from an ensemble of random graphs, and computing the average zeta function of the ensemble. In the limit of arbitrarily large size for the vertex set of the graph, we find an exponential decay of the likelihood for nontrivial codewords corresponding to graph cycles. This result provides a quantitative estimate of the effect of randomization in cybersecurity applications.