New Channel Coding Lower Bounds for Noisy Permutation Channels

TL;DR

This paper develops tighter bounds for noisy permutation channels using epsilon-packing and Kullback-Leibler divergence, with Gaussian approximations validated through numerical evaluation, advancing understanding in communication and biological storage systems.

Contribution

Introduces new achievability bounds for noisy permutation channels utilizing epsilon-packing and KL divergence, with Gaussian approximations for improved accuracy.

Findings

Bounds are tighter than previous results.

Gaussian approximations closely match numerical evaluations.

Applicable to point-to-point communication and biological storage.

Abstract

Motivated by the application of point-to-point communication networks and biological storage, we investigate new achievability bounds for noisy permutation channels with strictly positive and full-rank square matrices. Our new bounds use $\epsilon$-packing with Kullback-Leibler divergence as a metric to bound the distance between distributions and are tighter than existing bounds. Additionally, Gaussian approximations of achievability bounds are derived, and the numerical evaluation shows the precision of the approximation.