Capacity Bounds for the Poisson-Repeat Channel

TL;DR

This paper derives new upper and lower bounds on the capacity of Poisson-repeat channels, improving understanding of their information transmission limits by analyzing auxiliary channels and side information.

Contribution

It introduces tighter capacity bounds for Poisson-repeat channels using auxiliary channels and side information techniques, advancing theoretical understanding of these channels.

Findings

Upper bounds are significantly tighter for λ ≥ 0.35.

Capacity bounds are improved over previous results.

Method for obtaining lower bounds using auxiliary channel information.

Abstract

We develop bounds on the capacity of Poisson-repeat channels (PRCs) for which each input bit is independently repeated according to a Poisson distribution. The upper bounds are obtained by considering an auxiliary channel where the output lengths corresponding to input blocks of a given length are provided as side information at the receiver. Numerical results show that the resulting upper bounds are significantly tighter than the best known one for a large range of the PRC parameter $\lambda$ (specifically, for $\lambda\ge 0.35$). We also describe a way of obtaining capacity lower bounds using information rates of the auxiliary channel and the entropy rate of the provided side information.