Achievability of the Rate ${1/2}\log(1+\es)$ in the Discrete-Time Poisson Channel

TL;DR

This paper derives a simple lower bound for the capacity of the discrete-time Poisson channel, showing that a specific rate formula is achievable with a gamma-distributed input and a modified decoding scheme.

Contribution

It introduces a new lower bound for the Poisson channel capacity and demonstrates achievability using a gamma distribution and a modified minimum-distance decoder.

Findings

The rate ${1/2} ext{log}(1+ ext{es})$ is achievable in the Poisson channel.

A gamma distribution with parameter 1/2 optimizes the input.

A modified minimum-distance decoder achieves this rate.

Abstract

A simple lower bound to the capacity of the discrete-time Poisson channel with average energy $\es$ is derived. The rate ${1/2}\log(1+\es)$ is shown to be the generalized mutual information of a modified minimum-distance decoder, when the input follows a gamma distribution of parameter 1/2 and mean $\es$.