The Stochastic-Calculus Approach to Multi-Receiver Poisson Channels

TL;DR

This paper introduces a stochastic calculus-based framework for analyzing two-receiver Poisson channels, deriving a mutual information formula that facilitates capacity and ordering analyses for various channel configurations.

Contribution

It provides a novel stochastic calculus approach to derive a general mutual information formula for Poisson channels, enabling new capacity and ordering results.

Findings

Derived a general mutual information formula for Poisson channels.

Established conditions for channel ordering that differ from discretized models.

Determined capacity regions for multiple Poisson channel configurations.

Abstract

We study two-receiver Poisson channels using tools derived from stochastic calculus. We obtain a general formula for the mutual information over the Poisson channel that allows for conditioning and the use of auxiliary random variables. We then use this formula to compute necessary and sufficient conditions under which one Poisson channel is less noisy and/or more capable than another, which turn out to be distinct from the conditions under which this ordering holds for the discretized versions of the channels. We also use general formula to determine the capacity region of the more capable Poisson broadcast channel with independent message sets, the more capable Poisson wiretap channel, and the general two-decoder Poisson broadcast channel with degraded message sets.