The Poisson Channel with Side Information

TL;DR

This paper investigates the capacity of a Poisson channel with spurious counts, revealing that noncausal knowledge of spurious count times at the transmitter does not reduce capacity, unlike causal knowledge.

Contribution

It demonstrates that noncausal side information about spurious counts does not affect the channel capacity, providing insights into information theory with side information.

Findings

Noncausal knowledge of spurious counts does not reduce capacity.

Causal knowledge of spurious counts does not increase capacity.

Capacity equals that of the Poisson channel without spurious counts.

Abstract

The continuous-time, peak-limited, infinite-bandwidth Poisson channel with spurious counts is considered. It is shown that if the times at which the spurious counts occur are known noncausally to the transmitter but not to the receiver, then the capacity is equal to that of the Poisson channel with no spurious counts. Knowing the times at which the spurious counts occur only causally at the transmitter does not increase capacity.