Non-Asymptotic Capacity Upper Bounds for the Discrete-Time Poisson Channel with Positive Dark Current

TL;DR

This paper presents new, tighter upper bounds on the capacity of the discrete-time Poisson channel with dark current, using convex duality and modified digamma distributions, improving upon previous bounds under various constraints.

Contribution

The authors develop improved, easily computable upper bounds on the Poisson channel capacity that outperform previous results, even with additional peak-power constraints.

Findings

New upper bounds are tighter than previous results.

Bounds are easily computable using convex duality and modified distributions.

Results hold under average-power and arbitrary dark current constraints.

Abstract

We derive improved and easily computable upper bounds on the capacity of the discrete-time Poisson channel under an average-power constraint and an arbitrary constant dark current term. This is accomplished by combining a general convex duality framework with a modified version of the digamma distribution considered in previous work of the authors (Cheraghchi, J. ACM 2019; Cheraghchi, Ribeiro, IEEE Trans. Inf. Theory 2019). For most choices of parameters, our upper bounds improve upon previous results even when an additional peak-power constraint is imposed on the input.