Poisson Noise Channel with Dark Current: Numerical Computation of the Optimal Input Distribution

TL;DR

This paper develops a numerical method to analyze the capacity and optimal input distribution of a Poisson noise channel with dark current, relevant for optical communication systems, across different operational regimes.

Contribution

It introduces a gradient ascent and Blahut-Arimoto based algorithm to compute the channel capacity and optimal input distribution considering dark current effects.

Findings

Numerical results illustrate the structure of the optimal input distribution.

Capacity varies with amplitude constraint and dark current levels.

The algorithm effectively computes capacity for various channel parameters.

Abstract

This paper considers a discrete time-Poisson noise channel which is used to model pulse-amplitude modulated optical communication with a direct-detection receiver. The goal of this paper is to obtain insights into the capacity and the structure of the capacity-achieving distribution for the channel under the amplitude constraint $\mathsf{A}$ and in the presence of dark current $\lambda$. Using recent theoretical progress on the structure of the capacity-achieving distribution, this paper develops a numerical algorithm, based on the gradient ascent and Blahut-Arimoto algorithms, for computing the capacity and the capacity-achieving distribution. The algorithm is used to perform extensive numerical simulations for various regimes of $\mathsf{A}$ and $\lambda$.