A refined analysis of the Poisson channel in the high-photon-efficiency regime

TL;DR

This paper refines the capacity approximation of the discrete-time Poisson channel in the high-photon-efficiency regime, providing detailed second- and third-order characterizations and demonstrating near-optimality of pulse-position modulation.

Contribution

It offers a refined capacity approximation including second- and third-order terms for the Poisson channel at low photon levels, improving upon previous first-order results.

Findings

Derived exact second-order capacity term

Characterized third-order asymptotic behavior

Pulse-position modulation is nearly optimal in this regime

Abstract

We study the discrete-time Poisson channel under the constraint that its average input power (in photons per channel use) must not exceed some constant E. We consider the wideband, high-photon-efficiency extreme where E approaches zero, and where the channel's "dark current" approaches zero proportionally with E. Improving over a previously obtained first-order capacity approximation, we derive a refined approximation, which includes the exact characterization of the second-order term, as well as an asymptotic characterization of the third-order term with respect to the dark current. We also show that pulse-position modulation is nearly optimal in this regime.