One-Cold Poisson Channel: A Simple Continuous-Time Channel with Zero Dispersion

TL;DR

The paper introduces the one-cold Poisson channel (OCPC), a simple continuous-time memoryless channel with zero dispersion and a closed-form error probability, useful for optical communication and information theory.

Contribution

It presents the OCPC as the simplest nontrivial channel with a closed-form error probability and explores its properties, feedback, and coding strategies.

Findings

Capacity is 1 with zero dispersion.

Closed-form formula for optimal error probability.

Applicable to optical communication with tunable filters.

Abstract

We introduce the one-cold Poisson channel (OCPC), where the transmitter chooses one of several frequency bands to attenuate at a time. In particular, the perfect OCPC, where the number of bands is unlimited, is an extremely simple continuous-time memoryless channel. It has a capacity 1, zero channel dispersion, and an information spectrum being the degenerate distribution at 1. It is the only known nontrivial (discrete or continuous-time) memoryless channel with a closed-form formula for its optimal non-asymptotic error probability, making it the simplest channel in this sense. A potential application is optical communication with a tunable band rejection filter. Due to its simplicity, we may use it as a basic currency of information that is infinitely divisible, as an alternative to bits which are not infinitely divisible. OCPC with perfect feedback gives a generalization of prefix codes. We also study non-asymptotic coding and channel simulation results for the general OCPC.