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

2026-01-14

AI Summary

This work aims to construct the simplest continuous-time memoryless channel model that exhibits zero dispersion and admits analytically tractable non-asymptotic performance. To this end, the authors introduce the On-Off Cooled Poisson Channel (OCPC), in which the transmitter selects one among multiple frequency bands to attenuate. Leveraging information-spectrum methods, non-asymptotic coding analysis, and communication modeling with feedback, they prove that the OCPC achieves a capacity of one, zero dispersion, and a degenerate information spectrum. Moreover, they derive—for the first time—a closed-form expression for the non-asymptotically optimal error probability. This model constitutes the first nontrivial memoryless channel with closed-form non-asymptotic performance, providing an infinitely refinable elementary unit for information measures and extending the theory of feedback-assisted prefix-free codes.

Technology Category

• Machine Learning: Information Theory
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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.

Problem

• one-cold Poisson channel
• zero dispersion
• continuous-time channel
• non-asymptotic coding
• channel capacity

Innovation

• one-cold Poisson channel
• zero dispersion
• non-asymptotic error probability
• continuous-time memoryless channel
• infinitely divisible information