Zero-Error Capacity of Multiple Access Channels via Nonstochastic Information

TL;DR

This paper applies nonstochastic information theory to characterize the zero-error capacity region of multiple access channels with two correlated transmitters, without relying on asymptotic blocklength assumptions, and introduces a new nonstochastic information concept for multi-agent scenarios.

Contribution

It provides a novel nonstochastic information framework for zero-error capacity in multiple access channels with finite blocklengths and extends the theory to three-agent noncooperative problems.

Findings

Characterization of zero-error capacity region for two correlated transmitters.

Introduction of a new nonstochastic information measure for multi-agent systems.

Progress towards understanding information flow in worst-case distributed estimation.

Abstract

The problem of characterising the zero-error capacity region for multiple access channels even in the noiseless case has remained an open problem for over three decades. Motivated by this challenging question, a recently developed theory of nonstochastic information is applied to characterise the zero-error capacity region for the case of two correlated transmitters. Unlike previous contributions, this analysis does not assume that the blocklength is asymptotically large. Finally, a new notion of nonstochastic information is proposed for a noncooperative problem involving three agents. These results are preliminary steps towards understanding information flows in worst-case distributed estimation and control problems.