Common Randomness Generation from Sources with Infinite Polish Alphabet

TL;DR

This paper studies the generation of common randomness between two parties observing i.i.d. samples from sources over infinite Polish alphabets, providing bounds on the capacity with minimal communication.

Contribution

It establishes single-letter bounds on the common randomness capacity for sources with infinite Polish alphabets, extending previous finite-alphabet results.

Findings

Bounds hold with equality except at countably many points

Provides a theoretical framework for CR generation over infinite alphabets

Addresses discontinuity issues in capacity characterization

Abstract

We investigate the problem of common randomness (CR) generation in the basic two-party communication setting in which a sender and a receiver aim to agree on a common random variable with high probability. The terminals observe independent and identically distributed (i.i.d.) samples of sources with an arbitrary distribution defined on a Polish alphabet and are allowed to communicate as little as possible over a noisy, memoryless channel. We establish single-letter upper and lower bounds on the CR capacity for the specified model. The derived bounds hold with equality except for at most countably many points where discontinuity issues might arise.