A General Formula for Uniform Common Randomness Capacity

TL;DR

This paper extends the uniform common randomness capacity formula to include arbitrary single-user channels, broadening the understanding of common randomness generation in communication systems.

Contribution

It generalizes the existing formula from noiseless channels to arbitrary channels using Verdú and Han's capacity results.

Findings

Unified capacity formula for arbitrary channels

Extension of previous two-source models

Application of Verdú and Han's capacity theorem

Abstract

We generalize the uniform common randomness capacity formula, initially established by Ahslwede and Csisz\'ar for a two-source model for common randomness generation from independent and identically distributed (i.i.d.) discrete sources with unidirectional communication over rate-limited discrete noiseless channels to the case when the one-way communication is over arbitrary single-user channels. In our proof, we will make use of the transmission capacity formula established by Verd\'u and Han for arbitrary point-to-point channels.