Common Randomness Generation from Gaussian Sources

TL;DR

This paper characterizes the maximum rate of common randomness generation between two parties observing correlated Gaussian sources, providing a complete solution including a single-letter capacity formula and the case of perfect correlation.

Contribution

It offers the first single-letter characterization of CR capacity for Gaussian sources in a two-party setting, including the case of perfect correlation.

Findings

CR capacity is infinite for perfectly correlated sources.

The paper provides a rigorous proof of the capacity formula.

It fully solves the problem of CR generation for Gaussian sources.

Abstract

We study the problem of common randomness (CR) generation in the basic two-party communication setting in which the sender and the receiver aim to agree on a common random variable with high probability by observing independent and identically distributed (i.i.d.) samples of correlated Gaussian sources and while communicating as little as possible over a noisy memoryless channel. We completely solve the problem by giving a single-letter characterization of the CR capacity for the proposed model and by providing a rigorous proof of it. Interestingly, we prove that the CR capacity is infinite when the Gaussian sources are perfectly correlated.