$(\epsilon, n)$ Fixed-Length Strong Coordination Capacity

TL;DR

This paper derives a capacity result for fixed-length strong coordination, showing how the rate depends on mutual information, blocklength, and a Gaussian approximation term, advancing understanding of finite-length distribution synthesis.

Contribution

It provides a novel capacity characterization for fixed-length strong coordination incorporating finite blocklength effects and channel dispersion.

Findings

Capacity lower-bounded by mutual information plus a Gaussian approximation term.

Analytical proof of rate conditions for finite-length strong coordination.

Extension of asymptotic coordination results to finite blocklength regime.

Abstract

This paper investigates the problem of synthesizing joint distributions in the finite-length regime. For a fixed blocklength $n$ and an upper bound on the distribution approximation $\epsilon$, we prove a capacity result for fixed-length strong coordination. It is shown analytically that the rate conditions for the fixed-length regime are lower-bounded by the mutual information that appears in the asymptotical condition plus $Q^{-1} \left(\epsilon \right) \sqrt{ V/n}$, where $V$ is the channel dispersion, and $Q^{-1}$ is the inverse of the Gaussian cumulative distribution function.