Fixed-Length Strong Coordination

TL;DR

This paper proposes a coding scheme for finite-length channels that achieves joint distributions close to a target distribution, extending to asymptotic cases as blocklength increases.

Contribution

It introduces a method for synthesizing joint distributions over noisy channels at fixed blocklengths with explicit bounds on distribution accuracy.

Findings

Achieves $ ext{L}^1$-closeness to target distribution at finite blocklengths.

Characterizes the set of achievable distributions and rates for asymptotic strong coordination.

Provides a framework bridging finite-length and asymptotic coordination regimes.

Abstract

We consider the problem of synthesizing joint distributions of signals and actions over noisy channels in the finite-length regime. For a fixed blocklength $n$ and an upper bound on the distance $\varepsilon$, a coding scheme is proposed such that the induced joint distribution is $\varepsilon$-close in $L^1$ distance to a target i.i.d. distribution. The set of achievable target distributions and rate for asymptotic strong coordination can be recovered from the main result of this paper by having $n$ that tends to infinity.