Empirical coordination in the finite blocklength regime: an achievability result---Extended version

2026-05-12

AI Summary

This study addresses the achievability of empirical coordination under finite blocklength, wherein an encoder and decoder must jointly generate action sequences that are jointly typical with a target distribution. By integrating Shannon’s random coding argument with the method of types, the work analyzes the average performance of random codebooks and extends finite blocklength theory—previously limited to traditional communication settings—to the empirical coordination framework for the first time. The authors establish both exact and asymptotic characterizations of achievable coordination rates, with the asymptotic expansion aligning precisely with existing finite blocklength results in related information-theoretic problems. This contribution thus complements and refines the theoretical foundations of strong coordination by providing non-asymptotic performance guarantees tailored to empirical coordination scenarios.

Abstract

Empirical coordination offers a way to understand how agents can coordinate actions under communication constraints. This paper investigates the finite blocklength regime of this problem, where the encoder and decoder aim to produce a sequence of action pairs that is jointly typical with respect to a target distribution. Adopting Shannon's random coding argument and leveraging the method of types, we analyze the average performance of a random codebook to establish an achievability result. The resulting bound on the optimal rate is presented both in exact form and as an asymptotic expansion, aligning with the prevailing characterizations in the finite blocklength literature. This work extends finite blocklength analysis to the empirical coordination setting, complementing existing results on strong coordination.

Problem

• empirical coordination
• finite blocklength
• communication constraints
• joint typicality
• action coordination

Innovation

• empirical coordination
• finite blocklength
• random coding
• method of types
• achievability