Empirical coordination in the finite blocklength regime: an achievability result---Extended version
It extends finite blocklength analysis to empirical coordination, complementing results on strong coordination for information theorists.
This paper establishes an achievability result for empirical coordination in the finite blocklength regime, deriving a bound on the optimal rate that aligns with existing finite blocklength characterizations.
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.