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

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.