  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.
