Fixed-Length Strong Coordination

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 ε, a coding scheme is proposed such that the induced joint distribution is ε-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.