Multi-terminal Strong Coordination with Degraded Source Observations

We investigate the problem of multi-terminal strong coordination over a network of noiseless links with degraded source observations. In this setup, independent and identically distributed (i.i.d.) copies of correlated sources are observed by two transmitters, with one of the source observations being common while the other one is private. The transmitters communicate their source descriptions over noiseless links to the receiver, which must produce approximately i.i.d. copies of an output random variable jointly distributed with the two sources. This is aided by the presence of common randomness shared between all three parties. The communication and common randomness rate tuples which permit such channel simulation are of interest. We derive a complete characterization for this multi-terminal strong coordination problem. It is observed that the optimal scheme is based on a superposition structure, where the common source description forms the base layer and the private source description forms the top layer.