Strong coordination over multi-hop line networks using channel resolvability codebooks

We analyze the problem of strong coordination over a multi-hop line network in which the node initiating the coordination is a terminal network node. We assume that each node has access to a certain amount of randomness that is local to the node, and that the nodes also have shared common randomness, which are used together with explicit hop-by-hop communication to achieve information-theoretic strong coordination. We derive the trade-offs among the required rates of communication on the network links, the rates of local randomness available at network nodes, and the rate of common randomness to realize strong coordination. We present an achievable coding scheme built using multiple layers of channel resolvability codes, and establish several settings in which this scheme offers the best possible trade-offs among network resources.