Strong coordination over multi-hop line networks

We analyze the problem of strong coordination over a multi-hop line network where the node initiating the coordination is a terminal network node. We provide a characterization of the capacity region when the initiating node possesses unlimited local randomness and intermediate nodes operate under a functional regime. In this regime, next-hop messages are created only using common randomness and previous-hop incoming messages, i.e., local randomness at intermediate nodes is only used for generating actions.