Message and state cooperation in a relay channel when the relay has strictly causal state information

A state-dependent relay channel is studied in which strictly causal channel state information is available at the relay and no state information is available at the source and destination. Source and relay are connected via two unidirectional out-of-band orthogonal links of finite capacity, and a state-dependent memoryless channel connects source and relay, on one side, and the destination, on the other. Via the orthogonal links, the source can convey information about the message to be delivered to the destination to the relay while the relay can forward state information to the source. This exchange enables cooperation between source and relay on both transmission of message and state information to the destination. First, an achievable scheme, inspired by noisy network coding, is proposed that exploits both message and state cooperation. Next, based on the given achievable rate and appropriate upper bounds, capacity results are identified for some special cases. Finally, a Gaussian model is studied, along with corresponding numerical results that illuminate the relative merits of state and message cooperation.