On Discrete Memoryless Relay Channels with Designable Transmitter Side Information

In a relay channel with channel states, channel state information at transmitter (CSIT) can significantly improve performance. While perfect CSIT is hard or impossible to obtain, partial CSIT obtained through finite-rate feedback from the receivers is practical. The problem is how to design such feedback jointly with the transmission strategy to optimize the performance. For discrete memoryless relay channel employing decode-and-forward, we prove the maximum achievable rate and show that the optimal feedback and transmission strategy are both memoryless and deterministic, thus, proving that an obvious intuition is indeed optimal.