Rate-maximizing mappings for memoryless relaying

We study the problem of optimal design of relay mappings for the Gaussian relay channel in order to maximize the reliable transmission rate. We consider both Gaussian and modulation constrained signaling at the source. To optimize the relay mapping, we use an iterative integral equation as a necessary condition for optimality. The optimized relay mappings demonstrate significant rate improvement over conventional linear relaying (amplify-and-forward). The optimized mappings allow an efficient utilization of the side information received via the source-destination link at the destination. Hence, the proposed mappings can be considered as an analog, memoryless approach to implementing compress-and-forward relaying with Wyner-Ziv compression in the relay.