Optimized mappings for dimension-expansion relaying

We study the three-node Gaussian relay channel consisting of a source, a relay and a destination. We assume that the relay is memoryless, i.e., the transmitted signal from the relay depends only on the currently received signal. Additionally, we focus on dimension expansion relaying, where the relay has access to more channel uses for retransmission. We use the end-to-end mutual information to numerically optimize the relay mappings. We present several examples for two types of source input alphabets: continuous (Gaussian and uniform) and discrete (uniform PAM). The maximum rate attained by using the optimized mappings is considerably improved compared to conventional linear relaying.