Optimized analog network coding strategies for the white Gaussian multiple-access relay channel

We consider a Gaussian multiple-access relay channel with multiple sources, a relay and a destination. We assume that the received signals at the relay and the destination from different nodes are orthogonal. Additionally, we assume that the relay performs an instantaneous mapping to compress all received signals from different sources into one output symbol. We refer to this as analog network coding. We optimize the analog network coding mapping to maximize the achievable sum rate. We additionally introduce an algorithm to obtain an achievable rate region. The optimized mappings are in general non-linear and provide superior rates compared to those of linear mappings.