Transmission of Correlated Sources Over Gaussian Multiple Access Channel with Phase Shifts

In this paper, we address the problem of separate encoding of correlated sources observed by sensor nodes that send their encoded information through Gaussian multiple access channel (GMAC) with phase shifts. We suppose that the phases are perfectly known at the receiver and unknown to the transmitters. For discrete sources with finite-cardinality alphabets, we prove that the separation theorem holds for both random ergodic and arbitrary non-random models for the phase shifts, and consequently, the strategy of combining Slepian-Wolf coding to capacity achieving channel encoders is optimal for both.