Transmission of correlated sources over Gaussian multiple-access channels 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 a 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.