Communication and State Estimation over a State-Dependent Gaussian Multiple-Access Channel

A joint communication and state estimation problem in a Gaussian multiple access channel with common additive state is considered. The state process is assumed to be IID Gaussian, and known non-causally at both the transmitters. The receiver not only has to decode the messages from the transmitters, but also needs to estimate the state process to within some prescribed squared error distortion. We provide a complete characterization of the optimal sum-rate versus distortion performance.