Joint Communication and State Estimation Over a State-Dependent Fading Gaussian Channel

A joint message and state communication problem over a fading Gaussian channel with additive state is considered. The state process is assumed to be independent and identically distributed (i.i.d.) Gaussian, and known non-causally at the transmitter, while the instantaneous fading gain is assumed to be known at both the encoder and the decoder. The receiver not only has to decode the message from the transmitter, but also needs to estimate the state process to meet a prescribed distortion limit. A complete characterization of the optimal rate versus distortion performance is provided. Moreover, the converse proof presented here might be of independent interest, since it gives a simpler and more compact way of establishing the converse for settings with non-fading links studied in the literature – by virtue of relying only upon the differential entropy maximizing property of Gaussian random variables for a given variance.