Joint State Estimation and Communication Over a State-Dependent Gaussian Multiple Access Channel

A hybrid communication network with a common analog source signal and independent digital data streams at the transmitters of a multiple access network is considered. The receiver has to estimate the analog signal samples with a given fidelity, and decode the digital streams with a low error probability. The main goal of this paper is to characterize the optimal tradeoff between the mean-squared error distortion in source estimation and the data rates available to each user. To this end, we consider a Gaussian multiple access channel (GMAC) setup with additive state, where the state is nothing but a scaled version of the source process itself. The state process is assumed to be non-causally available to all the transmitting nodes. The problem now becomes that of the joint state estimation and message communication in a GMAC with state. We provide a complete characterization of the optimal distortion-rate tradeoff for an N - sender GMAC. Our results show that, similar to the single-user results, it is optimal to amplify the state using uncoded transmissions, whereas the digital streams are superposed using appropriate Gaussian codebooks in conjunction with dirty paper coding (DPC). Since the variance of the additive state is controlled by a scaling factor in our model, we also recover the results for communicating a common source and independent messages over a GMAC without state as a special case.