On the minimum energy of sending Gaussian multiterminal sources over the Gaussian MAC

We study the minimum energy of sending Gaussian multiterminal sources over the Gaussian multiple access channel (MAC). Distributed transmitters observe Gaussian multiterminal sources and describe their observations to a central decoder, which desires to reconstruct the sources under MSE constraints. We first lower bound the minimum energy by a cut-set argument which couples the transmitted signals and reconstruction errors. For achievability, separate source-channel coding is first studied as a benchmark. We then find out the minimum energy that can be achieved uncoded transmission. A hybrid digital/analog scheme is proposed to achieve the best known energy performance.