On Achievable Distortion in Sending Gaussian Sources over a Bandwidth-Matched Gaussian MAC with No Transmitter CSI

This paper investigates the minimum mean square error (MMSE) of communicating a pair of Gaussian sources over a a bandwidth-matched Gaussian multiple-access channel with block Rayleigh fading in the absence of channel state information (CSI) at the transmitters. The achievable MMSE is not known. To this end, we derive several upper-bounds to the minimum achievable average MMSE as a function of the transmitter powers, the average channel fading power-to-noise ratio, and the correlation coefficient of the two sources. To derive nontrivial upper bounds which improve on those of separate source-channel coding and uncoded transmission, we incorporate ideas from joint source-channel coding and hybrid digital–analog coding to construct specific coding schemes for which the achievable MMSE can be determined.