Sending a Bivariate Gaussian Source over a Gaussian MAC with Feedback

We consider the problem of transmitting a bivariate Gaussian source over a two-user additive Gaussian multiple-access channel with feedback. Each of the transmitters observes one of the source components and tries to describe it to the common receiver. We are interested in the minimal mean squared error at which the receiver can reconstruct each of the source components. In the "symmetric case" we show that, below a certain signal-to-noise ratio threshold which is determined by the source correlation, feedback is useless and the minimal distortion is achieved by uncoded transmission. For the general case we give necessary conditions for the achievability of a distortion pair.