Necessary Condition for Sending A Bivariate Gaussian Source over the "asymmetric" Gaussian Mac

We consider the transmission of a bivariate Gaussian memoryless source over a two-user additive Gaussian multiple-access channel with unidirectional conferencing. Here, prior to each transmission block Encoder 1 is allowed to communicate with Encoder 2 via a unidirectional noise-free bit-pipe of given capacity. We derive a necessary condition for the achievability of a distortion pair expressed as a function of the channel SNR and of the source correlation. In the high-SNR regime, and when the capacity of the conference channel is unlimited, the necessary condition is shown to agree with a sufficient condition derived previously by the authors. We evaluate the precise high-SNR asymptotics for a subset of distortion pairs when the conferencing capacity is unlimited in which case we show that the problem is separable.