Sending a bivariate Gaussian source over a Gaussian MAC with unidirectional conferencing encoders

We consider the transmission of a memoryless bivariate Gaussian source over a two-user additive Gaussian multiple-access channel with unidirectional conferencing encoders. Here, prior to each transmission block, Encoder 1, which observes the first source component, is allowed to communicate with Encoder 2, which observes the second source component, via a unidirectional noise-free bit-pipe of given capacity. The main results of this paper are sufficient conditions and a necessary condition for the achievability of a distortion pair expressed as a function of the channel SNR and of the source correlation. The main sufficient condition is obtained by an extension of the vector-quantizer scheme suggested by Lapidoth-Tinguely, for the case without conferencing, to the case with unidirectional conference. In the high-SNR regime, and when the capacity of the conference channel is unlimited, these necessary and sufficient conditions are shown to agree. We evaluate the precise high-SNR asymptotics for a subset of distortion pairs when the capacity of the conference channel is unlimited in which case we show that a separation-based scheme attains these optimal distortion pairs. However, with symmetric average-power constraints and fixed conferencing capacity, at high-SNR, the latter separation-based scheme is shown to be suboptimal.