  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 work 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.
