  We study the power versus distortion trade-off for the distributed
transmission of a memoryless bi-variate Gaussian source over a two-to-one
average-power limited Gaussian multiple-access channel. In this problem, each
of two separate transmitters observes a different component of a memoryless
bi-variate Gaussian source. The two transmitters then describe their source
component to a common receiver via an average-power constrained Gaussian
multiple-access channel. From the output of the multiple-access channel, the
receiver wishes to reconstruct each source component with the least possible
expected squared-error distortion. Our interest is in characterizing the
distortion pairs that are simultaneously achievable on the two source
components.
  We present sufficient conditions and necessary conditions for the
achievability of a distortion pair. These conditions are expressed as a
function of the channel signal-to-noise ratio (SNR) and of the source
correlation. In several cases the necessary conditions and sufficient
conditions are shown to agree. In particular, we show that if the channel SNR
is below a certain threshold, then an uncoded transmission scheme is optimal.
We also derive the precise high-SNR asymptotics of an optimal scheme.
