Correlated Gaussian sources over Gaussian weak interference channels

We consider the transmission of two correlated Gaussian sources over a Gaussian weak interference channel. Each transmitter has access to one component of a bivariate Gaussian source, and each of these components need to be reconstructed at the corresponding receiver, under the squared-error distortion measure. We are interested in characterizing the region of average distortion pairs achievable simultaneously at the two receivers. We derive an outer bound on the achievable region, and show that, under certain conditions, achievable distortion pair with uncoded transmission lies on this outer bound; therefore, it is optimal. In particular, optimality of uncoded transmission is shown to hold for all signal-to-noise ratio values below a certain threshold which depends on the correlation coefficient between the sources.