The achievable distortion region of bivariate Gaussian source on Gaussian broadcast channel

We provide a complete characterization of the achievable distortion region for the problem of sending a bivariate Gaussian source over a bandwidth-matched Gaussian broadcast channel, where each receiver is interested in only one component of the source. This setting naturally generalizes the simple single Gaussian source bandwidth-matched broadcast problem for which the uncoded scheme is known to be optimal. We show that a hybrid scheme can achieve the optimum for the bivariate case, but neither an uncoded scheme alone nor a separation-based scheme alone is sufficient.