Broadcasting correlated Gaussians is one of the cases where separate source-channel coding is suboptimal. In this dissertation, we will study the distortion region of sending correlated Gaussian sources over an AWGN-BC using hybrid digital-analog coding approach, where each receiver wishes to reconstruct one source component subject to the mean squared error distortion constraint.
First of all, the problem of transmitting m independent Gaussian source components over an AWGN-BC is studied. We show this problem setup is closely related to broadcasting correlated Gaussian sources with genie-aided receivers. Moreover, the separate source-channel coding approach is proven to be optimal in these setups.
Second, we consider two new scenarios and find the achievable distortion regions for both cases, where three Gaussian source components are sent to three receivers. The difference is that for the first scenario, the first two source components are correlated and they are independent of the third one while for the second scenario, the last two source components are correlated and they are independent of the first one. Inner bounds based on hybrid analog-digital coding and outer bounds based on genie-aided arguments are proposed for both cases and the optimality is proven.
Finally, we study two cases where side information is presented at one receiver. Hybrid analog-digital coding schemes are used and the optimality is proven.