Broadcasting Gaussian Sources Over Gaussian Channels

This dissertation studies several problems regarding the joint/separate source-channel coding in data transmission over networks. It has been known that separation based transmission schemes achieves optimality when there is only one sender and one receiver. However, other than this point-to-point case, separation is often suboptimal and it is generally unclear how to achieve optimality.In Chapter 2, several new hybrid digital/analog schemes are proposed for the problem of transmitting a Gaussian source over a Gaussian channel under different scenarios. Previously existing optimal schemes are combined in a way that the output of one encoder is taken as effective CSI at the other encoder. In each case, the optimum distortion-power tradeoff can be achieved by a continuum of auxiliary random variables for any power allocation between the two encoders.In Chapter 3, a new scheme is proposed for lossy transmission of a Gaussian source over a Gaussian broadcast channel with source side information available at each re- ceiver. The proposed scheme combines two schemes that were previously shown to achieve optimal point-to-point distortion/power tradeoff simultaneously at all receivers under two distinct conditions stated in terms of channel and side information quality parameters. For the two-receiver case, the combined scheme is shown to achieve the same kind of optimality for the entire region in the parameter space sandwiched between those two conditions. Crucial to this result is the new degree of freedom discovered in Chapter 2.In Chapter 4, the problem of broadcasting a pair of correlated Gaussian sources using optimal separate source and channel codes is studied. A universal upper bound of rate (bandwidth compression/expansion ratio) penalty is given and in particular, for a low-distortion scenario, separate coding can be shown to achieve optimum. For the case with a Gaussian broadcast channel, the power loss of separate coding is also dis- cussed. Although source-channel separation yields suboptimal performance in general, it is shown that the proposed scheme provides competitive performance comparing with best-known schemes