Some information theoretic aspects of reliable communication with transmitter side information

In many network communication problems, including broadcast channel and distributed source coding, there is a natural strategy of converting the problem into a point-to-point problem and a series of side-information problems: One user does its own, and the rest of users treat messages sent from previous users as side information. In this dissertation, we study such communication problems in two ways. First, we study the performance limits of these separation schemes. Point-to-point communication has been studied for a long time and fundamental performance limits have been established. So our focus is on side-information problems. Second, we study the optimality of the proposed separation-based architecture by relating it to the mathematical structure of an optimal scheme.;For the performance limits of communication with side information, we first consider the reliability of communication over Costa's dirty-paper channel. We show a surprising result that the reliability function of Costa's dirty-paper channel is the same as that of the zero interference additive white Gaussian noise (AWGN) channel, at least for rates near channel capacity. That is, the lack of knowledge of the side information at the receiver does not cause any loss in terms of not only channel capacity but also reliability function for rates near channel capacity. Next, we consider wideband communication with transmitter side information. Motivated by the fact that orthogonal signaling achieves the wideband capacity of point-to-point channels, we propose a simple scheme called opportunistic orthogonal signaling. We show that opportunistic orthogonal signaling achieves the capacity and the reliability function of the infinite-bandwidth Costa's dirty-paper channel. Furthermore, we show that a natural generalization of opportunistic orthogonal signaling achieves the capacity per unit cost of Gel'fand-Pinsker channels with a zero-cost input letter.;For the optimality of the separation architecture, we consider the problem of determining the capacity region of the multiple-input-multiple-output (MIMO) Gaussian broadcast channel. Our main result is a new extremal inequality as the underpinning mathematical structure for the MIMO Gaussian broadcast channel problem. In one special case, this inequality yields a generalization of the classical vector entropy-power inequality (EPI). In another special case, this inequality sheds insight into the problem of maximizing the differential entropy of the sum of two jointly distributed random variables.