UC San Diego

Feedback links from the receivers to the transmitters are natural resources in many real-world communication networks which are utilized to send back information about the decoding process as well as the channel dynamics. However, the theoretical understanding of the role of feedback in communication systems is yet far from being complete. In this thesis, we apply techniques from information theory, estimation and control, and optimization theory to investigate the benefits of feedback in improving fundamental limits on information flow in communication networks. We focus on three network models: Gaussian multiple access channels, Gaussian broadcast channels, and wiretap channels. First, combining the Lagrange duality technique and tools from information theory we derive an upper bound on the sum rate achievable by linear codes for the Gaussian multiple access channel with feedback. This upper bound is further shown to coincide with the known lower bound, hence establishing the linear sum capacity. Next, we study the application of tools from the theory of linear quadratic Gaussian (LQG) control in designing codes for feedback communications. For the Gaussian broadcast channel with feedback, we construct a linear code based on the LQG optimal control and establish the best known lower bound on the sum rate. In addition, depending on the spatial correlation of the noise across different receivers, it is shown that in the high signal-to-noise ratio regime, the sum rate achieved by this code can increase linearly with the number of receivers. Third, we consider the wiretap channel with an eavesdropper and study the benefits of a rate-limited feedback link. We propose a new technique based on which we derive an upper bound on the maximum rate of reliable and secure communication. For the special case in which the eavesdropper's signal is a degraded version of the legitimate receiver's signal, this upper bound matches the known lower bound establishing the secrecy capacity. Finally, we present results for the binary multiplying channel, one of the simplest two-way channels for which the capacity region is not known. We apply tools from stochastic control to establish sufficient conditions for optimality, and use the concept of directed information to analyze the performance of coding schemes