UC San Diego

As information networks grow in magnitude and complexity, new models and frameworks are necessary to understand the nature of information transmission. In this thesis we demonstrate how fundamental questions arising in the design of large wireless networks can be addressed by applying methods from information theory, physics, networking and control. We focus on three examples of emerging systems architecture. First, we investigate the maximum achievable throughput in a wireless ad-hoc network. By combining Maxwell's physics of wave propagation and Shannon's theory of information, and departing from idealistic stochastic channel models for signal propagation, we derive an upper bound to the law that determines the scaling of throughput with the population size of the network, and conclude that the scaling achieved by multi-hop communication is optimal in any constant density wireless network. Second, we study how to aggregate information from uncoordinated nodes by considering a random-access system with multiple nodes transmitting information to a common receiver. We characterize the maximum achievable throughput of channels of practical interest and demonstrate how the performance of current systems can be improved by allowing encoding rate adaptation at the transmitters and joint decoding at the receiver. Finally, we explore the fundamental limits of control over wireless channels and demonstrate the relationship between the degree of instability of a system and the time varying rate of communication in the feedback link