New results in network information theory

This dissertation addresses four problems in the field of network information theory, which is concerned with the theoretical limits on communication in multiterminal networks.; First, we determine the capacity region of a degraded Gaussian relay channel with multiple relay stages. This is done by building an inductive argument based on the single-relay capacity theorem of Cover and El Gamal. Based on this result, we derive the optimal power distribution strategy among the transmitter and the relays and analyze the behavior of the multi-relay Gaussian channel in the wideband case.; Second, we define the broadcast-relay channel as a broadcast channel where receivers are permitted to assist in the distribution of data to other receivers by relaying. We demonstrate that effective transmission strategies can be derived by combining well-known techniques for broadcast and relay channels. We derive outer bounds to capacity regions, which are tight in some cases.; Third, we consider the problem of maximizing the "transport capacity" of a broadcast network in a Gaussian power-law channel, where by transport capacity we mean a generalization of the bandwidth-distance product as a means of assigning value to the information delivered by a communication network. In the process of addressing this issue we also derive a transport-capacity maximizing resource allocation scheme for a general set of reward and channel penalty functions. The behavior of transport capacity for a very large network of receivers in a Gaussian power-law channel is also examined and a "large-scale" view of the optimal power allocation scheme for a given distance-payoff function is provided.; Finally, we consider a heterogeneous (also called "hybrid") ad-hoc network with wired and wireless links. This type of network was previously considered by Kulkarni and Viswanath who demonstrated achievable transport capacity growth rates for a structured wired infrastructure. We improve on this work by demonstrating that efficiency can be increased significantly if the wired links are introduced at random. Our approach to the problem provides a new analysis of a "small world network" built on a square grid.