Information Theoretic Perspective for Rate and Delay in Interference Limited Wireless Networks

This thesis investigates wireless networks through the study of two fundamental metrics: rate and delay. The main goal is to gain insight on communication limits that are intrinsic to an interference-limited network. To achieve this, information theoretic tools are applied to analyze the rate trade-off, represented by the capacity region, and the delay trade-off, represented by the completion time region, where the focus is on dealing with multi-user interference in the network.;Motivated by emerging heterogeneous cellular networks, in the first part of this thesis a class of broadcast interference channels is studied, which has not been thoroughly studied in the rich literature of network information theory. This channel models a communication scenario where one of the two broadcast receivers is interfered by a point-to-point transmission. The study is carried out by first analyzing the discrete memoryless version of the channel, where a concise representation of a capacity region inner bound is obtained using a combination of message splitting, superposition and binning coding. Two partial-order broadcast conditions: interference-oblivious less noisy and interference-cognizant less noisy are introduced to extend the usual less noisy condition for a regular broadcast channel by taking interference into account. These conditions further simplify the inner bound representation and lead to capacity results when interference is either strong or very strong. Following this analysis, the Gaussian broadcast interference channel is investigated. The achievability mostly follows the discrete memoryless counterpart and our efforts are concentrated on the converse proof. Combing existing bounding techniques for a Gaussian broadcast channel and a Gaussian interference channel and using a newly derived entropy-power-inequality based outer bound, either exact or approximate characterization of the capacity region and sum capacity under various conditions is provided.;Within the context of information theory, delay, in a sharp contrast to rate, has not witnessed the same kind of extensive research activity commensurate with its fundamental role in a wireless network. This is best explained as the consequence of the full-buffer assumption underlining many information theoretic formulations. In the second part of this thesis, a framework to study the so-called completion time problem is proposed, where completion time refers to the number of channel uses required to complete the transmission of some fixed amount of data for each user in the network. One unique feature of the completion time problem is the dynamics of reduced multi-user interference as users finish their transmission and turn off. To model the effect of such dynamics and to formulate the problem, users' codewords are allowed to span different block-lengths over which rates are defined. Analogous to the capacity region, the completion time region is introduced to describe all possible trade-offs among users' completion times. For three fundamental two-flow networks, including a multi-access channel, a broadcast channel and an interference channel, the exact completion time region or inner and outer bounds are then established.