| Capacity characterization of interference channels constitute a set of challenging problems in multi-terminal information theory. Even after decades of research, the answer to one of the simplest questions in this class, the capacity of a 2-user Gaussian interference channel, is known only approximately. Recently there has been significant progress on this question that not only builds on the existing upperbounds and achievable schemes devised in the last 40 years of research, but makes use of new techniques and ideas, in particular, a class of approximate models called the linear deterministic interference channels (LDIC). Even with this progress, there is still much that is unknown, especially when we consider interference channels with more than 2 users. This dissertation is aimed at improving understanding of such scenarios.;In the first part of the dissertation, we consider several classes of 3-user LDICs, where not all users interfere with each other. Upperbounds are derived using general deterministic models, while achievability is shown by explicit construction. Further, analysis of the deterministic cases enables us to approximately characterize the sum-capacity for the corresponding K-user Gaussian interference channels.;In the second part of the dissertation, we study an information theoretic game being played on the interference channel. We consider a general K-user LDIC with arbitrary connectivity and show the existence of equilibrium strategies using ideas of potential functions for weakly acyclic games. For some classes of LDICs for which either the capacity or sum-capacity is known, we also provide a characterization of the Nash equilibrium region. Efficiencies of such equilibria are also evaluated.;In the last part, we take an alternative look into the linear deterministic model using a novel graphical representation in terms of structures called 'interference chains'. This enables design of simple achievable schemes which are sum-rate optimal. Further, this representation of LDICs enables a better understanding of extensions like parallel LDICs and LDICs with output feedback; it also provides exact conditions under which separable coding across sub-channels is sum-rate optimal. |
