| The conventional design of wireless networks is based on a centralized architecture where a base station, or an access point, directly exchanges data with the end users, and communication is restricted to the one-to-many (broadcast) and many-to-one (multiple-access) single-hop paradigms. However, as the number of users and the data demand increase dramatically, and we move towards the future of wireless networks, multi-hop and multi-flow paradigms are expected to play a central role by enabling a denser spatial reuse of the spectrum and the adaptation to heterogeneous network scenarios characterized by the presence of low-power nodes, relays, and user-operated infrastructure.;A major challenge in multi-hop multi-flow wireless networks is that "interference management" and "relaying" are coupled with each other. In other words, wireless relay nodes must play a dual role: they serve as intermediate steps for multi-hop communication and as part of the mechanism that allows interference management schemes. Nonetheless, in the information theory literature, these two tasks have traditionally been addressed separately, and the fundamental principles of the "networks of the future" are currently not well understood. In this dissertation, we take a unified approach to relaying and interference management, and seek to develop tools to study the fundamentals of multi-hop multi-flow wireless networks.;In the first part of the dissertation, we study multi-hop multi-flow wireless networks from a high-SNR, or degrees-of-freedom (DoF) perspective. We first consider multi-hop two-unicast networks, and characterize the DoF as a function of the network graph. Then, we consider Kx KxK wireless networks and introduce a coding scheme called Aligned Network Diagonalization (AND) that allows the relays to neutralize all the interference experienced by the destinations. This proves that KxKx K wireless networks have K DoF and demonstrates the potential of a coupled approach to relaying and interference management.;In the second part of the dissertation, we present a characterization of the Gaussian noise as the worst-case additive noise in multi-hop multi-flow wireless networks. Besides generalizing a classical point-to-point information theory result, this provides theoretical support for the widespread adoption of Gaussian noise models and yields a tool for obtaining capacity outer bounds for Gaussian networks by considering networks with different noise statistics.;In the final part of the dissertation, we introduce new techniques to obtain capacity outer bounds for multi-hop multi-flow networks. First, we use the worst-case noise result to show that the capacity region of KxKxK wireless networks with general connectivity can be outer-bounded by the capacity region of the same network under the truncated deterministic model. We then present a generalization of the classical cut-set bound for multi-hop multi-flow deterministic networks, which, besides recovering and unifying other previously known bounds, yields new applications, in both deterministic and non-deterministic settings. In particular, we obtain a rank-based bound for the capacity of linear deterministic multi-flow networks and for the DoF of AWGN multi-flow networks, which yields graph-theoretic conditions for K DoF to be achievable in KxKxK networks with general connectivity. |
