Shannon's masterpiece, A Mathematical Theory of Communication (1948), is one of the most influential works in the history of communications. In this seminal work, Shannon characterized the fundamental limit for reliable communication over point-to-point channels and provided the architectural system design for achieving it. Extending this theory to network setting has been one of the greatest challenges in information theory over the past few decades. Progress in this area is expected to produce significant breakthrough in the design of distributed wireless networks of the future, such as ad-hoc networks. So far, most research efforts have approached this problem using the same generality and accuracy used by Shannon for point-to-point channels. However, meeting such a standard has proven to be extremely difficult, to the extent that the capacity of most basic networks is still unknown.
This research overcomes the limitations of prior work by presenting a new approach, which is based on changing the focus to seek approximate solutions accompanied by guarantees on the gap to optimality. At the heart of this approach is the development of simple, deterministic channel models that capture the main features of the wireless medium, and are utilized to approximate more complex models. Building on recent results of the PI, the work develops a unified framework to utilize this powerful approach to 1) approximate the capacity of wireless networks; 2) study the impact of incomplete network knowledge on the capacity; 3) design protocols that are robust against adversaries; and 4) utilize recent physical layer coding techniques for cross-layer protocol design. The project also includes significant outreach program to women and under-represented minorities in the form of presenting tutorials and organizing workshops.
