CIF: Small: Algebraic Network Information Theory

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The demand for data services has grown exponentially over the past decade, driven by data-hungry applications such as mobile video, and is forecasted to accelerate through the next decade. To keep up with this demand, new infrastructure is being built at a rapid pace, leading to denser, more complex deployments. Concurrently, mobile processing power has increased dramatically, which opens the door for the inclusion of more sophisticated communication techniques as part of developing standards. Within this context, network information theory acts as a powerful theoretical framework for assessing techniques across complex network topologies and setting benchmarks for practical deployments. Recent efforts have uncovered examples of techniques that sit outside this classical framework, and exploit the algebraic structure inherent to multi-user communication to attain higher performance. This project will develop an algebraic network information theory that unifies classical and modern communication techniques, and can serve as a foundation for future information-processing networks. The project is complemented by several educational and outreach activities, including workshops, summer schools, and tutorials.This project aims to take a comprehensive view of algebraic, information-theoretic techniques for efficient communication across networks. The overarching goal is to develop an algebraic network information theory starting from the accessible concepts of joint typicality and discrete memoryless channels and sources. The project is organized into three thrusts. The first thrust outlines a unifying problem statement based on joint typicality as well as algebraic packing and covering lemmas. The second thrust pursues a fundamental understanding of the limits of optimal decoding. Finally, the third thrust aims to transport geometric insights from lattice-based codes to obtain new bounds and algorithms for linear codes.