CIF:Small: Toward an Algebraic and Probabilistic Foundation for Network Information Theory based on Quasi Structured Codes

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Modern infrastructure, including transportation systems, power systems, climate and environment monitoring systems, and education systems, are increasingly interconnected through information networks. A recent forecast predicts no end in sight for humanity's hunger for information consumption and the concomitant information interconnection. Network information theory aims to address this challenge by developing a comprehensive theory of information storage, transmission, and processing in networks. This project develops new ideas and techniques in efficient distributed encoding and decoding of information in networks from a communication/information/signal-processing theory perspective. The project will be tightly integrated with a significant education and outreach program consisting of two focus areas: training students in interdisciplinary research, and broadly disseminating research outcomes in the forms of new curricular development and student involvement. This project considers two key concepts: (i) structured codes versus unstructured codes; and (ii) common information. A new fundamental connection between them is uncovered, which motivates the development of a new unified coding framework for the communication problems that form the building blocks of networks. This project is pillared on three key innovations developed in the recent past: (i) Quasi-structured codes that span the spectrum from completely structured codes to completely unstructured codes and whose performance can be characterized using single-letter information quantities; (ii) Conferencing common information among three or more random variables (or terminals) that characterizes new structures in the joint probability distributions that are the key to developing new information coding strategies in networks; and (iii) Practical code constructions for networks that approach the information-theoretic rate region using computationally efficient encoding and decoding algorithms. This project strives for a fundamental understanding of the algebraic code structure in network communication problems, as a precursor to developing computationally efficient encoding and decoding algorithms adapted to challenging multi-user information theory problems.