Collaborative Research: CIF: Small: A New Paradigm for Distributed Information Processing, Simulation and Inference in Networks: The Promise of Law of Small Numbers

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The ability to access, process, and store distributed data in a reliable, efficient, and secure manner has become indispensable in everyday lives. A variety of emerging applications such as augmented reality, autonomous vehicles, and cloud computing heavily rely on handling large amounts of distributed information. The pandemic has further accentuated the global need for technologies that enable communication, collaboration, education and scientific discourse whilst maintaining physical distance, and this has increased awareness of the critical nature of the communication network infrastructure. The exponentially increasing demands for faster data processing and higher communication rates pose new challenges. This project addresses these challenges by developing novel approaches and techniques for distributed information processing, randomness generation, data storage and transmission, and inference. The project will tightly integrate research with a significant education and outreach program consisting of two focus areas: (i) Training students in interdisciplinary research, and (ii) Broadly disseminating research outcomes in the forms of new curricular development and student involvement. A concerted effort will be made to broaden the participation of women and under-represented minority students in the project. The project is based on two research thrusts that are expected to provide a deeper understanding of the fundamental laws that govern the processing of information. In the first thrust, a new framework is developed based on two conceptual innovations: (i) A characterization of the fundamental memory structure of information processing functions using a novel notion of dependency spectrum, and (ii) Development of a new law of small numbers, which describes a fundamental interplay between the dependency spectrum and distributed cooperation. In particular, the project uncovers a trade-off between the correlation-preserving ability of distributed information-processing functions --- which is necessary for distributed cooperation --- and their ability to efficiently perform individual information-processing tasks. The second thrust addresses two application scenarios. (i) Building upon the concept of dependency spectrum, novel techniques are developed for distributed data compression, and transmission of information in interference and broadcast networks. (ii) The fundamental limits and practical design of distributed randomness generation algorithms are derived. These innovations lead to significant improvements over the state of the art both in terms of characterizations of asymptotic performance limits and constructive practical algorithms.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.