CIF: Small: Structured-Network Coding: Fundamental Limits via Submodular Function Optimization
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Distributed and cloud storage are emerging technologies that transform the way personal and enterprise data are managed today. This project proposes network coding as a modeling tool to study efficient design and operation of distributed and cloud storage systems. The principal aim of this project is to develop mathematical tools that build upon the submodularity of Shannon entropy to capture the structure of such engineering network coding problems, yielding strong yet easy-to-compute network coding bounds. Two specific focuses of this project are: 1) combinatorial characterization of subset entropy inequalities; and 2) generalized cut-set bounds for broadcast networks.Our proposed study of network coding represents a significant deviation from the traditional view, where network coding is seen as a collection of pure mathematical problems. This deviation allows us to focus on the appropriate tools from combinatorics and information theory and draw strength from engineering intuitions. Both the theoretical development and the engineering results from this project are expected to impact how the field of network coding evolves over the next few years. The proposed research programs are hand-in-hand with our continuing efforts in training undergraduate and graduate students, broadening the participation of women and African Americans in engineering, and encouraging future scientists through outreach to high-school students.