AF: Small: RUI: New Directions in Kolmogorov Complexity and Network Information Theory

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Data communication in systems with multiple senders and receivers raises difficult problems caused by the possibility of complex data correlation patterns, network topologies, and interaction scenarios. Traditionally, these problems have been tackled using tools from Information Theory (IT), which assumes that the data has been produced according to a certain generative model. In practice, most of the time the generative model is not known. Even if it is known, it is often more complicated than the models typically used in theoretical studies. This project will use tools from Algorithmic Information Theory (AIT, also known as Kolmogorov complexity), which equates the information in a piece of data with its minimal description length. The advantage is that the new approach does not rely on any model, and consequently the results obtained this way are valid in more general circumstances. The problems that will be studied are of interest to computer scientists, electrical engineers, and mathematicians. The project will promote a deep and dynamic exchange of ideas between these communities. This project will produce new insights in Kolmogorov complexity and communication complexity. These areas have applications in computational complexity, machine learning, constructive combinatorics, and other fields. The results will likely have an impact in many of these areas. The project will allow undergraduate and graduate students to participate in research activities that have a strong theoretical flavor and the promise of real-world applications.The project is timely and realistic because it has recently become apparent that some interesting questions (for instance, source coding of non-ergodic sources), which cannot be approached with tools based on Shannon entropy, can be solved in the AIT framework. In the other direction, there has been recent progress in some classical problems in Kolmogorov complexity inspired from results and techniques from IT. The project will: (1) isolate, understand, and develop certain aspects of Kolmogorov complexity that are particularly relevant for data communication; (2) use the newly-developed tools to make progress in outstanding problems in network communication such as channel coding, network coding, interactive protocols, and others; and (3) use the insights from the communication setting to advance the theory of Kolmogorov complexity.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.