CIF: Small: Collaborative Research: Between Shannon and Hamming

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Over the last 70 years, information theory and coding have enabled communication technologies that have had an astounding impact on everyday lives. This is possible due to the match between encoding/decoding strategies and corresponding models of the communication channel. Traditional models fall at two ends of a spectrum. Models which assume that the channel is random, such as those involving channel noise governed by a memoryless stochastic process, take an average-case view of the channel: such models are the basis of Shannon theory. At the other extreme, "Hamming"-like models take a worst-case view of the channel: the noise can be chosen adversarially with respect to the communication scheme. However, for several existing and emerging communication systems, the Shannon/average-case view may be too optimistic, whereas the Hamming/worst-case view may be too pessimistic. This project takes up the challenge of studying models that lie between the Shannon and Hamming extremes. The outcomes of this research will inform the design of codes for a multitude of practical settings where average-case interference models may be too optimistic and worst-case models may be too pessimistic, such as wireless multiple-frame communication systems in vehicular networks (VANETS) or the Internet of Things (IoT).The common way to view the distinction between average-case and worst-case analysis is operational: it is a difference in error criterion. This project takes a different perspective: the difference is in how the interference can depend on the transmitted codeword. This is modeled by assuming the interference is controlled by a jammer. A dependent jammer corresponds to the Hamming model while an independent one corresponds to that of Shannon. Restricting how jammer interference can depend on the codeword transmitted gives rise to models that lie between those of Shannon and Hamming. The project develops theoretical foundations for the study of communication models in which the jammer acts under varying degrees of uncertainty, and identifies new channel models, code designs, and capacity concepts. The project will develop a unified treatment of channel models that lie between the Shannon and Hamming model and abilities to (a) design optimal rate coding schemes that utilize the limitations posed on the jammer; (b) design secure communication schemes that leverage the jammer's constraints to improve traditional tradeoffs between capacity and security; and (c) inform the design of future practical codes.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.