CAREER: Network Information Theory: Coding for Communication, Control, and Computing

点击翻译按钮获取中文摘要

Despite significant advances in information theory and its application to point-to-point communications, a general theory governing optimal information flow over networks does not yet exist. Except for a few simple network models, the capacity region of a general memoryless network remains unknown, due to the complex tradeoff between competition and cooperation among many nodes in the network. Modern applications such as sensor networks, peer-to-peer systems, and distributed storages further bring up a new set of challenging problems spanning control, estimation, compression, computation,communication, as well as networking. This research program provides a common set of conceptual, mathematical, and algorithmic tools for the emerging convergence of computation, control, and communication over networks, with the ultimate goal of developing a unified framework for characterizing fundamental performance limits of such systems. Towards this goal, we focus on three concrete problems representing the intersection of computation, control, and communication -- 1) the capacity of the relay channel (how to summarize the relay's noisy observation of thecodeword: a list intersection technique via coding for distributed computing), 2) networked control (how to summarize the observation to stabilize a linear dynamical system: a variant of rate distortion coding for control), 3) collision avoidance for multiple access (how to build cooperation from a common source of randomness: a distributed generation of correlated random variables). Novel coding schemes will be proposed, while classical coding techniques will be reinterpreted and extended to broader applications. An algebraic framework for capacity regions is also developed to check the optimality of such coding schemes. The research program is complemented by educational activities that include the curriculum development for a graduate course on network information theory and the writing of an accompanied textbook.