Capacity and Coding Techniques for Channels with Memory and Feedback

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Abstract:The field of distributed networking and computation is on the verge of a technological revolution. Emerging applications in national security, transportation, communication, and commerce require distributed networks to be capable of multi-user communication and collaborative signal and information processing. One very important component of these networks is the underlying communication channel. These channels have memory, are often time-varying, and are often poorly modeled. Furthermore, in many of these networks, the nodes are power limited and only have modest computational resources. Feedback is a very important, though poorly understood, feature of modern communication systems. Feedback is useful because it can increase the capacity of a given channel with memory; it can increase the error exponent and hence decrease latency; it often leads to simpler coding schemes; and it allows the encoder to adapt to unknown channel variations.This research involves: (1) determining the fundamental limits and tradeoffs between the quality of channel feedback and the resulting Shannon capacity of the channel; (2) developing the sequential rate distortion theory for joint-source channel coding; (3) analyzing the convergence and accuracy of message-passing algorithms in general; and (4) developing message-passing, error-correcting codes specialized for channels with memory and feedback. The investigators use tools from the study of graphical models to jointly treat communication complexity and computational complexity.