Modern communication systems consist of channels which have memory, are time-varying, are often poorly modeled, and incorporate feedback. Furthermore, in many of these networks, the nodes are power limited and only have modest computational resources. Thus there is a pressing need for new single-user and multi-user communication techniques that treat channels with memory and feedback. This involves determining the capacity of these more complicated channels as well as designing error-correcting codes that perform well while incurring modest computational cost.
Feedback is a very important, though poorly understood, feature of modern communication systems. Feedback has many benefits including: (1) feedback can increase the capacity of a channel; (2) feedback can increase the error exponent and hence decrease latency; (3) feedback can often lead to simpler coding schemes; (4) feedback can allow for adaptation to unknown or time-varying channels; and (5) feedback can allow for coordination in multi-user settings. This research involves developing a general theory of feedback for reliable communication that fully exploits these different benefits. The four main objectives of this research are: (1) Determining fundamental limits and tradeoffs. This aspect of the project considers the fundamental limits and tradeoffs between the quality of the feedback and the resulting Shannon capacity of the channel. (2) Development of computational tools for computing capacity. This research will include software development. (3) Algorithm and error-correcting code development. This research supports the development of efficient codes that take advantage of feedback. (4) Educational development.
