In this research the goal is to develop a nonparametric adaptive communications receiver strategy by exploiting results from the theory of universal classification and data compression. Analysis based upon the "typicality" of the data has become one of the primary theoretical and practical concepts in modern information theory. The so-called "Type" (appropriate histogram estimators of the amplitude distribution) have not only been shown to be sufficient statistics for both classification and compression, but have also been shown to converge exponentially fast to the true underlying distribution. Because type-based detectors make no a priori assumptions about the channel characteristics and measure the quantities needed to provide asymptotically optimal reception, these detectors can theoretically achieve the same exponential error rate as the clairvoyant receiver that knows the channel characteristics perfectly and uses them optimally. Measurements made during succeeding transmissions, possibly using the data transmissions themselves in a decision feedback paradigm, can be used to track channel variations. The approach will be extended to deal with intersample dependencies and colored noise by using channel measurements in an optimally effective way. Two techniques drawn from data compression work, context trees and Lempel-Ziv (universal) coding, will be examined to determine which represents channel-induced dependencies most efficiently and which is most adaptable. By merging systems based on these two theories, a receiver that adapts to unknown, time-varying channels will be developed. It will be demonstrated that this receiver can be used in multiuser channels, both wireless and optical fiber, with little modification. The research will develop the theoretical underpinnings of this adaptive receiver strategy, and will develop a complete software implementation of the receiver, using as test data actual communication channel recordings. This work will be performed by a close collaboration of researchers from Rice University and George Mason University.
