An in-depth study of reliable communication over unknown channels with memory is proposed. Channels with memory are important in mobile wireless communication where they model random disturbances and distortions that vary in time due to the relative motion between the end-users and the dominant scatterers. In many applications the fast variations in the channel law are impossible to track, so that the encoding at the transmitter and the decoding at the receiver must be performed under channel law uncertainty. For this scenario Feder and Lapidoth have recently demonstrated the existence of a universal decoder. A universal decoder can be designed without knowing the channel in use, and yet it performs asymptotically as well as the optimal maximum-likelihood receiver tuned to the channel in use. The implementation of the universal decoder proposed by Feder and Lapidoth is, however, too complex, and in the proposed study a more efficient universal decoder will be sought. The issue of the transmitter design will be also addressed, and particularly the problem of designing error correcting codes that perform well on any channel in some family. Such codes should perform uniformly well and should lend themselves to universal decoding. The above problems relate to an additional problem that will be studied, namely the calculation of the compound channel capacity of a family of channels with memory. This capacity is the highest rate at which reliable communication can be guaranteed irrespective of which channel in the family is in use. This capacity is thus the ultimate bound on reliable communication when both transmitter and receiver are ignorant of the channel in use. Extension to the multiple-access channel, which models many-to-one communication (as in the reverse link from mobile subscribers to the base station in cellular telephony and in personal communications (PCS)), will be also considered. While the above problems are asymptotic in nature, a non-asymptotic analysis of the bit-error-rate that results when a convolutional code is decoded using a Viterbi decoder tuned to the wrong channel law is also proposed. This research is part of a five year career plan encompassing both teaching and research in information theory. The proposed research aims at bridging the gap between information theory and practical wireless communications and at simplifying some of the key ideas of information theory. Such simplifications will be used in order to supplement the electrical engineering and computer science undergraduate curriculum by introducing the notions of entropy, source coding, and channel coding early in a student's program. World Wide Web Link: http://lids.mit.edu/~lapidoth/amos.html
