The problem of optimally detecting coded data transmitted over channels which produce intersymbol interference is examined. The optimum bit-by-bit detector structure which directly estimates the transmitted data symbols from the received signal at the channel output is given. The performance of this joint detector is contrasted to that of a receiver in which the decision process is partitioned into the usual detector followed by a decoder. Even when the detector and decoder are separately optimized (bit-by-bit criterion), the joint detector is shown to considerably out perform the separately optimized structure, thereby illustrating the considerable loss of information resulting from partitioning of the decision process. Two near optimum algorithms which significantly reduce the complexity of the optimum joint detector are given. These relatively simple algorithms, which approximate the joint detector, are shown to be capable of performance superior to that of the more complex, separately optimized detector/decoder structure. The joint detector and the approximate algorithms presented offer an attractive alternative to the soft decision decoder which also attempts to overcome the loss of information resulting from sharp partitioning of the detector/ decoder decisions.

Tight upper and lower bounds on the average probability of error are obtained for the nonlinear optimum sequential detector with zero look ahead. A linear upper bound is obtained that is very tight over a wide range of signal-to-noise ratios and a wide range of values of the intersymbol interference. The structure of the linear detector whose performance is given by the linear bound is determined and shown to take the form of a semi-infinite transversal equalizer. The tap values of the equalizer are related to the channel impulse response and the performance of realizable truncated equalizers is obtained in the form of the average probability of error versus equalizer length.

The real-time minimal-bit-error probability (RTMBEP) decoding procedure recently presented by Lee is compared with the sequential compound decoding procedure originally described by Abend and Fritchman for the detection of symbols in the presence of intersymbol interference. We compare the number of computations and the amount of storage required for each algorithm as well as show how Lee's procedure can be made more efficient.

We present a new descriptive statistic for channels with memory and show its utility a) in evaluating and comparing existing models for such channels and b) as a theoretical tool in defining the error-gap distribution characteristics of real channels. We demonstrate that certain kinds of real channel behavior cannot be adequately described by previously proposed models and offer an example of a better model that includes many of the earlier models as special cases.

The characterization of binary communication channels using functions of finite-state Markov chains is considered. Two distributions which are relevant to code evaluation, i.e., the error-free run and error-cluster distributions, are derived. It is shown for anN-state model, partitioned into a group ofkerror-free states andN-kerror states, that the general form of the error-free run distribution is the weighted sum of at mostkexponentials, and that of the error-cluster distribution the weighted sum of at mostN-kexponentials. As evidence of the capability of such models to characterize real communication channels, a simple class of models is investigated and shown experimentally to be capable of representing HF radio statistics.