On receiver structures for channels having memory

This paper is concerned with -ary communication channels having intersymbol interference between time periods . Receiver structures are developed for making jointly optimum (minimum probability of error) decisions about consecutive symbols on the basis of the complete message received. The decision statistics are computed by a sequential procedure, and the number of computations increases only linearly with the message length. The method can be applied to the general problem of making decisions about the states of a discrete-state Markov information source which is observable only through a channel with additive Gaussian or non-Gaussian noise.