On receiver structures for channels having memory

This paper is concerned with
m
-ary communication channels
(m \geq 2)
having intersymbol interference between
L
time periods
(L \geq 2)
. Receiver structures are developed for making jointly optimum (minimum probability of error) decisions about
L
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.