The Bayesian decision procedure is given to determine a finite sequence of

-ary

digits that have been transmitted through a channel that has memory and introduces additive noise. Minimum probability of digit estimation error is used as the criterion of goodness. Intersymbol interference at the receiver input is assumed to exist between

successive digits. The parameter

is chosen so that

. This procedure is compared with several suboptimal procedures that are used to combat intersymbol interference and additive noise.