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A discrete receiver structure is introduced that consolidates the problems of bit detection and bit synchronization to provide optimal estimates of bit values without explicit knowledge of the transition epoch. Equations are developed for the propagation of the discrete a posteriori density function on an interval-by-interval basis. The general model is developed for a signal corrupted by additive and multiplicative noise, and the receiver structure is shown to be equivalent to a synchronous discrete receiver. The model is applied to on-off-keyed (OOK) modulation in the presence of multipath.