Abstract :
We consider an information source which is an i.i.d. binary sequence governed by unknown probability measures. The information sequence is transferred through a memoryless binary channel with unknown cross-over probabilities. The channel model also represents those cases in which an input quantizer is always used, so that the incoming information-bearing observations are threshold crossings of the observation process, and the unknown cross-over probabilities are associated with uncertainties concerning the signal-to-noise ratio. We derive and study the optimal (under a minimum error-probability criterion) sequence estimator (which utilizes the observed threshold crossings). The receiver is described by a practically implementable algorithm which involves a shortest path calculation, which is performed using the Viterbi algorithm, and appropriately incorporates the sufficient statistics of the unknown parameters. Its similarity to unsupervised decision directed learning procedures is noted.
