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We consider an information source that is an independent identically distributed (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 (SNR). 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 practical implementable algorithm that 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.