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We consider digital communications over channels affected by impulse noise. A two-state Markov channel model is adopted, which, unlike the memoryless models generally adopted in the literature, allows to describe the typical bursty nature of the impulse noise. We derive an algorithm for optimal maximum-a-posteriori symbol detection, which is first exploited for evaluating, by means of information-theoretical arguments, the ultimate performance limits imposed by the channel, and then is proposed as detection algorithm for practical communication systems employing iterative detection/decoding. The proposed scheme is finally shown to perform significantly better than the conventional ones which neglect the channel memory, and fairly close to the achievable theoretical limits.