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A reduced-complexity MAP equalizer (RMAP) is proposed, together with an associate channel estimator, where only H channel states having largest probability are adaptively retained over the total of N states, with H≪N. For a channel length L, RMAP reduces the complexity from LN to LH. Channel estimator complexity is LH2 + HL2 instead of LN2. Performance analysis shows that P-MAP allows practical applications using state-of-art low-cost DSP devices: this is the case of a HF digital modem recently developed at Marconi Mobile laboratories.