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Iterative decoding in the presence of unknown channel parameters requires the generation of symbol-by-symbol soft-decision metrics (SbSSDMs), jointly with parameter estimation. Traditional methods for the exact evaluation of these metrics have exponential complexity with the length of the data sequence. In this paper, a class of problems is identified, for which the exact SbSSDMs can be obtained with only polynomial complexity with the data sequence length. The applicability of this technique is demonstrated by considering the problem of iterative detection of low-density parity-check codes in the presence of unknown and time-varying carrier-phase offset.