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In digital communication systems, the error probability in the presence of intersymbol interference (II) and additive noise may be calculated to any desired degree of accuracy by well-known approximation methods which avoid the exponential computation growth (with the number of interferers) inherent in an exhaustive method, on the condition that a fast technique for computing II moments is available. Such a technique is indeed available at present, but it is strongly limited by the assumption that the data symbols are mutually independent. In this paper, this limitation is removed, and a fast procedure is given for computing H moments of correlated digital signals. The computations grow linearly with the number of interferers. The assumption made is that correlated symbols are produced by a general finite-state sequential machine. As illustrative examples, the fast procedure is applied to bipolar and Franaszek MS-43 codes.