Moments of correlated digital signals for error probability evaluation

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.