Computation of distributions and their moments in the trellis

Consider a function whose set of vector arguments with known distribution is described by a trellis. For a certain class of functions, the distribution of the function values can be calculated in the trellis. The for- ward/backward recursion known from the BCJR algorithm [2] is generalized to compute the moments of these distributions. In analogy to the symbol prob- abilities, by introducing a constraint at a certain depth in the trellis we obtain symbol distributions and symbol moments, respectively. These moments are required for an efficient implementation of the discriminated belief propaga- tion algorithm in [8], and can furthermore be utilized to compute conditional entropies in the trellis. The moment computation algorithm has the same asymptotic complexity as the BCJR algorithm. It is applicable to any commutative semi-ring, thus actually providing a generalization of the Viterbi algorithm [10].