Computation of Moments in the Trellis

Abstract

Decisions on sources with memory transmitted over independent channels can be taken by employing trellis calculations. In this paper, it is shown that for a certain class of functions their moments can be computed in the trellis, too. This is done by generalizing the forward/backward recursion known from the BCJR algorithm [1]. In analogy to the symbol probabilities, by introducing a constraint at a certain depth in the trellis we obtain symbol moments. These moments are required for an efficient implementation of the discriminated belief propagation algorithm in [2], 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 also providing a generalization of the Viterbi algorithm [3].