Trellis Computations

TL;DR

This paper generalizes the BCJR algorithm to compute moments of function value distributions in trellises, enabling efficient belief propagation and entropy calculations for a broad class of functions.

Contribution

It introduces a moment computation algorithm for trellises that extends BCJR, applicable to any commutative semi-ring, and generalizes the Viterbi algorithm.

Findings

Efficient computation of moments in trellises with complexity similar to BCJR.

Applicable to any commutative semi-ring, broadening the scope of algorithms.

Enables entropy and belief propagation computations in trellis-based models.

Abstract

For a certain class of functions, the distribution of the function values can be calculated in the trellis or a sub-trellis. The forward/backward recursion known from the BCJR algorithm is generalized to compute the moments of these distributions. 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 actually providing a generalization of the Viterbi algorithm.