# American Institute of Mathematical Sciences

November  2008, 2(4): 373-391. doi: 10.3934/amc.2008.2.373

## Computation of distributions and their moments in the trellis

 1 Institute of Telecommunications and Applied Information Theory, Ulm University, Albert-Einstein-Allee 43, 89083 Ulm, Germany, Germany 2 Computer Science and Communications Research Unit, University of Luxembourg, 6, rue Richard Coudenhove-Kalergi, L-1359 Luxembourg

Received  November 2007 Revised  June 2008 Published  November 2008

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 forward/backward recursion known from the BCJR algorithm [2] 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 distributions and symbol moments, respectively. These moments are required for an efficient implementation of the discriminated belief propagation 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].
Citation: Axel Heim, Vladimir Sidorenko, Uli Sorger. Computation of distributions and their moments in the trellis. Advances in Mathematics of Communications, 2008, 2 (4) : 373-391. doi: 10.3934/amc.2008.2.373
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