Factor graphs and the sum-product algorithm

Author

Kschischang, Frank R. ; Frey, Brendan J. ; Loeliger, Hans-Andrea

Author_Institution

Dept. of Electr. & Comput. Eng., Toronto Univ., Ont., Canada

Volume

47

Issue

2

fYear

2001

fDate

2/1/2001 12:00:00 AM

Firstpage

498

Lastpage

519

Abstract

Algorithms that must deal with complicated global functions of many variables often exploit the manner in which the given functions factor as a product of “local” functions, each of which depends on a subset of the variables. Such a factorization can be visualized with a bipartite graph that we call a factor graph, In this tutorial paper, we present a generic message-passing algorithm, the sum-product algorithm, that operates in a factor graph. Following a single, simple computational rule, the sum-product algorithm computes-either exactly or approximately-various marginal functions derived from the global function. A wide variety of algorithms developed in artificial intelligence, signal processing, and digital communications can be derived as specific instances of the sum-product algorithm, including the forward/backward algorithm, the Viterbi algorithm, the iterative “turbo” decoding algorithm, Pearl´s (1988) belief propagation algorithm for Bayesian networks, the Kalman filter, and certain fast Fourier transform (FFT) algorithms

Keywords

Kalman filters; Viterbi decoding; artificial intelligence; belief networks; digital communication; fast Fourier transforms; functional analysis; graph theory; hidden Markov models; iterative decoding; message passing; signal processing; turbo codes; Bayesian networks; FFT algorithms; HMM; Kalman filter; Viterbi algorithm; artificial intelligence; belief propagation algorithm; bipartite graph; computational rule; digital communications; factor graphs; factorization; fast Fourier transform; forward/backward algorithm; generic message-passing algorithm; global function; global functions; iterative turbo decoding algorithm; local functions; marginal functions; signal processing; sum-product algorithm; Artificial intelligence; Bipartite graph; Digital communication; Digital signal processing; Iterative algorithms; Iterative decoding; Signal processing algorithms; Sum product algorithm; Visualization; Viterbi algorithm;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.910572

Filename

910572