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Factor graphs and the sum-product algorithm

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3 Author(s)
Kschischang, F.R. ; Dept. of Electr. & Comput. Eng., Toronto Univ., Ont., Canada ; Frey, B.J. ; Loeliger, H.-A.

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

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Information Theory, IEEE Transactions on  (Volume:47 ,  Issue: 2 )