An Introduction to factor graphs - Signal Processing Magazine, IEEE

and artificial intelligence may be viewed as instances of the summary-product algorithm (or belief/probability propagation algorithm), which operates by message passing in a graphical model. Specific instances of such algorithms include Kalman filtering and smoothing; the forward–backward algorithm for hidden Markov models; probability propagation in Bayesian networks; and decoding algorithms for error-correcting codes such as the Viterbi algorithm, the BCJR algorithm, and the iterative decoding of turbo codes, low-density parity-check (LDPC) codes, and similar codes. New algorithms for complex detection and estimation problems can also be derived as instances of the summary-product algorithm. In this article, we give an introduction to this unified perspective in terms of (Forney-style) factor graphs. Hans-Andrea Loeliger