Generalized distributive law

The generalized distributive law (GDL) is a generalization of the ordinary distributive property that gives rise to a general message-passing algorithm usable across several fields of computation. It synthesizes work from researchers across information theory, digital communications, signal processing, statistics and artificial intelligence, unifying a family of algorithms that these fields had developed somewhat independently for computing marginal quantities efficiently over structured problems. The law and its associated algorithm were introduced together in a semi-tutorial paper by Srinivas M. Aji and Robert J. McEliece under the same title, and the resulting message-passing formulation underlies specific techniques such as belief propagation and the forward-backward algorithm that are applied within those separate fields.