{"doi":"10.1109/18.910572","title":"Factor graphs and the sum-product algorithm","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.","journal":"IEEE Transactions on Information Theory","year":2001,"id":6327,"datarank":27.44734090317676,"base_score":8.774467601446593,"endowment":8.774467601446593,"self_citation_contribution":1.3161701402169892,"citation_network_contribution":26.13117076295977,"self_endowment_contribution":1.3161701402169892,"citer_contribution":26.13117076295977,"corpus_percentile":96.8,"corpus_rank":2230,"citation_count":6466,"citer_count":195,"citers_with_citation_signal":195,"citers_with_endowment":195,"datacite_reuse_total":0,"is_dataset":false,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2001-01-01","authors":[{"id":58684,"name":"H.-A. Loeliger","orcid":null,"position":2,"is_corresponding":false},{"id":58685,"name":"Frank R. Kschischang","orcid":"0000-0002-4274-1785","position":3,"is_corresponding":false},{"id":53166,"name":"Brendan J. Frey","orcid":null,"position":4,"is_corresponding":false},{"id":58686,"name":"Hans‐Andrea Loeliger","orcid":"0000-0001-7153-7145","position":5,"is_corresponding":false},{"id":58682,"name":"F.R. Kschischang","orcid":null,"position":0,"is_corresponding":true}],"reference_count":33,"raw_metadata":{"citation_network_status":"fetched"},"created_at":"2026-03-01T18:20:47.508186Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}