{"id":"https://openalex.org/W1969010274","doi":"https://doi.org/10.1109/tit.2012.2217312","title":"Codes on Graphs: Observability, Controllability, and Local Reducibility","display_name":"Codes on Graphs: Observability, Controllability, and Local Reducibility","publication_year":2012,"publication_date":"2012-09-05","ids":{"openalex":"https://openalex.org/W1969010274","doi":"https://doi.org/10.1109/tit.2012.2217312","mag":"1969010274"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2012.2217312","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2012.2217312","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/1721.1/86145","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023619541","display_name":"G. David Forney","orcid":"https://orcid.org/0000-0003-1711-5974"},"institutions":[{"id":"https://openalex.org/I4210143601","display_name":"Decision Systems (United States)","ror":"https://ror.org/0434dpa13","country_code":"US","type":"company","lineage":["https://openalex.org/I4210143601"]},{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"G. David Forney","raw_affiliation_strings":["Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, MA, USA","Labs. for Inf. & Decision Syst., Massachusetts Inst. of Technol., Cambridge, MA, USA"],"affiliations":[{"raw_affiliation_string":"Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I4210143601","https://openalex.org/I63966007"]},{"raw_affiliation_string":"Labs. for Inf. & Decision Syst., Massachusetts Inst. of Technol., Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089040743","display_name":"Heide Gluesing-Luerssen","orcid":"https://orcid.org/0000-0002-2780-192X"},"institutions":[{"id":"https://openalex.org/I143302722","display_name":"University of Kentucky","ror":"https://ror.org/02k3smh20","country_code":"US","type":"education","lineage":["https://openalex.org/I143302722"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Heide Gluesing-Luerssen","raw_affiliation_strings":["Department of Mathematics, University of Kentucky, Lexington, KY, USA","Dept. of Math., Univ. of Kentucky, Lexington, KY, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Kentucky, Lexington, KY, USA","institution_ids":["https://openalex.org/I143302722"]},{"raw_affiliation_string":"Dept. of Math., Univ. of Kentucky, Lexington, KY, USA#TAB#","institution_ids":["https://openalex.org/I143302722"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5023619541"],"corresponding_institution_ids":["https://openalex.org/I4210143601","https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":3.008,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.9111183,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"59","issue":"1","first_page":"223","last_page":"237"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9923999905586243,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/unobservable","display_name":"Unobservable","score":0.7650003433227539},{"id":"https://openalex.org/keywords/controllability","display_name":"Controllability","score":0.7409268617630005},{"id":"https://openalex.org/keywords/observability","display_name":"Observability","score":0.7044482827186584},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6900312304496765},{"id":"https://openalex.org/keywords/realization","display_name":"Realization (probability)","score":0.6877725124359131},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.49668627977371216},{"id":"https://openalex.org/keywords/group-code","display_name":"Group code","score":0.4835624396800995},{"id":"https://openalex.org/keywords/observable","display_name":"Observable","score":0.48351767659187317},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.3370177149772644},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3291524648666382},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.32075732946395874},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.28447872400283813},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.21102529764175415},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.19088569283485413},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.13662084937095642}],"concepts":[{"id":"https://openalex.org/C2780695315","wikidata":"https://www.wikidata.org/wiki/Q3799040","display_name":"Unobservable","level":2,"score":0.7650003433227539},{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.7409268617630005},{"id":"https://openalex.org/C36299963","wikidata":"https://www.wikidata.org/wiki/Q1369844","display_name":"Observability","level":2,"score":0.7044482827186584},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6900312304496765},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.6877725124359131},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49668627977371216},{"id":"https://openalex.org/C3427991","wikidata":"https://www.wikidata.org/wiki/Q651426","display_name":"Group code","level":5,"score":0.4835624396800995},{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.48351767659187317},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.3370177149772644},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3291524648666382},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.32075732946395874},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.28447872400283813},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.21102529764175415},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19088569283485413},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.13662084937095642},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2012.2217312","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2012.2217312","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:dspace.mit.edu:1721.1/86145","is_oa":true,"landing_page_url":"http://hdl.handle.net/1721.1/86145","pdf_url":null,"source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv","raw_type":"http://purl.org/eprint/type/JournalArticle"}],"best_oa_location":{"id":"pmh:oai:dspace.mit.edu:1721.1/86145","is_oa":true,"landing_page_url":"http://hdl.handle.net/1721.1/86145","pdf_url":null,"source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv","raw_type":"http://purl.org/eprint/type/JournalArticle"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W63990713","https://openalex.org/W1556443961","https://openalex.org/W1557743522","https://openalex.org/W1571565904","https://openalex.org/W1588943481","https://openalex.org/W1970851820","https://openalex.org/W1973509019","https://openalex.org/W1983001515","https://openalex.org/W1991706950","https://openalex.org/W2079808112","https://openalex.org/W2083394863","https://openalex.org/W2095702447","https://openalex.org/W2100053622","https://openalex.org/W2101726023","https://openalex.org/W2109914229","https://openalex.org/W2110433946","https://openalex.org/W2115002719","https://openalex.org/W2116815462","https://openalex.org/W2127432024","https://openalex.org/W2133068391","https://openalex.org/W2133321180","https://openalex.org/W2137688127","https://openalex.org/W2138628599","https://openalex.org/W2139584447","https://openalex.org/W2142486636","https://openalex.org/W2155364287","https://openalex.org/W2159171897","https://openalex.org/W2169834720","https://openalex.org/W3099434145","https://openalex.org/W3102147737"],"related_works":["https://openalex.org/W2149686805","https://openalex.org/W4294689033","https://openalex.org/W4226462367","https://openalex.org/W1978158123","https://openalex.org/W2967463586","https://openalex.org/W2082642870","https://openalex.org/W2378270039","https://openalex.org/W1789159349","https://openalex.org/W4237217078","https://openalex.org/W4205600360"],"abstract_inverted_index":{"This":[0],"paper":[1],"investigates":[2],"properties":[3,24],"of":[4,6,25,164],"realizations":[5,125],"linear":[7,29,48,94],"or":[8,30,49,95,118],"group":[9,31,50,96],"codes":[10],"on":[11,52],"general":[12,160],"graphs":[13],"that":[14,37],"lead":[15],"to":[16],"local":[17,64],"reducibility.":[18],"Trimness":[19],"and":[20,42,60,69,84,86,101,129],"properness":[21],"are":[22,126],"dual":[23,105],"constraint":[26,35,65],"codes.":[27],"A":[28,47,71,93,108],"realization":[32,51,72,97,120],"with":[33],"a":[34,53,79,159,169],"code":[36,66],"is":[38,44,57,67,73,78,98,106,114,121,168],"not":[39,153],"both":[40],"trim":[41,68],"proper":[43],"locally":[45,122],"reducible.":[46,123],"finite":[54],"cycle-free":[55],"graph":[56],"minimal":[58],"if":[59,62,76,88,100,103,128,131],"only":[61,102,130],"every":[63],"proper.":[70],"called":[74],"observable":[75,99],"there":[77],"one-to-one":[80],"correspondence":[81],"between":[82],"codewords":[83],"configurations,":[85],"controllable":[87,127],"it":[89],"has":[90],"independent":[91,134],"constraints.":[92],"its":[104],"controllable.":[107],"simple":[109],"counting":[110],"test":[111],"for":[112,155],"controllability":[113],"given.":[115],"An":[116],"unobservable":[117,166],"uncontrollable":[119,139],"Parity-check":[124],"they":[132],"have":[133],"parity":[135],"checks.":[136],"In":[137],"an":[138,165],"tail-biting":[140],"trellis":[141],"realization,":[142],"the":[143,162],"behavior":[144],"partitions":[145],"into":[146],"disconnected":[147],"sub-behaviors,":[148],"but":[149],"this":[150],"property":[151],"does":[152],"hold":[154],"nontrellis":[156],"realizations.":[157],"On":[158],"graph,":[161],"support":[163],"configuration":[167],"generalized":[170],"cycle.":[171]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}