{"id":"https://openalex.org/W2006503652","doi":"https://doi.org/10.1109/tit.1985.1057084","title":"Mutual information in stationary channels with additive noise","display_name":"Mutual information in stationary channels with additive noise","publication_year":1985,"publication_date":"1985-09-01","ids":{"openalex":"https://openalex.org/W2006503652","doi":"https://doi.org/10.1109/tit.1985.1057084","mag":"2006503652"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1985.1057084","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1985.1057084","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028231335","display_name":"Shunsuke Ihara","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"S. Ihara","raw_affiliation_strings":["Department of Mathematics, Chime University, Matsuyama, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Chime University, Matsuyama, Japan","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5028231335"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.11302826,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"31","issue":"5","first_page":"602","last_page":"606"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9926999807357788,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9926999807357788,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10964","display_name":"Wireless Communication Security Techniques","score":0.9904000163078308,"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9348000288009644,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.4349536895751953},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.42708516120910645},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37055498361587524},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34974485635757446},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3325173854827881},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.07715216279029846},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.0629330575466156}],"concepts":[{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.4349536895751953},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.42708516120910645},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37055498361587524},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34974485635757446},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3325173854827881},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.07715216279029846},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0629330575466156},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1985.1057084","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1985.1057084","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1526288311","https://openalex.org/W1580104600","https://openalex.org/W1989008275","https://openalex.org/W2033079303","https://openalex.org/W2071290088","https://openalex.org/W2091891040","https://openalex.org/W2135479785","https://openalex.org/W2136175486","https://openalex.org/W2146045000","https://openalex.org/W2153634854","https://openalex.org/W2155348268","https://openalex.org/W2264297261","https://openalex.org/W2322745064","https://openalex.org/W2912526818","https://openalex.org/W4229844634","https://openalex.org/W4241060531","https://openalex.org/W4246157440","https://openalex.org/W4252713891","https://openalex.org/W6634959688","https://openalex.org/W6681716550"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2478288626","https://openalex.org/W4391913857"],"abstract_inverted_index":{"A":[0],"continuous":[1],"time":[2],"stationary":[3,30],"channel":[4,34,46],"with":[5,96],"additive":[6],"noise":[7],"presented":[8],"by":[9],"<tex":[10,20,24,41,62,75,91,99,105,139,147],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[11,21,25,42,63,76,92,100,106,140,148],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">Y(t)":[12],"=":[13],"X(t)":[14],"+":[15,94],"Z(t)</tex>":[16],"is":[17,49,132],"considered,":[18],"where":[19],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\\{X(t)\\}</tex>":[22],"and":[23,36,40,72,102,119,128],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\\{Z(t)\\}</tex>":[26],"are":[27],"mutually":[28],"independent":[29],"processes":[31],"representing":[32],"the":[33,37,45,56,60,73,89,112,117,120,123,126,129,136],"input":[35,61],"noise,":[38],"respectively,":[39],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\\{Y(t)\\}</tex>":[43],"represents":[44],"output.":[47],"It":[48,131],"shown":[50,134],"that,":[51],"under":[52],"some":[53],"general":[54],"assumptions,":[55],"mutual":[57,114],"information":[58],"between":[59,116],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\\{":[64,77],"X(t);":[65],"0":[66,79],"\\leq":[67,69,80,82],"t":[68,81],"T":[70,83],"\\}</tex>":[71,84],"output":[74,127],"Y(t);":[78],"can":[85],"be":[86],"expressed":[87],"in":[88,109],"form":[90],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">AT":[93],"B(T)</tex>":[95],"a":[97,103,144],"constant":[98,145],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">A</tex>":[101],"function":[104],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">B(T)</tex>":[107,141],"given":[108,122],"terms":[110],"of":[111,125],"conditional":[113],"informations":[115],"\"past\"":[118],"\"future\"":[121],"\"present\"":[124],"noise.":[130],"also":[133],"that":[135],"remainder":[137],"term":[138],"converges":[142],"to":[143,151],"as":[146],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">T</tex>":[149],"tends":[150],"infinity.":[152]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}