{"id":"https://openalex.org/W2120087366","doi":"https://doi.org/10.1109/tit.1957.1057416","title":"On the role of dynamic programming in statistical communication theory","display_name":"On the role of dynamic programming in statistical communication theory","publication_year":1957,"publication_date":"1957-09-01","ids":{"openalex":"https://openalex.org/W2120087366","doi":"https://doi.org/10.1109/tit.1957.1057416","mag":"2120087366"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1957.1057416","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1957.1057416","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/A5076973014","display_name":"Richard Bellman","orcid":null},"institutions":[{"id":"https://openalex.org/I1309849503","display_name":"RAND Corporation","ror":"https://ror.org/00f2z7n96","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I1309849503"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"R. Bellman","raw_affiliation_strings":["RAND Corporation, Santa Monica, CA, USA","RAND Corporation, Santa Monica CA, USA"],"affiliations":[{"raw_affiliation_string":"RAND Corporation, Santa Monica, CA, USA","institution_ids":["https://openalex.org/I1309849503"]},{"raw_affiliation_string":"RAND Corporation, Santa Monica CA, USA","institution_ids":["https://openalex.org/I1309849503"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113588041","display_name":"Robert E. Kalaba","orcid":null},"institutions":[{"id":"https://openalex.org/I1309849503","display_name":"RAND Corporation","ror":"https://ror.org/00f2z7n96","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I1309849503"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"R. Kalaba","raw_affiliation_strings":["RAND Corporation, Santa Monica, CA, USA","RAND Corporation, Santa Monica CA, USA"],"affiliations":[{"raw_affiliation_string":"RAND Corporation, Santa Monica, CA, USA","institution_ids":["https://openalex.org/I1309849503"]},{"raw_affiliation_string":"RAND Corporation, Santa Monica CA, USA","institution_ids":["https://openalex.org/I1309849503"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5076973014"],"corresponding_institution_ids":["https://openalex.org/I1309849503"],"apc_list":null,"apc_paid":null,"fwci":5.1887,"has_fulltext":false,"cited_by_count":98,"citation_normalized_percentile":{"value":0.95144158,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"3","issue":"3","first_page":"197","last_page":"203"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.9872000217437744,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9840999841690063,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6797372102737427},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"Dynamic programming","score":0.6618366241455078},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5636917948722839},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.5172591805458069},{"id":"https://openalex.org/keywords/stochastic-programming","display_name":"Stochastic programming","score":0.5092767477035522},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.49961161613464355},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.495828241109848},{"id":"https://openalex.org/keywords/communication-theory","display_name":"Communication theory","score":0.44580966234207153},{"id":"https://openalex.org/keywords/information-theory","display_name":"Information theory","score":0.43994849920272827},{"id":"https://openalex.org/keywords/decision-theory","display_name":"Decision theory","score":0.42004263401031494},{"id":"https://openalex.org/keywords/decision-problem","display_name":"Decision problem","score":0.4144919216632843},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.35213911533355713},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3111506700515747},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.20687603950500488}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6797372102737427},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.6618366241455078},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5636917948722839},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.5172591805458069},{"id":"https://openalex.org/C137631369","wikidata":"https://www.wikidata.org/wiki/Q7617831","display_name":"Stochastic programming","level":2,"score":0.5092767477035522},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.49961161613464355},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.495828241109848},{"id":"https://openalex.org/C3716254","wikidata":"https://www.wikidata.org/wiki/Q83966","display_name":"Communication theory","level":2,"score":0.44580966234207153},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.43994849920272827},{"id":"https://openalex.org/C28901747","wikidata":"https://www.wikidata.org/wiki/Q177571","display_name":"Decision theory","level":2,"score":0.42004263401031494},{"id":"https://openalex.org/C115988155","wikidata":"https://www.wikidata.org/wiki/Q3262192","display_name":"Decision problem","level":2,"score":0.4144919216632843},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.35213911533355713},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3111506700515747},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.20687603950500488},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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":1,"locations":[{"id":"doi:10.1109/tit.1957.1057416","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1957.1057416","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":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.7699999809265137}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1980516134","https://openalex.org/W1995875735","https://openalex.org/W1998498767","https://openalex.org/W2034489173","https://openalex.org/W2046495522","https://openalex.org/W2085610389","https://openalex.org/W2102672125","https://openalex.org/W2112008841","https://openalex.org/W2114509411","https://openalex.org/W2115931363","https://openalex.org/W2160580886","https://openalex.org/W4247878152","https://openalex.org/W6677233477"],"related_works":["https://openalex.org/W2019710194","https://openalex.org/W109523299","https://openalex.org/W2730638225","https://openalex.org/W2187982626","https://openalex.org/W3167044988","https://openalex.org/W3124982508","https://openalex.org/W1973492905","https://openalex.org/W2126014539","https://openalex.org/W2168607500","https://openalex.org/W2120087366"],"abstract_inverted_index":{"In":[0,105],"this":[1,106],"paper":[2],"we":[3,94,139],"wish":[4],"to":[5],"show":[6],"that":[7,113],"the":[8,13,29,47,60,86,89,117],"fundamental":[9],"problem":[10,27,62,100],"of":[11,15,31,35,46,49,59,65,72,85,88,91,119],"determining":[12],"utility":[14],"a":[16,26,82,99,129],"communication":[17],"channel":[18],"in":[19,63,97,144],"conveying":[20],"information":[21],"can":[22,125],"be":[23,42,126],"interpreted":[24],"as":[25,39,81,121],"within":[28],"framework":[30],"multistage":[32,66,131],"decision":[33,67,132],"processes":[34,75],"stochastic":[36,73],"type,":[37],"and":[38,76,152],"such":[40],"may":[41],"treated":[43],"by":[44,55,103,111,123],"means":[45],"theory":[48],"dynamic":[50,92],"programming.":[51],"We":[52],"shall":[53,95,140],"begin":[54],"formulating":[56],"some":[57,145],"aspects":[58],"general":[61],"terms":[64],"processes,":[68],"with":[69,134],"brief":[70],"descriptions":[71],"allocation":[74],"learning":[77],"processes.":[78],"Following":[79],"this,":[80],"simple":[83],"example":[84],"applicability":[87],"techniques":[90],"programming,":[93],"discuss":[96],"detail":[98],"posed":[101],"recently":[102],"Kelly.":[104],"paper,":[107],"it":[108],"is":[109],"shown":[110],"Kelly":[112],"under":[114],"certain":[115,130],"conditions,":[116],"rate":[118],"transmission,":[120],"defined":[122],"Shannon,":[124],"obtained":[127],"from":[128],"process":[133],"an":[135],"economic":[136],"criterion.":[137],"Here":[138],"complete":[141],"Kelly's":[142],"analysis":[143],"essential":[146],"points,":[147],"using":[148],"functional":[149],"equation":[150],"techniques,":[151],"considerably":[153],"extend":[154],"his":[155],"results.":[156]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-03-28T08:17:26.163206","created_date":"2025-10-10T00:00:00"}