{"id":"https://openalex.org/W2131024393","doi":"https://doi.org/10.1109/tit.1973.1055092","title":"Universal noiseless coding","display_name":"Universal noiseless coding","publication_year":1973,"publication_date":"1973-11-01","ids":{"openalex":"https://openalex.org/W2131024393","doi":"https://doi.org/10.1109/tit.1973.1055092","mag":"2131024393"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1973.1055092","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1973.1055092","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/A5068322739","display_name":"L. Davisson","orcid":null},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"L. Davisson","raw_affiliation_strings":["Department of Electrical Engineering, University of Southern California, Los Angeles, CA, USA","Department of Electrical Engineering , University of Southern California , Los Angeles, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Southern California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I1174212"]},{"raw_affiliation_string":"Department of Electrical Engineering , University of Southern California , Los Angeles, CA, USA","institution_ids":["https://openalex.org/I1174212"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5068322739"],"corresponding_institution_ids":["https://openalex.org/I1174212"],"apc_list":null,"apc_paid":null,"fwci":8.4604,"has_fulltext":false,"cited_by_count":374,"citation_normalized_percentile":{"value":0.97971602,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"19","issue":"6","first_page":"783","last_page":"795"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10964","display_name":"Wireless Communication Security Techniques","score":0.9786999821662903,"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"}},"topics":[{"id":"https://openalex.org/T10964","display_name":"Wireless Communication Security Techniques","score":0.9786999821662903,"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/T10901","display_name":"Advanced Data Compression Techniques","score":0.9523000121116638,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11269","display_name":"Algorithms and Data Compression","score":0.9417999982833862,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/variable-length-code","display_name":"Variable-length code","score":0.7167134284973145},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.679819643497467},{"id":"https://openalex.org/keywords/shannon\u2013fano-coding","display_name":"Shannon\u2013Fano coding","score":0.6411498785018921},{"id":"https://openalex.org/keywords/minimax","display_name":"Minimax","score":0.600987434387207},{"id":"https://openalex.org/keywords/conditional-entropy","display_name":"Conditional entropy","score":0.5576347708702087},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5226811766624451},{"id":"https://openalex.org/keywords/entropy-rate","display_name":"Entropy rate","score":0.48986169695854187},{"id":"https://openalex.org/keywords/entropy-encoding","display_name":"Entropy encoding","score":0.46471962332725525},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.4564620554447174},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.45510804653167725},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4345620572566986},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.3796458840370178},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3461213707923889},{"id":"https://openalex.org/keywords/binary-entropy-function","display_name":"Binary entropy function","score":0.3454029858112335},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.2255343496799469},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.22011595964431763},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.17101532220840454},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.1494600772857666},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11316025257110596}],"concepts":[{"id":"https://openalex.org/C60603091","wikidata":"https://www.wikidata.org/wiki/Q2981616","display_name":"Variable-length code","level":3,"score":0.7167134284973145},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.679819643497467},{"id":"https://openalex.org/C130811719","wikidata":"https://www.wikidata.org/wiki/Q2645","display_name":"Shannon\u2013Fano coding","level":4,"score":0.6411498785018921},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.600987434387207},{"id":"https://openalex.org/C101721835","wikidata":"https://www.wikidata.org/wiki/Q813908","display_name":"Conditional entropy","level":3,"score":0.5576347708702087},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5226811766624451},{"id":"https://openalex.org/C125252325","wikidata":"https://www.wikidata.org/wiki/Q1345213","display_name":"Entropy rate","level":4,"score":0.48986169695854187},{"id":"https://openalex.org/C1769480","wikidata":"https://www.wikidata.org/wiki/Q1345239","display_name":"Entropy encoding","level":3,"score":0.46471962332725525},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.4564620554447174},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.45510804653167725},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4345620572566986},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.3796458840370178},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3461213707923889},{"id":"https://openalex.org/C44415725","wikidata":"https://www.wikidata.org/wiki/Q4913893","display_name":"Binary entropy function","level":3,"score":0.3454029858112335},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.2255343496799469},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.22011595964431763},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.17101532220840454},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.1494600772857666},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11316025257110596},{"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1973.1055092","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1973.1055092","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":[{"display_name":"Quality Education","id":"https://metadata.un.org/sdg/4","score":0.46000000834465027}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W778417515","https://openalex.org/W1608472120","https://openalex.org/W1990992471","https://openalex.org/W2005097301","https://openalex.org/W2016003972","https://openalex.org/W2016927358","https://openalex.org/W2034323860","https://openalex.org/W2061192159","https://openalex.org/W2097645910","https://openalex.org/W2135828943","https://openalex.org/W2141463438","https://openalex.org/W2295019788"],"related_works":["https://openalex.org/W1587903609","https://openalex.org/W2156106714","https://openalex.org/W2479819259","https://openalex.org/W2668751350","https://openalex.org/W4251361844","https://openalex.org/W1579872668","https://openalex.org/W4230922438","https://openalex.org/W1568325880","https://openalex.org/W2139507220","https://openalex.org/W2131024393"],"abstract_inverted_index":{"Universal":[0,86,107],"coding":[1,11,21,39,60,87,108,208],"is":[2,53,65,84,88,105,109,139,151,168,181,189,201,209],"any":[3,161],"asymptotically":[4],"optimum":[5],"method":[6],"of":[7,28,37,125,134,205,219],"block-to-block":[8],"memoryless":[9],"source":[10,46],"for":[12,22,129,160],"sources":[13,154],"with":[14,31,213],"unknown":[15,50,127],"parameters.":[16],"This":[17],"paper":[18],"considers":[19],"noiseless":[20],"such":[23,171],"sources,":[24,172],"primarily":[25],"in":[26,61,90,111],"terms":[27],"variable-length":[29],"coding,":[30],"performance":[32,214],"measured":[33,215],"as":[34],"a":[35,62,91,112,119,217],"function":[36,122],"the":[38,43,49,71,77,81,98,102,126,131,135,147,165,179,187],"redundancy":[40],"relative":[41,132],"to":[42,145,153],"per-letter":[44,72],"conditional":[45],"entropy":[47,133,188,198],"given":[48,144,152,211],"parameter.":[51],"It":[52],"found":[54],"that":[55,155],"universal":[56,174,192,207],"(i.e.,":[57],"zero":[58],"redundancy)":[59],"weighted":[63,173],"sense":[64,93,114],"possible":[66,89,110],"if":[67,70,94,97,115,118,178,186,195],"and":[68,80,95,116,158],"only":[69,96,117],"average":[73],"mutual":[74],"information":[75],"between":[76,101],"parameter":[78,163],"space":[79,83],"message":[82],"zero.":[85,106,140],"maximin":[92],"channel":[99],"capacity":[100],"two":[103],"spaces":[104],"minimax":[113],"probability":[120,218],"mass":[121],"exists,":[123],"independent":[124],"parameter,":[128],"which":[130],"known":[136],"conditional-probability":[137],"mass-function":[138],"Several":[141],"examples":[142],"are":[143,156],"illustrate":[146],"ideas.":[148],"Particular":[149],"attention":[150],"stationary":[157],"ergodic":[159],"fixed":[162],"although":[164],"whole":[166],"ensemble":[167],"not.":[169],"For":[170],"codes":[175,193],"always":[176],"exist":[177],"alphabet":[180],"finite,":[182],"or":[183],"more":[184],"generally":[185],"finite.":[190],"Minimax":[191],"result":[194],"an":[196],"additional":[197],"stability":[199],"constraint":[200],"applied.":[202],"A":[203],"discussion":[204],"fixed-rate":[206],"also":[210],"briefly":[212],"by":[216],"error.":[220]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":16},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":13}],"updated_date":"2026-05-12T08:28:47.272897","created_date":"2025-10-10T00:00:00"}