{"id":"https://openalex.org/W2055094761","doi":"https://doi.org/10.1109/tit.1981.1056377","title":"The error exponent for the noiseless encoding of finite ergodic Markov sources","display_name":"The error exponent for the noiseless encoding of finite ergodic Markov sources","publication_year":1981,"publication_date":"1981-07-01","ids":{"openalex":"https://openalex.org/W2055094761","doi":"https://doi.org/10.1109/tit.1981.1056377","mag":"2055094761"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1981.1056377","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1981.1056377","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/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"L. Davisson","raw_affiliation_strings":["Department of Electrical Engineering, University of Maryland, College Park, MD, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Maryland, College Park, MD, USA","institution_ids":["https://openalex.org/I66946132"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028392415","display_name":"G. Longo","orcid":"https://orcid.org/0000-0002-9182-8414"},"institutions":[{"id":"https://openalex.org/I142444530","display_name":"University of Trieste","ror":"https://ror.org/02n742c10","country_code":"IT","type":"education","lineage":["https://openalex.org/I142444530"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"G. Longo","raw_affiliation_strings":["Instituto di Electrotecnica ed Elettronica, Universita di Trieste, Trieste, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto di Electrotecnica ed Elettronica, Universita di Trieste, Trieste, Italy","institution_ids":["https://openalex.org/I142444530"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031727612","display_name":"Andrea Sgarro","orcid":"https://orcid.org/0000-0002-7048-1466"},"institutions":[{"id":"https://openalex.org/I2802561039","display_name":"Elettra-Sincrotrone Trieste S.C.p.A.","ror":"https://ror.org/01c3rrh15","country_code":"IT","type":"facility","lineage":["https://openalex.org/I2801626668","https://openalex.org/I2802561039"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"A. Sgarro","raw_affiliation_strings":["Istituto diElettrotecnica edElettronica and the Istituto diMatematica, Universita di Trieste, Trieste, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Istituto diElettrotecnica edElettronica and the Istituto diMatematica, Universita di Trieste, Trieste, Italy","institution_ids":["https://openalex.org/I2802561039"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7789,"has_fulltext":false,"cited_by_count":85,"citation_normalized_percentile":{"value":0.84109025,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"27","issue":"4","first_page":"431","last_page":"438"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10964","display_name":"Wireless Communication Security Techniques","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9944000244140625,"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"}},{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9878000020980835,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/ergodic-theory","display_name":"Ergodic theory","score":0.8047597408294678},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.6636399626731873},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6077823042869568},{"id":"https://openalex.org/keywords/corollary","display_name":"Corollary","score":0.5494942665100098},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5428604483604431},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.49577435851097107},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.4868744909763336},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.43153250217437744},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.4268289804458618},{"id":"https://openalex.org/keywords/shannons-source-coding-theorem","display_name":"Shannon's source coding theorem","score":0.4135044515132904},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.33582162857055664},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3357440233230591},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.303083598613739},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.14513757824897766},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11725825071334839},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.08153781294822693}],"concepts":[{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.8047597408294678},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.6636399626731873},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6077823042869568},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.5494942665100098},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5428604483604431},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.49577435851097107},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.4868744909763336},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.43153250217437744},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.4268289804458618},{"id":"https://openalex.org/C177409962","wikidata":"https://www.wikidata.org/wiki/Q2411312","display_name":"Shannon's source coding theorem","level":5,"score":0.4135044515132904},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.33582162857055664},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3357440233230591},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.303083598613739},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.14513757824897766},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11725825071334839},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.08153781294822693},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C49775889","wikidata":"https://www.wikidata.org/wiki/Q6795896","display_name":"Maximum entropy thermodynamics","level":4,"score":0.0},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"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/C44415725","wikidata":"https://www.wikidata.org/wiki/Q4913893","display_name":"Binary entropy function","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1981.1056377","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1981.1056377","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1530753374","https://openalex.org/W1549664537","https://openalex.org/W2024387237","https://openalex.org/W2057756383","https://openalex.org/W2079976550","https://openalex.org/W2113348989","https://openalex.org/W2751862591","https://openalex.org/W3160337542","https://openalex.org/W7065666170"],"related_works":["https://openalex.org/W2171296020","https://openalex.org/W2132038253","https://openalex.org/W2901423989","https://openalex.org/W2502624504","https://openalex.org/W2941284322","https://openalex.org/W1978306740","https://openalex.org/W1644122836","https://openalex.org/W1982997203","https://openalex.org/W2883856176","https://openalex.org/W3013412531"],"abstract_inverted_index":{"A":[0],"new":[1],"approach":[2,22],"to":[3,49,71],"the":[4,14,39,43,54,80,84,91,97],"classical":[5,92],"fixed-length":[6],"noiseless":[7],"source":[8,40,93],"coding":[9,94],"problem":[10],"is":[11,23,51,60,69,86,100],"proposed":[12],"for":[13],"case":[15],"of":[16,32,56,76,83],"finite":[17],"ergodic":[18],"Markov":[19],"sources.":[20],"This":[21],"based":[24],"on":[25],"simple":[26],"counting":[27],"arguments.":[28],"The":[29,66],"central":[30],"notion":[31],"\"Markov":[33],"type\"":[34],"(a":[35],"set":[36,59],"containing":[37],"all":[38],"sequences":[41],"having":[42],"same":[44],"transition":[45],"counts":[46],"from":[47],"letter":[48],"letter)":[50],"introduced":[52],"and":[53,79],"cardinality":[55],"such":[57],"a":[58,73,89],"evaluated":[61],"via":[62],"graph":[63],"theoretical":[64],"tools.":[65],"error":[67],"exponent":[68],"shown":[70],"be":[72],"weighted":[74],"average":[75],"informational":[77],"divergences,":[78],"universal":[81],"character":[82],"result":[85],"stressed.":[87],"As":[88],"corollary,":[90],"theorem":[95],"(determining":[96],"achievable":[98],"rates)":[99],"rederived.":[101]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}