{"id":"https://openalex.org/W2115468292","doi":"https://doi.org/10.1109/tit.1974.1055248","title":"Source coding theorems without the ergodic assumption","display_name":"Source coding theorems without the ergodic assumption","publication_year":1974,"publication_date":"1974-07-01","ids":{"openalex":"https://openalex.org/W2115468292","doi":"https://doi.org/10.1109/tit.1974.1055248","mag":"2115468292"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1974.1055248","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1974.1055248","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/A5061042317","display_name":"Robert M. Gray","orcid":"https://orcid.org/0000-0002-6947-3637"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"R. Gray","raw_affiliation_strings":["Department of Electrical Engineering, University of Stanford, Stanford, CA, USA","[Department of Electrical Engineering, University of Stanford, Stanford, CA, USA]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Stanford, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"[Department of Electrical Engineering, University of Stanford, Stanford, CA, USA]","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"last","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":false,"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":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.3954,"has_fulltext":false,"cited_by_count":73,"citation_normalized_percentile":{"value":0.97787106,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"20","issue":"4","first_page":"502","last_page":"516"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10964","display_name":"Wireless Communication Security Techniques","score":0.9975000023841858,"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":0.9975000023841858,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9972000122070312,"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"}},{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.996399998664856,"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/ergodic-theory","display_name":"Ergodic theory","score":0.8903621435165405},{"id":"https://openalex.org/keywords/stationary-ergodic-process","display_name":"Stationary ergodic process","score":0.6949815154075623},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6847150325775146},{"id":"https://openalex.org/keywords/source-code","display_name":"Source code","score":0.6084384322166443},{"id":"https://openalex.org/keywords/rate\u2013distortion-theory","display_name":"Rate\u2013distortion theory","score":0.5438814759254456},{"id":"https://openalex.org/keywords/distortion","display_name":"Distortion (music)","score":0.4968107044696808},{"id":"https://openalex.org/keywords/fidelity","display_name":"Fidelity","score":0.48447608947753906},{"id":"https://openalex.org/keywords/shannon\u2013fano-coding","display_name":"Shannon\u2013Fano coding","score":0.4788251221179962},{"id":"https://openalex.org/keywords/distortion-function","display_name":"Distortion function","score":0.47337406873703003},{"id":"https://openalex.org/keywords/variable-length-code","display_name":"Variable-length code","score":0.4374704957008362},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.39666324853897095},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3841034770011902},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34289270639419556},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.31493568420410156},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24218636751174927},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1983756721019745},{"id":"https://openalex.org/keywords/invariant-measure","display_name":"Invariant measure","score":0.1891099512577057},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.1835518777370453},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.16726580262184143},{"id":"https://openalex.org/keywords/bandwidth","display_name":"Bandwidth (computing)","score":0.07199645042419434}],"concepts":[{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.8903621435165405},{"id":"https://openalex.org/C151424130","wikidata":"https://www.wikidata.org/wiki/Q17123911","display_name":"Stationary ergodic process","level":4,"score":0.6949815154075623},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6847150325775146},{"id":"https://openalex.org/C43126263","wikidata":"https://www.wikidata.org/wiki/Q128751","display_name":"Source code","level":2,"score":0.6084384322166443},{"id":"https://openalex.org/C64185310","wikidata":"https://www.wikidata.org/wiki/Q843483","display_name":"Rate\u2013distortion theory","level":3,"score":0.5438814759254456},{"id":"https://openalex.org/C126780896","wikidata":"https://www.wikidata.org/wiki/Q899871","display_name":"Distortion (music)","level":4,"score":0.4968107044696808},{"id":"https://openalex.org/C2776459999","wikidata":"https://www.wikidata.org/wiki/Q2119376","display_name":"Fidelity","level":2,"score":0.48447608947753906},{"id":"https://openalex.org/C130811719","wikidata":"https://www.wikidata.org/wiki/Q2645","display_name":"Shannon\u2013Fano coding","level":4,"score":0.4788251221179962},{"id":"https://openalex.org/C2780803321","wikidata":"https://www.wikidata.org/wiki/Q5283073","display_name":"Distortion function","level":3,"score":0.47337406873703003},{"id":"https://openalex.org/C60603091","wikidata":"https://www.wikidata.org/wiki/Q2981616","display_name":"Variable-length code","level":3,"score":0.4374704957008362},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.39666324853897095},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3841034770011902},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34289270639419556},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.31493568420410156},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24218636751174927},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1983756721019745},{"id":"https://openalex.org/C115667082","wikidata":"https://www.wikidata.org/wiki/Q4200518","display_name":"Invariant measure","level":3,"score":0.1891099512577057},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.1835518777370453},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.16726580262184143},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.07199645042419434},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C194257627","wikidata":"https://www.wikidata.org/wiki/Q211554","display_name":"Amplifier","level":3,"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/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1974.1055248","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1974.1055248","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":21,"referenced_works":["https://openalex.org/W586626860","https://openalex.org/W1555934787","https://openalex.org/W1577906631","https://openalex.org/W1590624540","https://openalex.org/W1594563152","https://openalex.org/W1989008275","https://openalex.org/W1997176148","https://openalex.org/W2029071561","https://openalex.org/W2048692459","https://openalex.org/W2070648893","https://openalex.org/W2075002608","https://openalex.org/W2123170467","https://openalex.org/W2131024393","https://openalex.org/W2159963124","https://openalex.org/W2160646668","https://openalex.org/W2312450606","https://openalex.org/W2407517355","https://openalex.org/W2914202085","https://openalex.org/W4234225207","https://openalex.org/W4255034261","https://openalex.org/W4298054937"],"related_works":["https://openalex.org/W4312628177","https://openalex.org/W2123072960","https://openalex.org/W2148686647","https://openalex.org/W1607635215","https://openalex.org/W2213686625","https://openalex.org/W1579872668","https://openalex.org/W1981833143","https://openalex.org/W2103203125","https://openalex.org/W2142368118","https://openalex.org/W2153621579"],"abstract_inverted_index":{"Source":[0],"coding":[1,90],"theorems":[2],"are":[3,95],"proved":[4],"for":[5,46],"discrete-time":[6],"stationary":[7],"processes":[8],"subject":[9],"to":[10,21,33,87],"a":[11,23,47,68,92],"fidelity":[12,93],"criterion.":[13],"The":[14],"alphabet":[15],"of":[16,57,71,75,82],"the":[17,28,37,42,54,58,72,79,83],"process":[18,29,38],"is":[19,30,39,50,64],"assumed":[20,32],"be":[22,34],"separable":[24],"metric":[25],"space,":[26],"but":[27],"not":[31,40,51],"ergodic.":[35],"When":[36],"ergodic,":[41],"minimum":[43],"average":[44,70],"distortion":[45],"fixed-rate":[48],"code":[49],"given":[52,65],"by":[53,67],"distortion-rate":[55,73],"function":[56],"source":[59,89],"as":[60],"usually":[61],"defined.":[62],"It":[63],"instead":[66],"weighted":[69],"functions":[74],"ergodic":[76,80],"subsources":[77],"comprising":[78],"decomposition":[81],"source.":[84],"Potential":[85],"applications":[86],"universal":[88],"with":[91],"criterion":[94],"discussed.":[96]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
