{"id":"https://openalex.org/W1992214737","doi":"https://doi.org/10.1109/tit.1980.1056164","title":"Distortion-rate theory for individual sequences","display_name":"Distortion-rate theory for individual sequences","publication_year":1980,"publication_date":"1980-03-01","ids":{"openalex":"https://openalex.org/W1992214737","doi":"https://doi.org/10.1109/tit.1980.1056164","mag":"1992214737"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1980.1056164","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1980.1056164","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/A5009331032","display_name":"J. Ziv","orcid":null},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"J. Ziv","raw_affiliation_strings":["Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa, Israel"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5009331032"],"corresponding_institution_ids":["https://openalex.org/I174306211"],"apc_list":null,"apc_paid":null,"fwci":1.3894,"has_fulltext":false,"cited_by_count":73,"citation_normalized_percentile":{"value":0.85679117,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"26","issue":"2","first_page":"137","last_page":"143"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9994999766349792,"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"}},{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9994999766349792,"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/T12029","display_name":"DNA and Biological Computing","score":0.9991999864578247,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/encoder","display_name":"Encoder","score":0.52946937084198},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4766070246696472},{"id":"https://openalex.org/keywords/distortion","display_name":"Distortion (music)","score":0.44648152589797974},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.41891512274742126},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4102305769920349},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3805901110172272},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.32647836208343506},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1758289337158203},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.07364550232887268}],"concepts":[{"id":"https://openalex.org/C118505674","wikidata":"https://www.wikidata.org/wiki/Q42586063","display_name":"Encoder","level":2,"score":0.52946937084198},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4766070246696472},{"id":"https://openalex.org/C126780896","wikidata":"https://www.wikidata.org/wiki/Q899871","display_name":"Distortion (music)","level":4,"score":0.44648152589797974},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.41891512274742126},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4102305769920349},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3805901110172272},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32647836208343506},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1758289337158203},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.07364550232887268},{"id":"https://openalex.org/C194257627","wikidata":"https://www.wikidata.org/wiki/Q211554","display_name":"Amplifier","level":3,"score":0.0},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1980.1056164","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1980.1056164","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":4,"referenced_works":["https://openalex.org/W1989008275","https://openalex.org/W1990992471","https://openalex.org/W2122962290","https://openalex.org/W2136864990"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W4390516098","https://openalex.org/W2181948922","https://openalex.org/W2384362569","https://openalex.org/W2053286651","https://openalex.org/W4205302943","https://openalex.org/W2142795561","https://openalex.org/W2366163563","https://openalex.org/W2163885456"],"abstract_inverted_index":{"For":[0],"every":[1,89,120],"individual":[2,100],"infinite":[3,90],"sequence":[4,91,122],"<tex":[5,13,34,49,69,109,123,143,148],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[6,14,35,50,70,110,124,144,149],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">u</tex>":[7,36,71,125],"we":[8],"define":[9],"a":[10,44,59,93,103,107],"distortion-rate":[11],"function":[12],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">d(R|u)</tex>":[15],"which":[16,41,84],"is":[17,54,72,112,116,139,151],"shown":[18,117],"to":[19,135],"be":[20,31],"an":[21],"asymptotically":[22,86,152],"attainable":[23],"lower":[24,140],"bound":[25],"on":[26],"the":[27,78,130,136],"distortion":[28,132],"that":[29],"can":[30],"achieved":[32],"for":[33,88,119],"by":[37,56,142],"any":[38,127],"finite-state":[39,128],"encoder":[40],"operates":[42],"at":[43],"fixed":[45],"output":[46],"information":[47],"rate":[48],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">R</tex>":[51],".":[52,146],"This":[53],"done":[55],"means":[57],"of":[58,68,80,99],"coding":[60,75],"theorem":[61,76],"and":[62,126],"its":[63],"converse.":[64],"No":[65],"probabilistic":[66],"characterization":[67],"assumed.":[73],"The":[74,97],"demonstrates":[77],"existence":[79],"{\\em":[81],"universal}":[82],"encoders":[83],"are":[85],"optimal":[87],"over":[92],"given":[94,121],"finite":[95],"alphabet.":[96],"transmission":[98],"sequences":[101],"via":[102],"noisy":[104],"channel":[105,137],"with":[106,133],"capacity":[108],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">C</tex>":[111],"also":[113],"investigated.":[114],"It":[115],"that,":[118],"encoder,":[129],"average":[131],"respect":[134],"statistics":[138],"bounded":[141],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">d(C|u)</tex>":[145,150],"Furthermore":[147],"attainable.":[153]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}