{"id":"https://openalex.org/W2064761104","doi":"https://doi.org/10.1109/tit.2014.2358679","title":"On the Limiting Distribution of Lempel-Ziv\u201978 Redundancy for Memoryless Sources","display_name":"On the Limiting Distribution of Lempel-Ziv\u201978 Redundancy for Memoryless Sources","publication_year":2014,"publication_date":"2014-09-17","ids":{"openalex":"https://openalex.org/W2064761104","doi":"https://doi.org/10.1109/tit.2014.2358679","mag":"2064761104"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2014.2358679","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2014.2358679","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/A5102728318","display_name":"Philippe Jacquet","orcid":"https://orcid.org/0000-0001-7919-1206"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Philippe Jacquet","raw_affiliation_strings":["Alcatel-Lucent Bell Labs, Nozay, France"],"affiliations":[{"raw_affiliation_string":"Alcatel-Lucent Bell Labs, Nozay, France","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019536160","display_name":"Wojciech Szpankowski","orcid":"https://orcid.org/0000-0001-9062-0067"},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]},{"id":"https://openalex.org/I169333911","display_name":"Gda\u0144sk University of Technology","ror":"https://ror.org/006x4sc24","country_code":"PL","type":"education","lineage":["https://openalex.org/I169333911"]}],"countries":["PL","US"],"is_corresponding":false,"raw_author_name":"Wojciech Szpankowski","raw_affiliation_strings":["Department of Computer Science, Purdue University, West Lafayette, IN, USA","Faculty of Electronics, Telecommunications and Informatics, Gda\u0144sk University of Technology, Gda\u0144sk, Poland"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Purdue University, West Lafayette, IN, USA","institution_ids":["https://openalex.org/I219193219"]},{"raw_affiliation_string":"Faculty of Electronics, Telecommunications and Informatics, Gda\u0144sk University of Technology, Gda\u0144sk, Poland","institution_ids":["https://openalex.org/I169333911"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5102728318"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8487,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.81565331,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"60","issue":"11","first_page":"6917","last_page":"6930"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":1.0,"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":1.0,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9984999895095825,"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/T12162","display_name":"Cellular Automata and Applications","score":0.998199999332428,"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/mathematics","display_name":"Mathematics","score":0.7316714525222778},{"id":"https://openalex.org/keywords/redundancy","display_name":"Redundancy (engineering)","score":0.6775006651878357},{"id":"https://openalex.org/keywords/central-limit-theorem","display_name":"Central limit theorem","score":0.6651059985160828},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5521815419197083},{"id":"https://openalex.org/keywords/large-deviations-theory","display_name":"Large deviations theory","score":0.5091013312339783},{"id":"https://openalex.org/keywords/reliability-theory","display_name":"Reliability theory","score":0.4869009554386139},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.4782252013683319},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4425016939640045},{"id":"https://openalex.org/keywords/limiting","display_name":"Limiting","score":0.43739330768585205},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4175738990306854},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3921101689338684},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38744857907295227},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2924761176109314},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18095019459724426},{"id":"https://openalex.org/keywords/failure-rate","display_name":"Failure rate","score":0.16161075234413147},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.0851219892501831}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7316714525222778},{"id":"https://openalex.org/C152124472","wikidata":"https://www.wikidata.org/wiki/Q1204361","display_name":"Redundancy (engineering)","level":2,"score":0.6775006651878357},{"id":"https://openalex.org/C166785042","wikidata":"https://www.wikidata.org/wiki/Q190391","display_name":"Central limit theorem","level":2,"score":0.6651059985160828},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5521815419197083},{"id":"https://openalex.org/C75438885","wikidata":"https://www.wikidata.org/wiki/Q3403615","display_name":"Large deviations theory","level":2,"score":0.5091013312339783},{"id":"https://openalex.org/C201729545","wikidata":"https://www.wikidata.org/wiki/Q2193887","display_name":"Reliability theory","level":3,"score":0.4869009554386139},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4782252013683319},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4425016939640045},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.43739330768585205},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4175738990306854},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3921101689338684},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38744857907295227},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2924761176109314},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18095019459724426},{"id":"https://openalex.org/C163164238","wikidata":"https://www.wikidata.org/wiki/Q2737027","display_name":"Failure rate","level":2,"score":0.16161075234413147},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.0851219892501831},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"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/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.2014.2358679","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2014.2358679","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":[{"id":"https://openalex.org/G1892891731","display_name":null,"funder_award_id":"H98230-11-1-0141","funder_id":"https://openalex.org/F4320311089","funder_display_name":"National Security Agency"}],"funders":[{"id":"https://openalex.org/F4320311089","display_name":"National Security Agency","ror":"https://ror.org/0047bvr32"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1475522821","https://openalex.org/W1597723816","https://openalex.org/W1968884246","https://openalex.org/W1977970493","https://openalex.org/W2042464140","https://openalex.org/W2052638374","https://openalex.org/W2073613132","https://openalex.org/W2085901659","https://openalex.org/W2099111195","https://openalex.org/W2102021175","https://openalex.org/W2116952242","https://openalex.org/W2122962290","https://openalex.org/W2137902998","https://openalex.org/W2148107416","https://openalex.org/W2478708596","https://openalex.org/W2500470525","https://openalex.org/W2752853835","https://openalex.org/W2802739963","https://openalex.org/W3198160809","https://openalex.org/W4242659711","https://openalex.org/W4299533062"],"related_works":["https://openalex.org/W2076965643","https://openalex.org/W1984367576","https://openalex.org/W2063518863","https://openalex.org/W2613823738","https://openalex.org/W4297976967","https://openalex.org/W2963218531","https://openalex.org/W4313398236","https://openalex.org/W4296550467","https://openalex.org/W4299526956","https://openalex.org/W2769873724"],"abstract_inverted_index":{"We":[0,20,53],"study":[1],"the":[2,39,45,50,56,60,65,98,109,117,129,138,141],"Lempel-Ziv'78":[3],"algorithm":[4,92],"and":[5,103,106,125],"show":[6],"that":[7,116,128],"its":[8],"(normalized)":[9,110],"redundancy":[10,119],"rate":[11,120],"tends":[12],"to":[13,93],"a":[14,34,75],"Gaussian":[15],"distribution":[16],"for":[17,44,82,108],"memoryless":[18],"sources.":[19],"accomplish":[21],"it":[22],"by":[23,32],"extending":[24],"findings":[25],"from":[26,71],"our":[27,88],"1995":[28],"paper,":[29],"in":[30,49,64],"particular,":[31,113],"presenting":[33],"new":[35,95],"simplified":[36],"proof":[37],"of":[38,47,59,90,100,132,140],"central":[40],"limit":[41],"theorem":[42],"(CLT)":[43],"number":[46],"phrases":[48],"LZ'78":[51,83,91],"algorithm.":[52],"first":[54],"analyze":[55],"asymptotic":[57],"behavior":[58],"total":[61],"path":[62],"length":[63,139],"associated":[66],"digital":[67],"search":[68],"tree":[69],"built":[70],"independent":[72],"sequences.":[73],"Then,":[74],"renewal":[76],"theory":[77],"type":[78],"argument":[79],"yields":[80],"CLT":[81,107],"scheme.":[84],"Here,":[85],"we":[86,114,126],"extend":[87],"analysis":[89],"present":[94],"results":[96],"on":[97],"convergence":[99],"moments,":[101],"moderate":[102],"large":[104],"deviations,":[105],"redundancy.":[111],"In":[112],"confirm":[115],"average":[118],"decays":[121],"as":[122],"1/log":[123],"n,":[124],"find":[127],"variance":[130],"is":[131,137],"order":[133],"1/n,":[134],"where":[135],"n":[136],"text.":[142]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-03-27T14:29:43.386196","created_date":"2025-10-10T00:00:00"}