{"id":"https://openalex.org/W2798943785","doi":"https://doi.org/10.1109/isit.2018.8437740","title":"Rate-Distortion Theory for General Sets and Measures","display_name":"Rate-Distortion Theory for General Sets and Measures","publication_year":2018,"publication_date":"2018-06-01","ids":{"openalex":"https://openalex.org/W2798943785","doi":"https://doi.org/10.1109/isit.2018.8437740","mag":"2798943785"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2018.8437740","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2018.8437740","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1804.08980","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103188218","display_name":"Erwin Riegler","orcid":"https://orcid.org/0000-0003-1691-9479"},"institutions":[{"id":"https://openalex.org/I2799323385","display_name":"Board of the Swiss Federal Institutes of Technology","ror":"https://ror.org/01rvn4p91","country_code":"CH","type":"government","lineage":["https://openalex.org/I2799323385"]},{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Erwin Riegler","raw_affiliation_strings":["Eidgenossische Technische Hochschule Zurich, Zurich, ZH, CH"],"affiliations":[{"raw_affiliation_string":"Eidgenossische Technische Hochschule Zurich, Zurich, ZH, CH","institution_ids":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079321311","display_name":"Helmut B\u00f6lcskei","orcid":null},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Helmut Bolcskei","raw_affiliation_strings":["Dept. IT & EE, ETH Zurich, Zurich, Switzerland"],"affiliations":[{"raw_affiliation_string":"Dept. IT & EE, ETH Zurich, Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050384689","display_name":"G\u00fcnther Koliander","orcid":"https://orcid.org/0000-0002-4750-3305"},"institutions":[{"id":"https://openalex.org/I138211613","display_name":"Austrian Academy of Sciences","ror":"https://ror.org/03anc3s24","country_code":"AT","type":"government","lineage":["https://openalex.org/I138211613"]},{"id":"https://openalex.org/I2800119247","display_name":"Acoustics Research Institute","ror":"https://ror.org/04jd9ff79","country_code":"AT","type":"facility","lineage":["https://openalex.org/I138211613","https://openalex.org/I2800119247"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Gunther Koliander","raw_affiliation_strings":["Acoustics Research Institute, Austrian Academy of Sciences, Vienna, Austria"],"affiliations":[{"raw_affiliation_string":"Acoustics Research Institute, Austrian Academy of Sciences, Vienna, Austria","institution_ids":["https://openalex.org/I138211613","https://openalex.org/I2800119247"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5103188218"],"corresponding_institution_ids":["https://openalex.org/I2799323385","https://openalex.org/I35440088"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.070963,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"101","last_page":"105"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9724000096321106,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9692000150680542,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7219429016113281},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6420963406562805},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.6272277235984802},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.5808680057525635},{"id":"https://openalex.org/keywords/cantor-set","display_name":"Cantor set","score":0.5397080183029175},{"id":"https://openalex.org/keywords/distortion","display_name":"Distortion (music)","score":0.5194920301437378},{"id":"https://openalex.org/keywords/rate\u2013distortion-theory","display_name":"Rate\u2013distortion theory","score":0.4539596140384674},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.4525543451309204},{"id":"https://openalex.org/keywords/fractal","display_name":"Fractal","score":0.4306827783584595},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.4228183329105377},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.41956645250320435},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.411723792552948},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38347941637039185},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3419416546821594},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3401614725589752},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32785764336586},{"id":"https://openalex.org/keywords/data-compression","display_name":"Data compression","score":0.22621208429336548},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16310787200927734},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15169420838356018},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.129054456949234}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7219429016113281},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6420963406562805},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.6272277235984802},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.5808680057525635},{"id":"https://openalex.org/C36605576","wikidata":"https://www.wikidata.org/wiki/Q273188","display_name":"Cantor set","level":2,"score":0.5397080183029175},{"id":"https://openalex.org/C126780896","wikidata":"https://www.wikidata.org/wiki/Q899871","display_name":"Distortion (music)","level":4,"score":0.5194920301437378},{"id":"https://openalex.org/C64185310","wikidata":"https://www.wikidata.org/wiki/Q843483","display_name":"Rate\u2013distortion theory","level":3,"score":0.4539596140384674},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.4525543451309204},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.4306827783584595},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.4228183329105377},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.41956645250320435},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.411723792552948},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38347941637039185},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3419416546821594},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3401614725589752},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32785764336586},{"id":"https://openalex.org/C78548338","wikidata":"https://www.wikidata.org/wiki/Q2493","display_name":"Data compression","level":2,"score":0.22621208429336548},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16310787200927734},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15169420838356018},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.129054456949234},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"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/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"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/C194257627","wikidata":"https://www.wikidata.org/wiki/Q211554","display_name":"Amplifier","level":3,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/isit.2018.8437740","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2018.8437740","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1804.08980","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1804.08980","pdf_url":"https://arxiv.org/pdf/1804.08980","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2798943785","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1804.08980","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1804.08980","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1804.08980","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1804.08980","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1804.08980","pdf_url":"https://arxiv.org/pdf/1804.08980","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2798943785.pdf","grobid_xml":"https://content.openalex.org/works/W2798943785.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W656592592","https://openalex.org/W862060148","https://openalex.org/W1480714962","https://openalex.org/W1496462336","https://openalex.org/W1576475658","https://openalex.org/W1603226434","https://openalex.org/W1608472120","https://openalex.org/W1613756672","https://openalex.org/W1973387369","https://openalex.org/W1986736933","https://openalex.org/W1991207049","https://openalex.org/W2105607047","https://openalex.org/W2105818147","https://openalex.org/W2108050299","https://openalex.org/W2111842831","https://openalex.org/W2114361399","https://openalex.org/W2157962569","https://openalex.org/W2162451874","https://openalex.org/W2308818299","https://openalex.org/W2592082291","https://openalex.org/W2609738705","https://openalex.org/W2611328865","https://openalex.org/W2790435756","https://openalex.org/W2963260187","https://openalex.org/W2964268537","https://openalex.org/W3106440465","https://openalex.org/W3158116462","https://openalex.org/W4254197176","https://openalex.org/W6749366016"],"related_works":["https://openalex.org/W2988154586","https://openalex.org/W1959552729","https://openalex.org/W64895808","https://openalex.org/W3005391585","https://openalex.org/W1974243430","https://openalex.org/W2962923175","https://openalex.org/W2072409701","https://openalex.org/W3104763254","https://openalex.org/W2085382945","https://openalex.org/W2150786674","https://openalex.org/W2149263910","https://openalex.org/W2035598542","https://openalex.org/W3090177494","https://openalex.org/W2008748451","https://openalex.org/W3197096721","https://openalex.org/W3084831968","https://openalex.org/W2043702293","https://openalex.org/W2955728402","https://openalex.org/W2953306722","https://openalex.org/W3003739484"],"abstract_inverted_index":{"This":[0,171],"paper":[1],"is":[2,99,125,164,173],"concerned":[3],"with":[4,14,150],"a":[5,60,103,108,113,129,145,167,207,213,220,226],"rate-distortion":[6,66],"theory":[7],"for":[8,83,120,140,206],"sequences":[9],"of":[10,55,76,128,190,198],"i.i.d.":[11],"random":[12,71,208,221],"variables":[13,72],"general":[15,19,77,175],"distribution":[16,78],"supported":[17],"on":[18,63,188,212,225],"sets":[20,46],"including":[21],"manifolds":[22],"and":[23,41,52,82,155,176,219],"fractal":[24],"sets.":[25],"Manifold":[26],"structures":[27],"are":[28],"prevalent":[29],"in":[30,34,49,53,112],"data":[31],"science,":[32],"e.g.,":[33],"compressed":[35],"sensing,":[36],"machine":[37],"learning,":[38],"image":[39,50],"processing,":[40],"handwritten":[42],"digit":[43],"recognition.":[44],"Fractal":[45],"find":[47],"application":[48],"compression":[51],"modeling":[54],"Ethernet":[56],"traffic.":[57],"We":[58],"derive":[59],"lower":[61,93,97,204],"bound":[62,98,122,205],"the":[64,90,121,126,158,178,195,203,216,230],"(single-letter)":[65],"function":[67],"that":[68,157],"applies":[69],"to":[70,89,102,123],"<tex":[73,79,85,130,136,141,147,151,161,181],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[74,80,86,131,137,142,148,152,162,182],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$X$</tex>":[75,87,143],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$\\mu_{X}$</tex>":[81],"continuous":[84],"reduces":[88],"classical":[91],"Shannon":[92],"bound.":[94],"Moreover,":[95],"our":[96,199],"explicit":[100],"up":[101],"parameter":[104],"obtained":[105],"by":[106],"solving":[107],"convex":[109],"optimization":[110],"problem":[111],"nonnegative":[114],"real":[115],"variable.":[116],"The":[117],"only":[118],"requirement":[119],"apply":[124],"existence":[127],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$\\sigma$</tex>":[132],"-finite":[133],"reference":[134,179],"measure":[135,146,180],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$\\mu$</tex>":[138,149,183],",":[139],"(i.e.,":[144],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$\\mu":[153],"x\\ll\\mu$</tex>":[154],"such":[156],"generalized":[159],"entropy":[160],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$h_{\\mu}(X)$</tex>":[163],"finite)":[165],"satisfying":[166],"certain":[168],"subregularity":[169],"condition.":[170],"condition":[172],"very":[174],"prevents":[177],"from":[184],"being":[185],"highly":[186],"concentrated":[187],"balls":[189],"small":[191],"radii.":[192],"To":[193],"illustrate":[194],"wide":[196],"applicability":[197],"result,":[200],"we":[201],"evaluate":[202],"variable":[209,222],"distributed":[210,223],"uniformly":[211,224],"manifold,":[214],"namely,":[215,229],"unit":[217],"circle,":[218],"self-similar":[227],"set,":[228],"middle":[231],"third":[232],"Cantor":[233],"set.":[234]},"counts_by_year":[],"updated_date":"2026-03-25T23:56:10.502304","created_date":"2025-10-10T00:00:00"}
