{"id":"https://openalex.org/W2127244382","doi":"https://doi.org/10.1109/wiopt.2009.5291559","title":"The finite-dimensional Witsenhausen counterexample","display_name":"The finite-dimensional Witsenhausen counterexample","publication_year":2009,"publication_date":"2009-06-01","ids":{"openalex":"https://openalex.org/W2127244382","doi":"https://doi.org/10.1109/wiopt.2009.5291559","mag":"2127244382"},"language":"en","primary_location":{"id":"doi:10.1109/wiopt.2009.5291559","is_oa":false,"landing_page_url":"https://doi.org/10.1109/wiopt.2009.5291559","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 7th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1003.0514","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054746425","display_name":"Pulkit Grover","orcid":"https://orcid.org/0000-0001-7651-7776"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"P. Grover","raw_affiliation_strings":["Wireless Foundations, Department of EECS, University of California, Berkeley, CA, USA","Wireless Foundations, Department of EECS, University of California at Berkeley, 94720, USA"],"affiliations":[{"raw_affiliation_string":"Wireless Foundations, Department of EECS, University of California, Berkeley, CA, USA","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"Wireless Foundations, Department of EECS, University of California at Berkeley, 94720, USA","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079317491","display_name":"Anant Sahai","orcid":"https://orcid.org/0000-0001-9263-7719"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A. Sahai","raw_affiliation_strings":["Wireless Foundations, Department of EECS, University of California, Berkeley, CA, USA","Wireless Foundations, Department of EECS, University of California at Berkeley, 94720, USA"],"affiliations":[{"raw_affiliation_string":"Wireless Foundations, Department of EECS, University of California, Berkeley, CA, USA","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"Wireless Foundations, Department of EECS, University of California at Berkeley, 94720, USA","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036846976","display_name":"S. H. Park","orcid":null},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"SeYong Park","raw_affiliation_strings":["Wireless Foundations, Department of EECS, University of California at Berkeley, 94720, USA"],"affiliations":[{"raw_affiliation_string":"Wireless Foundations, Department of EECS, University of California at Berkeley, 94720, USA","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5054746425"],"corresponding_institution_ids":["https://openalex.org/I95457486"],"apc_list":null,"apc_paid":null,"fwci":8.3386,"has_fulltext":false,"cited_by_count":33,"citation_normalized_percentile":{"value":0.97785807,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"10"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9818000197410583,"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"}},"topics":[{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9818000197410583,"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/T10964","display_name":"Wireless Communication Security Techniques","score":0.9814000129699707,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9786999821662903,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/counterexample","display_name":"Counterexample","score":0.8576635122299194},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.7663915157318115},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6750100255012512},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5285747647285461},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.5059325098991394},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4873086214065552},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.47309210896492004},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37581294775009155},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3537863492965698},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.26642662286758423},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2539898455142975},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1799098551273346},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09870368242263794}],"concepts":[{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.8576635122299194},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7663915157318115},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6750100255012512},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5285747647285461},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5059325098991394},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4873086214065552},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.47309210896492004},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37581294775009155},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3537863492965698},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26642662286758423},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2539898455142975},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1799098551273346},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09870368242263794},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1109/wiopt.2009.5291559","is_oa":false,"landing_page_url":"https://doi.org/10.1109/wiopt.2009.5291559","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 7th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1003.0514","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1003.0514","pdf_url":"https://arxiv.org/pdf/1003.0514","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":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.152.3872","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.152.3872","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.eecs.berkeley.edu/~sahai/Papers/WitsenhausenSpherePackingLong.as.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.152.6308","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.152.6308","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.eecs.berkeley.edu/~pulkit/papers/ConCom09.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.156.9774","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.156.9774","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.eecs.berkeley.edu/~pulkit/papers/WitsenhausenFiniteLengthJournalDec9.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.164.840","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.164.840","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.eecs.berkeley.edu/~sahai/Papers/WitsenhausenFiniteLength.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1003.0514","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1003.0514","pdf_url":"https://arxiv.org/pdf/1003.0514","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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320332195","display_name":"Samsung","ror":"https://ror.org/04w3jy968"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":68,"referenced_works":["https://openalex.org/W96086662","https://openalex.org/W156752663","https://openalex.org/W285471286","https://openalex.org/W1485280854","https://openalex.org/W1499237070","https://openalex.org/W1549664537","https://openalex.org/W1599295008","https://openalex.org/W1622420187","https://openalex.org/W1802395297","https://openalex.org/W1910209878","https://openalex.org/W1964538510","https://openalex.org/W1976109068","https://openalex.org/W1995990042","https://openalex.org/W2020595357","https://openalex.org/W2030546921","https://openalex.org/W2046494998","https://openalex.org/W2054371071","https://openalex.org/W2069525910","https://openalex.org/W2069534200","https://openalex.org/W2087705319","https://openalex.org/W2100288479","https://openalex.org/W2102617152","https://openalex.org/W2107543180","https://openalex.org/W2109962983","https://openalex.org/W2109963441","https://openalex.org/W2112354652","https://openalex.org/W2112537312","https://openalex.org/W2114473301","https://openalex.org/W2115118348","https://openalex.org/W2115485545","https://openalex.org/W2117896158","https://openalex.org/W2118152952","https://openalex.org/W2122621581","https://openalex.org/W2122949380","https://openalex.org/W2123562147","https://openalex.org/W2126151527","https://openalex.org/W2127244382","https://openalex.org/W2129977719","https://openalex.org/W2131229447","https://openalex.org/W2134582956","https://openalex.org/W2137560895","https://openalex.org/W2142901448","https://openalex.org/W2146572375","https://openalex.org/W2147378124","https://openalex.org/W2151533263","https://openalex.org/W2151716818","https://openalex.org/W2156274800","https://openalex.org/W2156971172","https://openalex.org/W2157989362","https://openalex.org/W2165894964","https://openalex.org/W2178161518","https://openalex.org/W2296510033","https://openalex.org/W2505777393","https://openalex.org/W2576544140","https://openalex.org/W2949718428","https://openalex.org/W2971364697","https://openalex.org/W3015200071","https://openalex.org/W3100170933","https://openalex.org/W4205855417","https://openalex.org/W4231172027","https://openalex.org/W4285719527","https://openalex.org/W4293259454","https://openalex.org/W4300203081","https://openalex.org/W4302068590","https://openalex.org/W4377205735","https://openalex.org/W4403969132","https://openalex.org/W6638211556","https://openalex.org/W6767466149"],"related_works":["https://openalex.org/W2349952486","https://openalex.org/W1489260687","https://openalex.org/W2775700832","https://openalex.org/W2587222766","https://openalex.org/W3204670144","https://openalex.org/W2163101548","https://openalex.org/W2158905189","https://openalex.org/W4319874546","https://openalex.org/W4299524164","https://openalex.org/W2951535879"],"abstract_inverted_index":{"Recently,":[0],"we":[1,104,164],"considered":[2,50],"a":[3,11,31,67,112,145],"vector":[4,23,47,53,127,176],"version":[5],"of":[6,21,34,84,115,147,149],"Witsenhausen's":[7,130],"counterexample":[8],"and":[9,160],"used":[10],"new":[12,100],"lower":[13,68,102],"bound":[14,69],"to":[15,70,136],"show":[16,105],"that":[17,19,80,106],"in":[18,156],"limit":[20],"infinite":[22],"length,":[24],"certain":[25],"quantization-based":[26],"strategies":[27,93,109,142,170],"are":[28,49],"provably":[29],"within":[30,111,144],"constant":[32,113],"factor":[33,114,146],"the":[35,52,64,71,85,99,107,116,126,137,150,157,161,168],"optimal":[36,72,117,151,169],"cost":[37,73,118],"for":[38,74,94,173],"all":[39,121],"possible":[40,122],"problem":[41,60,77,123,132],"parameters.":[42],"In":[43],"this":[44,75],"paper,":[45],"finite":[46,96,175],"lengths":[48],"with":[51],"length":[54],"being":[55],"viewed":[56],"as":[57],"an":[58],"additional":[59],"parameter.":[61],"By":[62],"applying":[63],"ldquosphere-packingrdquo":[65],"philosophy,":[66],"finite-length":[76,101],"is":[78],"derived":[79],"uses":[81],"appropriate":[82],"shadows":[83],"infinite-length":[86],"bounds.":[87],"We":[88],"also":[89,165],"introduce":[90],"lattice-based":[91,108,141],"quantization":[92],"any":[95,174],"length.":[97,128,177],"Using":[98],"bound,":[103],"achieve":[110],"uniformly":[119],"over":[120],"parameters,":[124],"including":[125],"For":[129],"original":[131],"-":[133,140],"which":[134],"corresponds":[135],"scalar":[138,158],"case":[139,159],"attain":[143],"8":[148],"cost.":[152],"Based":[153],"on":[154],"observations":[155],"infinite-dimensional":[162],"case,":[163],"conjecture":[166],"what":[167],"could":[171],"be":[172]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2015,"cited_by_count":4},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":5}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}