{"id":"https://openalex.org/W2511028299","doi":"https://doi.org/10.1109/isit.2016.7541507","title":"Canonical conditions for K/2 degrees of freedom","display_name":"Canonical conditions for K/2 degrees of freedom","publication_year":2016,"publication_date":"2016-07-01","ids":{"openalex":"https://openalex.org/W2511028299","doi":"https://doi.org/10.1109/isit.2016.7541507","mag":"2511028299"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2016.7541507","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2016.7541507","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://escholarship.org/uc/item/4dd7t61w","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030034393","display_name":"David Stotz","orcid":"https://orcid.org/0000-0002-3786-9602"},"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":true,"raw_author_name":"David Stotz","raw_affiliation_strings":["ETH Zurich, Switzerland"],"affiliations":[{"raw_affiliation_string":"ETH Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049553679","display_name":"Syed A. Jafar","orcid":"https://orcid.org/0000-0003-2038-2977"},"institutions":[{"id":"https://openalex.org/I204250578","display_name":"University of California, Irvine","ror":"https://ror.org/04gyf1771","country_code":"US","type":"education","lineage":["https://openalex.org/I204250578"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Syed Ali Jafar","raw_affiliation_strings":["University of California at Irvine, USA","University of California, Irvine, CA, USA"],"affiliations":[{"raw_affiliation_string":"University of California at Irvine, USA","institution_ids":["https://openalex.org/I204250578"]},{"raw_affiliation_string":"University of California, Irvine, CA, USA","institution_ids":["https://openalex.org/I204250578"]}]},{"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 B\u00f6lcskei","raw_affiliation_strings":["ETH Zurich, Switzerland"],"affiliations":[{"raw_affiliation_string":"ETH Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025989795","display_name":"Shlomo Shamai","orcid":"https://orcid.org/0000-0002-6594-3371"},"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":false,"raw_author_name":"Shlomo Shamai","raw_affiliation_strings":["Technion - Israel Institute of Technology, Israel","Technion Israel Institute of Technology, Haifa, Haifa, IL"],"affiliations":[{"raw_affiliation_string":"Technion - Israel Institute of Technology, Israel","institution_ids":["https://openalex.org/I174306211"]},{"raw_affiliation_string":"Technion Israel Institute of Technology, Haifa, Haifa, IL","institution_ids":["https://openalex.org/I174306211"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5030034393"],"corresponding_institution_ids":["https://openalex.org/I35440088"],"apc_list":null,"apc_paid":null,"fwci":0.1867,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.58066723,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"1292","last_page":"1296"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10148","display_name":"Advanced MIMO Systems Optimization","score":0.9998000264167786,"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/T10148","display_name":"Advanced MIMO Systems Optimization","score":0.9998000264167786,"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/T10069","display_name":"Antenna Design and Analysis","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T12791","display_name":"Full-Duplex Wireless Communications","score":0.9991000294685364,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/monomial","display_name":"Monomial","score":0.668125569820404},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.6031299233436584},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5852104425430298},{"id":"https://openalex.org/keywords/degrees-of-freedom","display_name":"Degrees of freedom (physics and chemistry)","score":0.5700588226318359},{"id":"https://openalex.org/keywords/rational-number","display_name":"Rational number","score":0.5698044896125793},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5680718421936035},{"id":"https://openalex.org/keywords/interference","display_name":"Interference (communication)","score":0.5612704753875732},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5505094528198242},{"id":"https://openalex.org/keywords/condition-number","display_name":"Condition number","score":0.5327192544937134},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5132834911346436},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5046547651290894},{"id":"https://openalex.org/keywords/interference-alignment","display_name":"Interference alignment","score":0.4105220139026642},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3586805462837219},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3513363003730774},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3496268391609192},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2650315761566162},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2630573511123657},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.15359726548194885},{"id":"https://openalex.org/keywords/mimo","display_name":"MIMO","score":0.1492740511894226},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12815755605697632},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07501402497291565}],"concepts":[{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.668125569820404},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.6031299233436584},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5852104425430298},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.5700588226318359},{"id":"https://openalex.org/C46875033","wikidata":"https://www.wikidata.org/wiki/Q1244890","display_name":"Rational number","level":2,"score":0.5698044896125793},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5680718421936035},{"id":"https://openalex.org/C32022120","wikidata":"https://www.wikidata.org/wiki/Q797225","display_name":"Interference (communication)","level":3,"score":0.5612704753875732},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5505094528198242},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.5327192544937134},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5132834911346436},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5046547651290894},{"id":"https://openalex.org/C2982854036","wikidata":"https://www.wikidata.org/wiki/Q797225","display_name":"Interference alignment","level":4,"score":0.4105220139026642},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3586805462837219},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3513363003730774},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3496268391609192},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2650315761566162},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2630573511123657},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.15359726548194885},{"id":"https://openalex.org/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.1492740511894226},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12815755605697632},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07501402497291565},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/isit.2016.7541507","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2016.7541507","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"},{"id":"pmh:oai:escholarship.org:ark:/13030/qt4dd7t61w","is_oa":true,"landing_page_url":"https://escholarship.org/uc/item/4dd7t61w","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:escholarship.org:ark:/13030/qt4dd7t61w","is_oa":true,"landing_page_url":"https://escholarship.org/uc/item/4dd7t61w","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.7799999713897705,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1494099594","https://openalex.org/W1979408141","https://openalex.org/W2000418561","https://openalex.org/W2005914283","https://openalex.org/W2012462504","https://openalex.org/W2089318831","https://openalex.org/W2100842176","https://openalex.org/W2130172876","https://openalex.org/W2763610741","https://openalex.org/W2962936372","https://openalex.org/W3100335223","https://openalex.org/W3106263997","https://openalex.org/W4300840296","https://openalex.org/W6691597635"],"related_works":["https://openalex.org/W2963438473","https://openalex.org/W2037307649","https://openalex.org/W4300895095","https://openalex.org/W2171681635","https://openalex.org/W2111349105","https://openalex.org/W2950569304","https://openalex.org/W2038016299","https://openalex.org/W2058081374","https://openalex.org/W2556113510","https://openalex.org/W2004357868"],"abstract_inverted_index":{"Stotz":[0,102],"and":[1,40,103,141],"B\u00f6lcskei,":[2],"2015,":[3],"identified":[4],"an":[5],"explicit":[6],"condition":[7,21,78,100,111,135],"for":[8,43,79,84,87],"K/2":[9,59,80],"degrees":[10],"of":[11,26,36,54,70,106,117,121,126,131,139],"freedom":[12],"(DoF)":[13],"in":[14,24,32,114,129],"constant":[15],"single-antenna":[16],"interference":[17,122],"channels":[18],"(ICs).":[19],"This":[20],"is":[22,41,74,105,112],"expressed":[23,128],"terms":[25,130],"linear":[27],"independence\u2014over":[28],"the":[29,33,37,71,98,109,115,119],"rationals\u2014of":[30],"monomials":[31],"off-diagonal":[34],"entries":[35],"IC":[38,46,55],"matrix":[39],"satisfied":[42],"almost":[44],"all":[45],"matrices.":[47],"There":[48],"is,":[49],"however,":[50],"a":[51,75,132],"prominent":[52],"class":[53],"matrices":[56],"that":[57,136],"admits":[58],"DoF":[60,81,86],"but":[61],"fails":[62],"to":[63],"satisfy":[64],"this":[65,94],"condition.":[66],"The":[67],"main":[68],"contribution":[69],"present":[72],"paper":[73],"more":[76],"general":[77],"(in":[82],"fact":[83],"1/2":[85],"each":[88],"user)":[89],"that,":[90],"inter":[91],"alia,":[92],"encompasses":[93],"example":[95],"class.":[96],"While":[97],"existing":[99],"by":[101,124],"B\u00f6lcskei":[104],"algebraic":[107],"nature,":[108],"new":[110],"canonical":[113],"sense":[116],"capturing":[118],"essence":[120],"alignment":[123],"virtue":[125],"being":[127],"generic":[133],"injectivity":[134],"guarantees":[137],"separability":[138],"signal":[140],"interference.":[142]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}