{"id":"https://openalex.org/W2100842176","doi":"https://doi.org/10.1109/tit.2009.2030473","title":"The Degrees-of-Freedom of the $K$-User Gaussian Interference Channel Is Discontinuous at Rational Channel Coefficients","display_name":"The Degrees-of-Freedom of the $K$-User Gaussian Interference Channel Is Discontinuous at Rational Channel Coefficients","publication_year":2009,"publication_date":"2009-10-27","ids":{"openalex":"https://openalex.org/W2100842176","doi":"https://doi.org/10.1109/tit.2009.2030473","mag":"2100842176"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2009.2030473","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2009.2030473","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/A5032571804","display_name":"Ra\u00fal Etkin","orcid":null},"institutions":[{"id":"https://openalex.org/I1324840837","display_name":"Hewlett-Packard (United States)","ror":"https://ror.org/059rn9488","country_code":"US","type":"company","lineage":["https://openalex.org/I1324840837"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ra\u00dal H. Etkin","raw_affiliation_strings":["Hewlett Packard Laboratories, Palo Alto, CA, USA","Hewlett\u2013Packard Laboratories, Palo Alto, CA, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hewlett Packard Laboratories, Palo Alto, CA, USA","institution_ids":["https://openalex.org/I1324840837"]},{"raw_affiliation_string":"Hewlett\u2013Packard Laboratories, Palo Alto, CA, USA#TAB#","institution_ids":["https://openalex.org/I1324840837"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006239162","display_name":"Erik Ordentlich","orcid":null},"institutions":[{"id":"https://openalex.org/I1324840837","display_name":"Hewlett-Packard (United States)","ror":"https://ror.org/059rn9488","country_code":"US","type":"company","lineage":["https://openalex.org/I1324840837"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Erik Ordentlich","raw_affiliation_strings":["Hewlett Packard Laboratories, Palo Alto, CA, USA","Hewlett\u2013Packard Laboratories, Palo Alto, CA, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hewlett Packard Laboratories, Palo Alto, CA, USA","institution_ids":["https://openalex.org/I1324840837"]},{"raw_affiliation_string":"Hewlett\u2013Packard Laboratories, Palo Alto, CA, USA#TAB#","institution_ids":["https://openalex.org/I1324840837"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":11.9018,"has_fulltext":false,"cited_by_count":102,"citation_normalized_percentile":{"value":0.98929238,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"55","issue":"11","first_page":"4932","last_page":"4946"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10964","display_name":"Wireless Communication Security Techniques","score":1.0,"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/T10964","display_name":"Wireless Communication Security Techniques","score":1.0,"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/T11392","display_name":"Energy Harvesting in Wireless Networks","score":0.998199999332428,"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/T10148","display_name":"Advanced MIMO Systems Optimization","score":0.9965999722480774,"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/computer-science","display_name":"Computer science","score":0.37980443239212036},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36289557814598083},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32655683159828186},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2572789192199707}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37980443239212036},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36289557814598083},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32655683159828186},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2572789192199707}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2009.2030473","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2009.2030473","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.243.8140","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.243.8140","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0901.1695v1.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.7300000190734863}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W1592482298","https://openalex.org/W1979408141","https://openalex.org/W1988783205","https://openalex.org/W1990208988","https://openalex.org/W1995691260","https://openalex.org/W2062610219","https://openalex.org/W2068118751","https://openalex.org/W2082957515","https://openalex.org/W2088831296","https://openalex.org/W2089318831","https://openalex.org/W2100842176","https://openalex.org/W2110115072","https://openalex.org/W2113758011","https://openalex.org/W2116788385","https://openalex.org/W2129885443","https://openalex.org/W2130781639","https://openalex.org/W2135536003","https://openalex.org/W2136608712","https://openalex.org/W2147055067","https://openalex.org/W2147775941","https://openalex.org/W2151027523","https://openalex.org/W2157989362","https://openalex.org/W2166720624","https://openalex.org/W2168957483","https://openalex.org/W2293033173","https://openalex.org/W2478708596","https://openalex.org/W2577604059","https://openalex.org/W2912209775","https://openalex.org/W2950813095","https://openalex.org/W2963825315","https://openalex.org/W6635532581"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2478288626","https://openalex.org/W4391913857"],"abstract_inverted_index":{"The":[0],"degrees-of-freedom":[1,52,115,124],"of":[2,19,34,53,65,75,95],"a":[3,63,93],"<i":[4,20,26,41,86,96,111,136],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[5,21,24,27,42,87,97,112,137],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">K</i>":[6,88,98,113,138],"-user":[7,99],"Gaussian":[8],"interference":[9],"channel":[10,67],"(GIC)":[11],"has":[12],"been":[13],"defined":[14],"to":[15],"be":[16],"the":[17,31,51,66,76,105,123],"multiple":[18],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">(1/2)log</i>":[22],"<sub":[23],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sub>":[25],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">P</i>":[28,43],"at":[29,71],"which":[30,110],"maximum":[32],"sum":[33],"achievable":[35],"rates":[36],"grows":[37],"with":[38,128,147],"increasing":[39],"power":[40],".":[44],"In":[45],"this":[46],"paper,":[47],"we":[48,91,120],"establish":[49],"that":[50,101,122],"three":[54],"or":[55],"more":[56],"user,":[57],"real,":[58],"scalar":[59],"GICs,":[60],"viewed":[61],"as":[62],"function":[64],"coefficients,":[68],"is":[69,102,132],"discontinuous":[70],"points":[72],"where":[73],"all":[74,85],"coefficients":[77,131],"are":[78,116,142],"nonzero":[79,129],"rational":[80,130],"numbers.":[81],"More":[82],"specifically,":[83],"for":[84,109,125],">":[89],"2,":[90],"find":[92],"class":[94],"GICs":[100],"dense":[103],"in":[104],"GIC":[106,127],"parameter":[107],"space":[108],"/2":[114],"exactly":[117],"achievable,":[118],"and":[119,150],"show":[121],"any":[126],"strictly":[133],"smaller":[134],"than":[135],"/2.":[139],"These":[140],"results":[141],"proved":[143],"using":[144],"new":[145],"connections":[146],"number":[148],"theory":[149],"additive":[151],"combinatorics.":[152]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":16},{"year":2013,"cited_by_count":12},{"year":2012,"cited_by_count":17}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}