{"id":"https://openalex.org/W2089230212","doi":"https://doi.org/10.1109/isit.2013.6620273","title":"On frames from abelian group codes","display_name":"On frames from abelian group codes","publication_year":2013,"publication_date":"2013-07-01","ids":{"openalex":"https://openalex.org/W2089230212","doi":"https://doi.org/10.1109/isit.2013.6620273","mag":"2089230212"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2013.6620273","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2013.6620273","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 IEEE International Symposium on Information Theory","raw_type":"proceedings-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/A5000402268","display_name":"Matthew Thill","orcid":"https://orcid.org/0000-0003-0885-6260"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Matthew Thill","raw_affiliation_strings":["Department of Electrical Engineering, Caltech, Pasadena, CA, USA","[Dept. of Electr. Eng., Caltech, Pasadena, CA, USA]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Caltech, Pasadena, CA, USA","institution_ids":["https://openalex.org/I122411786"]},{"raw_affiliation_string":"[Dept. of Electr. Eng., Caltech, Pasadena, CA, USA]","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002430773","display_name":"Babak Hassibi","orcid":"https://orcid.org/0000-0002-1375-5838"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Babak Hassibi","raw_affiliation_strings":["Department of Electrical Engineering, Caltech, Pasadena, CA, USA","[Dept. of Electr. Eng., Caltech, Pasadena, CA, USA]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Caltech, Pasadena, CA, USA","institution_ids":["https://openalex.org/I122411786"]},{"raw_affiliation_string":"[Dept. of Electr. Eng., Caltech, Pasadena, CA, USA]","institution_ids":["https://openalex.org/I122411786"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I122411786"],"apc_list":null,"apc_paid":null,"fwci":0.343,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.64130215,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"47","issue":null,"first_page":"484","last_page":"488"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9958999752998352,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9958999752998352,"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"}},{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.995199978351593,"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/T12024","display_name":"Ultra-Wideband Communications Technology","score":0.9919999837875366,"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/abelian-group","display_name":"Abelian group","score":0.7265148162841797},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5781241655349731},{"id":"https://openalex.org/keywords/exploit","display_name":"Exploit","score":0.4739786982536316},{"id":"https://openalex.org/keywords/coherence","display_name":"Coherence (philosophical gambling strategy)","score":0.4522772431373596},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4477998614311218},{"id":"https://openalex.org/keywords/unitary-state","display_name":"Unitary state","score":0.4374329447746277},{"id":"https://openalex.org/keywords/frame","display_name":"Frame (networking)","score":0.43570899963378906},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.4314667582511902},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.41902679204940796},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.39713579416275024},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3785829544067383},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3643503189086914},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35849010944366455},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2614060342311859},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.17555010318756104},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11858475208282471},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.09168761968612671},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08603999018669128},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.07258355617523193}],"concepts":[{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.7265148162841797},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5781241655349731},{"id":"https://openalex.org/C165696696","wikidata":"https://www.wikidata.org/wiki/Q11287","display_name":"Exploit","level":2,"score":0.4739786982536316},{"id":"https://openalex.org/C2781181686","wikidata":"https://www.wikidata.org/wiki/Q4226068","display_name":"Coherence (philosophical gambling strategy)","level":2,"score":0.4522772431373596},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4477998614311218},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.4374329447746277},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.43570899963378906},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.4314667582511902},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.41902679204940796},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.39713579416275024},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3785829544067383},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3643503189086914},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35849010944366455},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2614060342311859},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.17555010318756104},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11858475208282471},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.09168761968612671},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08603999018669128},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.07258355617523193},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"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/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/isit.2013.6620273","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2013.6620273","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 IEEE International Symposium on Information Theory","raw_type":"proceedings-article"},{"id":"pmh:oai:authors.library.caltech.edu:55128","is_oa":false,"landing_page_url":"https://resolver.caltech.edu/CaltechAUTHORS:20150224-072315309","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Book Section"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1571821595","https://openalex.org/W1624195452","https://openalex.org/W1974565454","https://openalex.org/W1979598217","https://openalex.org/W2015418199","https://openalex.org/W2015864565","https://openalex.org/W2037814692","https://openalex.org/W2039312417","https://openalex.org/W2046273783","https://openalex.org/W2059846882","https://openalex.org/W2075769032","https://openalex.org/W2086869478","https://openalex.org/W2094235750","https://openalex.org/W2096971955","https://openalex.org/W2099641086","https://openalex.org/W2106100486","https://openalex.org/W2119239426","https://openalex.org/W2121743251","https://openalex.org/W2127271355","https://openalex.org/W2129131372","https://openalex.org/W2132702454","https://openalex.org/W2144424682","https://openalex.org/W2154332973","https://openalex.org/W2164452299","https://openalex.org/W2584020404","https://openalex.org/W3099753513"],"related_works":["https://openalex.org/W17155033","https://openalex.org/W3207760230","https://openalex.org/W1496222301","https://openalex.org/W1590307681","https://openalex.org/W4312814274","https://openalex.org/W4285370786","https://openalex.org/W2296488620","https://openalex.org/W2358353312","https://openalex.org/W2353836703","https://openalex.org/W41015297"],"abstract_inverted_index":{"Designing":[0],"low":[1],"coherence":[2],"matrices":[3],"and":[4,20,66,92,111,130],"low-correlation":[5],"frames":[6,61,105],"is":[7,25],"a":[8],"point":[9],"of":[10,55,73,89],"interest":[11],"in":[12,68],"many":[13],"fields":[14],"including":[15],"compressed":[16],"sensing,":[17],"MIMO":[18],"communications":[19],"quantum":[21],"measurements.":[22],"The":[23],"challenge":[24],"that":[26,106],"one":[27],"must":[28],"control":[29],"the":[30,43,51,71,108],"(":[31],"<sup":[32],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[33,36],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</sup>":[34],"<sub":[35],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sub>":[37],")":[38],"pairwise":[39],"inner":[40,75,112],"products":[41,76,113],"between":[42],"frame":[44],"elements.":[45],"In":[46],"this":[47],"paper,":[48],"we":[49,93],"exploit":[50],"group":[52,64],"code":[53],"approach":[54],"David":[56],"Slepian":[57],"[1],":[58],"which":[59,67],"constructs":[60],"using":[62],"unitary":[63],"representations":[65,88],"general":[69],"reduces":[70],"number":[72],"distinct":[74],"to":[77,84,102],"n":[78],"-":[79],"1.":[80],"We":[81,123],"demonstrate":[82],"how":[83,95],"efficiently":[85],"find":[86],"optimal":[87],"cyclic":[90],"groups,":[91],"show":[94],"basic":[96],"abelian":[97],"groups":[98],"can":[99],"be":[100],"used":[101],"construct":[103],"tight":[104],"have":[107],"same":[109],"dimensions":[110],"as":[114],"those":[115],"arising":[116],"from":[117],"certain":[118],"more":[119],"complex":[120],"nonabelian":[121],"groups.":[122],"support":[124],"our":[125],"work":[126],"with":[127],"theoretical":[128],"bounds":[129],"simulations.":[131]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}
