{"id":"https://openalex.org/W2029666412","doi":"https://doi.org/10.1109/isit.2012.6283069","title":"Expurgated infinite constellations at finite dimensions","display_name":"Expurgated infinite constellations at finite dimensions","publication_year":2012,"publication_date":"2012-07-01","ids":{"openalex":"https://openalex.org/W2029666412","doi":"https://doi.org/10.1109/isit.2012.6283069","mag":"2029666412"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2012.6283069","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2012.6283069","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE International Symposium on Information Theory Proceedings","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/A5016461327","display_name":"Amir Ingber","orcid":"https://orcid.org/0000-0001-6639-8240"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Amir Ingber","raw_affiliation_strings":["Department of Electrical Engineering, University of Stanford, USA","Dept of Electrical Engineering, Stanford University"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Stanford, USA","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Dept of Electrical Engineering, Stanford University","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027550575","display_name":"Ram Zamir","orcid":"https://orcid.org/0000-0003-1800-3886"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Ram Zamir","raw_affiliation_strings":["Department of EE-Systems, Tel Aviv University, Israel","Dept. of EE-Systems, Tel Aviv Univ"],"affiliations":[{"raw_affiliation_string":"Department of EE-Systems, Tel Aviv University, Israel","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"Dept. of EE-Systems, Tel Aviv Univ","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5016461327"],"corresponding_institution_ids":["https://openalex.org/I97018004"],"apc_list":null,"apc_paid":null,"fwci":1.4979,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.83836629,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"130","last_page":"134"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10964","display_name":"Wireless Communication Security Techniques","score":0.9995999932289124,"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":0.9995999932289124,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9921000003814697,"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/T10148","display_name":"Advanced MIMO Systems Optimization","score":0.9883000254631042,"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/exponent","display_name":"Exponent","score":0.7390491962432861},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5913119316101074},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5303963422775269},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.5267685651779175},{"id":"https://openalex.org/keywords/channel-code","display_name":"Channel code","score":0.5244876742362976},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5178409218788147},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.5076349973678589},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.49289560317993164},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.47906050086021423},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.47304099798202515},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.44748905301094055},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.4409655034542084},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.43610697984695435},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.4139328598976135},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.41226115822792053},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3448335528373718},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34304529428482056},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3253024220466614},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3111817240715027},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15608707070350647},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.13775375485420227},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12372669577598572},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11819490790367126},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.09475487470626831}],"concepts":[{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.7390491962432861},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5913119316101074},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5303963422775269},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.5267685651779175},{"id":"https://openalex.org/C166366890","wikidata":"https://www.wikidata.org/wiki/Q602136","display_name":"Channel code","level":3,"score":0.5244876742362976},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5178409218788147},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.5076349973678589},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.49289560317993164},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.47906050086021423},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47304099798202515},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.44748905301094055},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.4409655034542084},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.43610697984695435},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.4139328598976135},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.41226115822792053},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3448335528373718},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34304529428482056},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3253024220466614},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3111817240715027},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15608707070350647},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.13775375485420227},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12372669577598572},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11819490790367126},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.09475487470626831},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit.2012.6283069","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2012.6283069","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE International Symposium on Information Theory Proceedings","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1512015702","https://openalex.org/W1989008275","https://openalex.org/W2015850986","https://openalex.org/W2026869314","https://openalex.org/W2044180609","https://openalex.org/W2103604544","https://openalex.org/W2151450116","https://openalex.org/W2160973043","https://openalex.org/W2170608172","https://openalex.org/W3106027096"],"related_works":["https://openalex.org/W2090152127","https://openalex.org/W1965169884","https://openalex.org/W3125580510","https://openalex.org/W2008939113","https://openalex.org/W2033213447","https://openalex.org/W14679004","https://openalex.org/W1566651525","https://openalex.org/W2977652649","https://openalex.org/W2318206461","https://openalex.org/W2105228010"],"abstract_inverted_index":{"We":[0,32],"revisit":[1],"the":[2,15,29,34,41,44,48,59,64,88,107,112],"setting":[3],"of":[4,28,43,97,106],"a":[5,54,73,94],"Gaussian":[6],"channel":[7],"without":[8],"power":[9],"constraints,":[10],"proposed":[11],"by":[12,38],"Poltyrev,":[13],"where":[14],"codewords":[16],"are":[17],"points":[18],"in":[19],"Euclidean":[20],"space":[21],"and":[22,52,110],"their":[23],"density":[24],"is":[25,91],"considered":[26],"instead":[27],"communication":[30],"rate.":[31],"refine":[33],"expurgation":[35,60,89,108],"technique":[36,90],"(proposed":[37],"Poltyrev":[39],"for":[40,69,85,93],"derivation":[42],"error":[45],"exponent)":[46],"to":[47,118],"finite":[49,86],"dimensions":[50,87],"case":[51],"obtain":[53],"finite-dimensional":[55],"achievability":[56],"bound.":[57],"While":[58],"exponent":[61,67],"improves":[62],"upon":[63],"random":[65],"coding":[66],"only":[68],"certain":[70],"rates":[71],"(below":[72],"rate":[74],"known":[75],"as":[76],"\u03b4":[77],"<sub":[78],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[79],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">ex</sub>":[80],"),":[81],"we":[82,101],"show":[83],"that":[84],"useful":[92],"broader":[95],"range":[96],"rates.":[98],"In":[99],"addition,":[100],"present":[102],"precise":[103],"asymptotical":[104],"analysis":[105],"bound":[109],"find":[111],"sub-exponential":[113],"terms,":[114],"which":[115],"turn":[116],"out":[117],"be":[119],"non-negligible.":[120]},"counts_by_year":[{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
