{"id":"https://openalex.org/W1991523744","doi":"https://doi.org/10.1109/tit.2013.2253596","title":"Effects of the LLL Reduction on the Success Probability of the Babai Point and on the Complexity of Sphere Decoding","display_name":"Effects of the LLL Reduction on the Success Probability of the Babai Point and on the Complexity of Sphere Decoding","publication_year":2013,"publication_date":"2013-06-20","ids":{"openalex":"https://openalex.org/W1991523744","doi":"https://doi.org/10.1109/tit.2013.2253596","mag":"1991523744"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2013.2253596","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2013.2253596","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/A5062087251","display_name":"Xiao-Wen Chang","orcid":"https://orcid.org/0000-0001-9251-2959"},"institutions":[{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Xiao-Wen Chang","raw_affiliation_strings":["School of Computer Science, McGill University, Montreal, QUE, Canada","[Sch. of Comput. Sci., McGill Univ., Montreal, QC, Canada]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science, McGill University, Montreal, QUE, Canada","institution_ids":["https://openalex.org/I5023651"]},{"raw_affiliation_string":"[Sch. of Comput. Sci., McGill Univ., Montreal, QC, Canada]","institution_ids":["https://openalex.org/I5023651"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080664346","display_name":"Jinming Wen","orcid":"https://orcid.org/0000-0002-8181-0958"},"institutions":[{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Jinming Wen","raw_affiliation_strings":["Department ofMathematics and Statistics, McGill University, Montreal, QUE, Canada","Dept. of Math. & Stat., McGill Univ., Montreal, QC, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department ofMathematics and Statistics, McGill University, Montreal, QUE, Canada","institution_ids":["https://openalex.org/I5023651"]},{"raw_affiliation_string":"Dept. of Math. & Stat., McGill Univ., Montreal, QC, Canada","institution_ids":["https://openalex.org/I5023651"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053031538","display_name":"Xiaohu Xie","orcid":null},"institutions":[{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Xiaohu Xie","raw_affiliation_strings":["School of Computer Science, McGill University, Montreal, QUE, Canada","[Sch. of Comput. Sci., McGill Univ., Montreal, QC, Canada]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science, McGill University, Montreal, QUE, Canada","institution_ids":["https://openalex.org/I5023651"]},{"raw_affiliation_string":"[Sch. of Comput. Sci., McGill Univ., Montreal, QC, Canada]","institution_ids":["https://openalex.org/I5023651"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I5023651"],"apc_list":null,"apc_paid":null,"fwci":4.4625,"has_fulltext":false,"cited_by_count":53,"citation_normalized_percentile":{"value":0.94804157,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"59","issue":"8","first_page":"4915","last_page":"4926"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.9997000098228455,"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/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.9997000098228455,"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/T11130","display_name":"Coding theory and cryptography","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11269","display_name":"Algorithms and Data Compression","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7390514016151428},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.7327483892440796},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.702202320098877},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.6302192211151123},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5478923916816711},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5091297030448914},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4717472493648529},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.4663402736186981},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45369768142700195},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4231402575969696},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19521844387054443},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11321896314620972}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7390514016151428},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.7327483892440796},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.702202320098877},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.6302192211151123},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5478923916816711},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5091297030448914},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4717472493648529},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.4663402736186981},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45369768142700195},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4231402575969696},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19521844387054443},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11321896314620972},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2013.2253596","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2013.2253596","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:10.1.1.380.9475","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.380.9475","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.mcgill.ca/~chang/pub/ChaWX13.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W324457701","https://openalex.org/W1981068750","https://openalex.org/W1981117933","https://openalex.org/W1996359168","https://openalex.org/W2015450103","https://openalex.org/W2054620919","https://openalex.org/W2059504953","https://openalex.org/W2072079288","https://openalex.org/W2077635241","https://openalex.org/W2096765600","https://openalex.org/W2101362102","https://openalex.org/W2111416661","https://openalex.org/W2113870620","https://openalex.org/W2114071526","https://openalex.org/W2115237178","https://openalex.org/W2123831057","https://openalex.org/W2126483728","https://openalex.org/W2127739274","https://openalex.org/W2138293524","https://openalex.org/W2140940105","https://openalex.org/W2141040012","https://openalex.org/W2148907454","https://openalex.org/W2165913606","https://openalex.org/W2170470889","https://openalex.org/W2529481588","https://openalex.org/W4293005804","https://openalex.org/W4362230038","https://openalex.org/W6677317213"],"related_works":["https://openalex.org/W4287880334","https://openalex.org/W4366700029","https://openalex.org/W4285230481","https://openalex.org/W3203142394","https://openalex.org/W4385769873","https://openalex.org/W2015759683","https://openalex.org/W4281634296","https://openalex.org/W4319161863","https://openalex.org/W2371687270","https://openalex.org/W1525049041"],"abstract_inverted_index":{"A":[0,23],"common":[1],"method":[2],"to":[3,15,26,132],"estimate":[4],"an":[5,17,28],"unknown":[6],"integer":[7,18],"parameter":[8],"vector":[9],"in":[10,186,190],"a":[11,36,60,79],"linear":[12],"model":[13],"is":[14,31,44,59,90,178],"solve":[16],"least":[19],"squares":[20],"(ILS)":[21],"problem.":[22,66],"typical":[24],"approach":[25],"solving":[27],"ILS":[29,65,88],"problem":[30],"sphere":[32,37,175],"decoding.":[33],"To":[34],"make":[35],"decoder":[38],"faster,":[39],"the":[40,54,64,71,75,83,87,93,108,114,118,151,155,164,171,182,187,191],"well-known":[41],"LLL":[42,109,165],"reduction":[43,110,166],"often":[45,141],"used":[46,142],"as":[47,78],"preprocessing.":[48],"The":[49],"Babai":[50,55,76,119,156],"point":[51,77,120],"produced":[52],"by":[53,97,181],"nearest":[56],"plane":[57],"algorithm":[58,111,167],"suboptimal":[61],"solution":[62],"of":[63,74,86,117,154,174,184],"First,":[67],"we":[68,103,159],"prove":[69],"that":[70,106,134,162],"success":[72,84,115,152],"probability":[73,85,116,153],"lower":[80,94],"bound":[81,95],"on":[82],"estimator":[89],"sharper":[91],"than":[92],"given":[96],"Hassibi":[98],"and":[99,121,125,147],"Boyd":[100],"[1].":[101],"Then,":[102],"show":[104,133,160],"rigorously":[105,161],"applying":[107,163],"will":[112,168],"increase":[113],"give":[122,130],"some":[123],"theoretical":[124],"numerical":[126],"test":[127],"results.":[128],"We":[129],"examples":[131],"unlike":[135],"LLL's":[136],"column":[137,143],"permutation":[138,144],"strategy,":[139],"two":[140],"strategies":[145],"SQRD":[146],"V-BLAST":[148],"may":[149],"decrease":[150],"point.":[157],"Finally,":[158],"also":[169],"reduce":[170],"computational":[172],"complexity":[173],"decoders,":[176],"which":[177],"measured":[179],"approximately":[180],"number":[183],"nodes":[185],"search":[188],"tree":[189],"literature.":[192]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}