{"id":"https://openalex.org/W2093759883","doi":"https://doi.org/10.1109/tvlsi.2014.2322573","title":"Revisiting Central Limit Theorem: Accurate Gaussian Random Number Generation in VLSI","display_name":"Revisiting Central Limit Theorem: Accurate Gaussian Random Number Generation in VLSI","publication_year":2014,"publication_date":"2014-06-19","ids":{"openalex":"https://openalex.org/W2093759883","doi":"https://doi.org/10.1109/tvlsi.2014.2322573","mag":"2093759883"},"language":"en","primary_location":{"id":"doi:10.1109/tvlsi.2014.2322573","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvlsi.2014.2322573","pdf_url":null,"source":{"id":"https://openalex.org/S37538908","display_name":"IEEE Transactions on Very Large Scale Integration (VLSI) Systems","issn_l":"1063-8210","issn":["1063-8210","1557-9999"],"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 Very Large Scale Integration (VLSI) Systems","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/A5012780000","display_name":"Jamshaid Sarwar Malik","orcid":null},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]},{"id":"https://openalex.org/I929597975","display_name":"National University of Sciences and Technology","ror":"https://ror.org/03w2j5y17","country_code":"PK","type":"education","lineage":["https://openalex.org/I929597975"]}],"countries":["PK","SE"],"is_corresponding":true,"raw_author_name":"Jamshaid Sarwar Malik","raw_affiliation_strings":["KTH Royal Institute of Technology, Stockholm, Sweden","National University of Sciences and Technology, Islamabad, Pakistan","KTH Royal Institute of Technology; Stockholm Sweden"],"affiliations":[{"raw_affiliation_string":"KTH Royal Institute of Technology, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]},{"raw_affiliation_string":"National University of Sciences and Technology, Islamabad, Pakistan","institution_ids":["https://openalex.org/I929597975"]},{"raw_affiliation_string":"KTH Royal Institute of Technology; Stockholm Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026355063","display_name":"Ahmed Hemani","orcid":"https://orcid.org/0000-0003-0565-9376"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Ahmed Hemani","raw_affiliation_strings":["KTH Royal Institute of Technology, Stockholm, Sweden","KTH Royal Institute of Technology; Stockholm Sweden"],"affiliations":[{"raw_affiliation_string":"KTH Royal Institute of Technology, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]},{"raw_affiliation_string":"KTH Royal Institute of Technology; Stockholm Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040515200","display_name":"Jameel Nawaz Malik","orcid":null},"institutions":[{"id":"https://openalex.org/I110357561","display_name":"University of the Sciences","ror":"https://ror.org/048gmay44","country_code":"US","type":"education","lineage":["https://openalex.org/I110357561"]},{"id":"https://openalex.org/I929597975","display_name":"National University of Sciences and Technology","ror":"https://ror.org/03w2j5y17","country_code":"PK","type":"education","lineage":["https://openalex.org/I929597975"]},{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["PK","SE","US"],"is_corresponding":false,"raw_author_name":"Jameel Nawaz Malik","raw_affiliation_strings":["KTH Royal Institute of Technology, Stockholm, Sweden","National University of Sciences and Technology, Islamabad, Pakistan","National University of Sciences and Technology, Islamabad, PAKISTAN"],"affiliations":[{"raw_affiliation_string":"KTH Royal Institute of Technology, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]},{"raw_affiliation_string":"National University of Sciences and Technology, Islamabad, Pakistan","institution_ids":["https://openalex.org/I929597975"]},{"raw_affiliation_string":"National University of Sciences and Technology, Islamabad, PAKISTAN","institution_ids":["https://openalex.org/I110357561"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021092453","display_name":"Ben Silmane","orcid":null},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Ben Silmane","raw_affiliation_strings":["KTH Royal Institute of Technology, Stockholm, Sweden","KTH Royal Institute of Technology; Stockholm Sweden"],"affiliations":[{"raw_affiliation_string":"KTH Royal Institute of Technology, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]},{"raw_affiliation_string":"KTH Royal Institute of Technology; Stockholm Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032575129","display_name":"N. D. Gohar","orcid":null},"institutions":[{"id":"https://openalex.org/I929597975","display_name":"National University of Sciences and Technology","ror":"https://ror.org/03w2j5y17","country_code":"PK","type":"education","lineage":["https://openalex.org/I929597975"]},{"id":"https://openalex.org/I110357561","display_name":"University of the Sciences","ror":"https://ror.org/048gmay44","country_code":"US","type":"education","lineage":["https://openalex.org/I110357561"]}],"countries":["PK","US"],"is_corresponding":false,"raw_author_name":"Nasirud Din Gohar","raw_affiliation_strings":["National University of Sciences and Technology, Islamabad, Pakistan","National University of Sciences and Technology, Islamabad, PAKISTAN"],"affiliations":[{"raw_affiliation_string":"National University of Sciences and Technology, Islamabad, Pakistan","institution_ids":["https://openalex.org/I929597975"]},{"raw_affiliation_string":"National University of Sciences and Technology, Islamabad, PAKISTAN","institution_ids":["https://openalex.org/I110357561"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5012780000"],"corresponding_institution_ids":["https://openalex.org/I86987016","https://openalex.org/I929597975"],"apc_list":null,"apc_paid":null,"fwci":1.0682,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.78672478,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"23","issue":"5","first_page":"842","last_page":"855"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10363","display_name":"Low-power high-performance VLSI design","score":0.9914000034332275,"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/central-limit-theorem","display_name":"Central limit theorem","score":0.708399772644043},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.6392971873283386},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.6154171824455261},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6146928668022156},{"id":"https://openalex.org/keywords/very-large-scale-integration","display_name":"Very-large-scale integration","score":0.6128944754600525},{"id":"https://openalex.org/keywords/design-space-exploration","display_name":"Design space exploration","score":0.5113782286643982},{"id":"https://openalex.org/keywords/random-number-generation","display_name":"Random number generation","score":0.49127715826034546},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45200130343437195},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.44635283946990967},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.4309624433517456},{"id":"https://openalex.org/keywords/computer-engineering","display_name":"Computer engineering","score":0.42028704285621643},{"id":"https://openalex.org/keywords/gate-array","display_name":"Gate array","score":0.4202338457107544},{"id":"https://openalex.org/keywords/field-programmable-gate-array","display_name":"Field-programmable gate array","score":0.35864782333374023},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.264830619096756},{"id":"https://openalex.org/keywords/computer-hardware","display_name":"Computer hardware","score":0.19789046049118042},{"id":"https://openalex.org/keywords/embedded-system","display_name":"Embedded system","score":0.1739242970943451}],"concepts":[{"id":"https://openalex.org/C166785042","wikidata":"https://www.wikidata.org/wiki/Q190391","display_name":"Central limit theorem","level":2,"score":0.708399772644043},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.6392971873283386},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6154171824455261},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6146928668022156},{"id":"https://openalex.org/C14580979","wikidata":"https://www.wikidata.org/wiki/Q876049","display_name":"Very-large-scale integration","level":2,"score":0.6128944754600525},{"id":"https://openalex.org/C2776221188","wikidata":"https://www.wikidata.org/wiki/Q21072556","display_name":"Design space exploration","level":2,"score":0.5113782286643982},{"id":"https://openalex.org/C201866948","wikidata":"https://www.wikidata.org/wiki/Q228206","display_name":"Random number generation","level":2,"score":0.49127715826034546},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45200130343437195},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.44635283946990967},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.4309624433517456},{"id":"https://openalex.org/C113775141","wikidata":"https://www.wikidata.org/wiki/Q428691","display_name":"Computer engineering","level":1,"score":0.42028704285621643},{"id":"https://openalex.org/C114237110","wikidata":"https://www.wikidata.org/wiki/Q114901","display_name":"Gate array","level":3,"score":0.4202338457107544},{"id":"https://openalex.org/C42935608","wikidata":"https://www.wikidata.org/wiki/Q190411","display_name":"Field-programmable gate array","level":2,"score":0.35864782333374023},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.264830619096756},{"id":"https://openalex.org/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.19789046049118042},{"id":"https://openalex.org/C149635348","wikidata":"https://www.wikidata.org/wiki/Q193040","display_name":"Embedded system","level":1,"score":0.1739242970943451},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tvlsi.2014.2322573","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvlsi.2014.2322573","pdf_url":null,"source":{"id":"https://openalex.org/S37538908","display_name":"IEEE Transactions on Very Large Scale Integration (VLSI) Systems","issn_l":"1063-8210","issn":["1063-8210","1557-9999"],"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 Very Large Scale Integration (VLSI) Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W29152108","https://openalex.org/W589733436","https://openalex.org/W617691326","https://openalex.org/W1491431717","https://openalex.org/W1498855283","https://openalex.org/W1505109187","https://openalex.org/W1522106723","https://openalex.org/W1540584048","https://openalex.org/W1568404366","https://openalex.org/W1582019318","https://openalex.org/W1583465493","https://openalex.org/W1939348723","https://openalex.org/W1965612527","https://openalex.org/W1979081194","https://openalex.org/W1981663184","https://openalex.org/W1990842406","https://openalex.org/W2011398297","https://openalex.org/W2031648200","https://openalex.org/W2061364950","https://openalex.org/W2086688806","https://openalex.org/W2089389313","https://openalex.org/W2097774686","https://openalex.org/W2101832782","https://openalex.org/W2104093342","https://openalex.org/W2113978128","https://openalex.org/W2127673207","https://openalex.org/W2137900810","https://openalex.org/W2141116325","https://openalex.org/W2142840816","https://openalex.org/W2151439684","https://openalex.org/W2157652868","https://openalex.org/W2160495765","https://openalex.org/W2162074762","https://openalex.org/W2164610260","https://openalex.org/W2169485677","https://openalex.org/W2170039990","https://openalex.org/W2189305330","https://openalex.org/W2752853835","https://openalex.org/W2796936280","https://openalex.org/W3104594640","https://openalex.org/W4285310632","https://openalex.org/W6601138359","https://openalex.org/W6675661131","https://openalex.org/W6678992122","https://openalex.org/W6685184648"],"related_works":["https://openalex.org/W2798819106","https://openalex.org/W2897876927","https://openalex.org/W3092094169","https://openalex.org/W3148717199","https://openalex.org/W4382565725","https://openalex.org/W2189170925","https://openalex.org/W2946330045","https://openalex.org/W2905070931","https://openalex.org/W2916414482","https://openalex.org/W1995613452"],"abstract_inverted_index":{"Gaussian":[0,18],"random":[1],"numbers":[2],"(GRNs)":[3],"generated":[4],"by":[5,189],"central":[6],"limit":[7],"theorem":[8],"(CLT)":[9],"suffer":[10],"from":[11,16,132],"errors":[12],"due":[13],"to":[14,36,61,79,93,135],"deviation":[15],"ideal":[17],"behavior":[19],"for":[20],"any":[21],"finite":[22],"number":[23],"of":[24,77,83,102,106,112,148,153,166],"additions.":[25],"In":[26],"this":[27,90,149],"paper,":[28],"we":[29,179],"will":[30,55,99,161,180],"show":[31],"that":[32],"it":[33],"is":[34],"possible":[35],"compensate":[37],"the":[38,44,51,63],"error":[39,64],"in":[40,50,65,110,151,169],"CLT,":[41],"thereby":[42],"correcting":[43],"resultant":[45],"probability":[46],"density":[47],"function,":[48],"particularly":[49],"tail":[52],"regions.":[53],"We":[54,98,160],"provide":[56,163],"a":[57,69,81],"detailed":[58],"mathematical":[59],"analysis":[60],"quantify":[62],"CLT.":[66],"This":[67],"provides":[68],"design":[70,91],"space":[71,92],"with":[72,141,185],"more":[73],"than":[74],"four":[75],"degrees":[76],"freedom":[78],"build":[80],"variety":[82],"GRN":[84],"generators":[85],"(GRNGs).":[86],"A":[87,139],"framework":[88],"utilizes":[89],"generate":[94],"customized":[95],"hardware":[96,156],"architectures.":[97],"demonstrate":[100],"designs":[101,144,168],"five":[103],"different":[104],"architectures":[105,128,187],"GRNGs,":[107],"which":[108],"vary":[109],"terms":[111,152],"consumed":[113,155],"memory,":[114],"logic":[115],"slices,":[116],"and":[117,158],"multipliers":[118],"on":[119],"field-programmable":[120],"gate":[121],"array.":[122],"Similarly,":[123],"depending":[124],"upon":[125],"application,":[126],"these":[127],"exhibit":[129],"statistical":[130],"accuracy":[131],"low":[133],"(4\u03c3)":[134],"extremely":[136],"high":[137],"(12\u03c3).":[138],"comparison":[140],"previously":[142],"published":[143],"clearly":[145],"indicate":[146],"advantages":[147],"methodology":[150],"both":[154],"resources":[157],"accuracy.":[159],"also":[162],"synthesis":[164],"results":[165],"same":[167],"application-specific":[170],"integrated":[171],"circuit":[172],"using":[173],"65-nm":[174],"standard":[175],"cell":[176],"library.":[177],"Finally,":[178],"highlight":[181],"some":[182],"shortcomings":[183],"associated":[184],"such":[186],"followed":[188],"their":[190],"remedies.":[191]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
