{"id":"https://openalex.org/W2951864881","doi":"https://doi.org/10.1109/tac.2021.3126679","title":"Exact Minimum Number of Bits to Stabilize a Linear System","display_name":"Exact Minimum Number of Bits to Stabilize a Linear System","publication_year":2021,"publication_date":"2021-11-09","ids":{"openalex":"https://openalex.org/W2951864881","doi":"https://doi.org/10.1109/tac.2021.3126679","mag":"2951864881"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2021.3126679","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2021.3126679","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1807.07686","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001633086","display_name":"Victoria Kostina","orcid":"https://orcid.org/0000-0002-2406-7440"},"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":"Victoria Kostina","raw_affiliation_strings":["California Institute of Technology, Pasadena, CA, USA","#N##TAB##TAB##TAB##TAB# California Institute of Technology#N##TAB##TAB##TAB#"],"raw_orcid":"https://orcid.org/0000-0002-2406-7440","affiliations":[{"raw_affiliation_string":"California Institute of Technology, Pasadena, CA, USA","institution_ids":["https://openalex.org/I122411786"]},{"raw_affiliation_string":"#N##TAB##TAB##TAB##TAB# California Institute of Technology#N##TAB##TAB##TAB#","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020836845","display_name":"Yuval Peres","orcid":"https://orcid.org/0000-0001-5456-6323"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yuval Peres","raw_affiliation_strings":["Independent Researcher, Kent, OH, USA","[Mathematics, Independent researcher, Kent, OH, United States of America, 44242 (e-mail: yperes@gmail.com)]"],"raw_orcid":"https://orcid.org/0000-0001-5456-6323","affiliations":[{"raw_affiliation_string":"Independent Researcher, Kent, OH, USA","institution_ids":[]},{"raw_affiliation_string":"[Mathematics, Independent researcher, Kent, OH, United States of America, 44242 (e-mail: yperes@gmail.com)]","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055069190","display_name":"Gireeja Ranade","orcid":"https://orcid.org/0000-0002-6747-4492"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Gireeja Ranade","raw_affiliation_strings":["University of California, Berkeley, CA, USA","University of California\u2013Berkeley"],"raw_orcid":"https://orcid.org/0000-0002-6747-4492","affiliations":[{"raw_affiliation_string":"University of California, Berkeley, CA, USA","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"University of California\u2013Berkeley","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012362703","display_name":"Mark Sellke","orcid":"https://orcid.org/0000-0001-9166-8185"},"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":false,"raw_author_name":"Mark Sellke","raw_affiliation_strings":["Stanford University, Stanford, CA, USA","Stanford University ()"],"raw_orcid":"https://orcid.org/0000-0001-9166-8185","affiliations":[{"raw_affiliation_string":"Stanford University, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Stanford University ()","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.00188575,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"67","issue":"10","first_page":"5548","last_page":"5554"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T11236","display_name":"Control Systems and Identification","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9926999807357788,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6799538731575012},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6352999806404114},{"id":"https://openalex.org/keywords/converse","display_name":"Converse","score":0.5356504321098328},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4873290956020355},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.4783739149570465},{"id":"https://openalex.org/keywords/fraction","display_name":"Fraction (chemistry)","score":0.42025405168533325},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4142581820487976},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4131395220756531},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13763314485549927},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12604022026062012}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6799538731575012},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6352999806404114},{"id":"https://openalex.org/C2776809875","wikidata":"https://www.wikidata.org/wiki/Q1375963","display_name":"Converse","level":2,"score":0.5356504321098328},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4873290956020355},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.4783739149570465},{"id":"https://openalex.org/C149629883","wikidata":"https://www.wikidata.org/wiki/Q660926","display_name":"Fraction (chemistry)","level":2,"score":0.42025405168533325},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4142581820487976},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4131395220756531},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13763314485549927},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12604022026062012},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1109/tac.2021.3126679","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2021.3126679","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1807.07686","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1807.07686","pdf_url":"https://arxiv.org/pdf/1807.07686","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:arXiv.org:1807.07686","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1807.07686","pdf_url":"https://arxiv.org/pdf/1807.07686","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2951864881","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1807.07686.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:authors.library.caltech.edu:112526","is_oa":false,"landing_page_url":"https://authors.library.caltech.edu/112526/","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":"Article"},{"id":"pmh:oai:authors.library.caltech.edu:92630","is_oa":false,"landing_page_url":"https://authors.library.caltech.edu/92630/","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"},{"id":"doi:10.48550/arxiv.1807.07686","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1807.07686","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1807.07686","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1807.07686","pdf_url":"https://arxiv.org/pdf/1807.07686","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1129440314","display_name":"Collaborative research: Weighted Estimates with Matrix Weights and Non-Homogeneous Harmonic Analysis","funder_award_id":"1900008","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2580377013","display_name":null,"funder_award_id":"CCF-1751356","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4822468588","display_name":"CAREER: Information Theory of Dynamical Systems","funder_award_id":"1751356","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8200666928","display_name":null,"funder_award_id":"CCF-1751356","funder_id":"https://openalex.org/F4320335353","funder_display_name":"National Science Foundation of Sri Lanka"},{"id":"https://openalex.org/G8218500360","display_name":null,"funder_award_id":"DMS-1900008","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8555123736","display_name":null,"funder_award_id":"DMS-1900008","funder_id":"https://openalex.org/F4320335353","funder_display_name":"National Science Foundation of Sri Lanka"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320334164","display_name":"Simons Institute for the Theory of Computing, University of California Berkeley","ror":null},{"id":"https://openalex.org/F4320335353","display_name":"National Science Foundation of Sri Lanka","ror":"https://ror.org/010xaa060"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W105181866","https://openalex.org/W585548487","https://openalex.org/W1554496325","https://openalex.org/W1608115085","https://openalex.org/W1647263699","https://openalex.org/W1759288767","https://openalex.org/W1968834184","https://openalex.org/W1978848993","https://openalex.org/W1985997249","https://openalex.org/W1995875735","https://openalex.org/W2011970734","https://openalex.org/W2034574658","https://openalex.org/W2043371182","https://openalex.org/W2045663703","https://openalex.org/W2053836930","https://openalex.org/W2065169455","https://openalex.org/W2080096734","https://openalex.org/W2084071523","https://openalex.org/W2095363739","https://openalex.org/W2103684573","https://openalex.org/W2110502851","https://openalex.org/W2110761557","https://openalex.org/W2113231618","https://openalex.org/W2113846837","https://openalex.org/W2116343044","https://openalex.org/W2122161467","https://openalex.org/W2125369456","https://openalex.org/W2142044905","https://openalex.org/W2142804613","https://openalex.org/W2155024125","https://openalex.org/W2156216606","https://openalex.org/W2157076370","https://openalex.org/W2243309170","https://openalex.org/W2783339878","https://openalex.org/W2804194814","https://openalex.org/W2883287107","https://openalex.org/W2941237017","https://openalex.org/W2962807165","https://openalex.org/W2962827319","https://openalex.org/W2963854974","https://openalex.org/W2964215972","https://openalex.org/W3080683916","https://openalex.org/W3102156549","https://openalex.org/W3212606888","https://openalex.org/W4244096180","https://openalex.org/W6604201397"],"related_works":["https://openalex.org/W2883287107","https://openalex.org/W1483514891","https://openalex.org/W2142486118","https://openalex.org/W2786829989","https://openalex.org/W2970552274","https://openalex.org/W2509209082","https://openalex.org/W2003358226","https://openalex.org/W2989787172","https://openalex.org/W3013835216","https://openalex.org/W2943874423","https://openalex.org/W2187127157","https://openalex.org/W3103345129","https://openalex.org/W2954429781","https://openalex.org/W2963951786","https://openalex.org/W2885482639","https://openalex.org/W2614226439","https://openalex.org/W3094857862","https://openalex.org/W2912610280","https://openalex.org/W2966363981","https://openalex.org/W1778948012"],"abstract_inverted_index":{"We":[0,90,156,166],"consider":[1],"an":[2],"unstable":[3],"scalar":[4],"linear":[5],"stochastic":[6],"system,":[7],"<inline-formula":[8,19,29,40,47,71,85,95,106,114],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[9,20,30,41,48,72,86,96,107,115],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex-math":[10,21,31,42,49,73,87,97,108,116],"notation=\"LaTeX\">$X_{n+1}=a":[11],"X_n":[12],"+":[13],"Z_n":[14],"-":[15],"U_n$</tex-math></inline-formula>":[16],",":[17],"where":[18],"notation=\"LaTeX\">$a":[22],"\\geq":[23],"1$</tex-math></inline-formula>":[24],"is":[25,101,124,202],"the":[26,53,129,142,148,153,158,192],"system":[27,83],"gain,":[28],"notation=\"LaTeX\">$Z_n$</tex-math></inline-formula>":[32],"s":[33,51],"are":[34,52,57],"independent":[35],"random":[36],"variables":[37],"with":[38,186],"bounded":[39],"notation=\"LaTeX\">$\\alpha$</tex-math></inline-formula>":[43],"th":[44],"moments,":[45],"and":[46,103,190],"notation=\"LaTeX\">$U_n$</tex-math></inline-formula>":[50],"control":[54],"actions":[55],"that":[56,94,132],"chosen":[58],"by":[59],"a":[60,64,68,125,168,172,196],"controller":[61,143],"who":[62],"receives":[63],"single":[65],"element":[66],"of":[67,128,147,160,171,199],"finite":[69],"set":[70],"notation=\"LaTeX\">$\\lbrace":[74],"1,":[75],"\\ldots,":[76],"M\\rbrace$</tex-math></inline-formula>":[77],"as":[78],"its":[79,145],"only":[80],"information":[81],"about":[82],"state":[84],"notation=\"LaTeX\">$X_i$</tex-math></inline-formula>":[88],".":[89,120],"show":[91,167],"new":[92],"proofs":[93],"notation=\"LaTeX\">$M":[98],"&gt;":[99],"a$</tex-math></inline-formula>":[100],"necessary":[102],"sufficient":[104],"for":[105,112,138],"notation=\"LaTeX\">$\\beta$</tex-math></inline-formula>":[109],"-moment":[110],"stability,":[111],"any":[113],"notation=\"LaTeX\">$\\beta":[117],"&lt;":[118],"\\alpha$</tex-math></inline-formula>":[119],"Our":[121,178],"achievable":[122],"scheme":[123,162],"uniform":[126],"quantizer":[127],"zoom-in/zoom-out":[130],"type":[131],"codes":[133],"over":[134],"multiple":[135],"time":[136],"instants":[137],"data":[139],"rate":[140],"efficiency;":[141],"uses":[144],"memory":[146],"past":[149],"to":[150,181,184,191],"correctly":[151],"interpret":[152],"received":[154],"bits.":[155],"analyze":[157],"performance":[159],"our":[161],"using":[163,175],"probabilistic":[164],"arguments.":[165],"simple":[169],"proof":[170],"matching":[173],"converse":[174],"information-theoretic":[176],"techniques.":[177],"results":[179],"generalize":[180],"vector":[182],"systems,":[183],"systems":[185],"dependent":[187],"Gaussian":[188],"noise,":[189],"scenario":[193],"in":[194],"which":[195],"small":[197],"fraction":[198],"transmitted":[200],"messages":[201],"lost.":[203]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
