{"id":"https://openalex.org/W3209153759","doi":"https://doi.org/10.1109/tit.2021.3123497","title":"Threshold Rates for Properties of Random Codes","display_name":"Threshold Rates for Properties of Random Codes","publication_year":2021,"publication_date":"2021-10-27","ids":{"openalex":"https://openalex.org/W3209153759","doi":"https://doi.org/10.1109/tit.2021.3123497","mag":"3209153759"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2021.3123497","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2021.3123497","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2009.04553","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068388812","display_name":"Venkatesan Guruswami","orcid":"https://orcid.org/0000-0001-7926-3396"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Venkatesan Guruswami","raw_affiliation_strings":["Computer Science Department, Carnegie Mellon University, Pittsburgh, PA, USA"],"affiliations":[{"raw_affiliation_string":"Computer Science Department, Carnegie Mellon University, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011716651","display_name":"Jonathan Mosheiff","orcid":"https://orcid.org/0000-0002-7947-1205"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jonathan Mosheiff","raw_affiliation_strings":["School of Computer Science, Carnegie Mellon University, Pittsburgh, PA, USA"],"affiliations":[{"raw_affiliation_string":"School of Computer Science, Carnegie Mellon University, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065218643","display_name":"Nicolas Resch","orcid":"https://orcid.org/0000-0002-5133-5631"},"institutions":[{"id":"https://openalex.org/I1341640284","display_name":"Centrum Wiskunde & Informatica","ror":"https://ror.org/00x7ekv49","country_code":"NL","type":"facility","lineage":["https://openalex.org/I1341640284","https://openalex.org/I2800991832"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Nicolas Resch","raw_affiliation_strings":["Centrum Wiskunde en Informatica, Amsterdam, XG, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Centrum Wiskunde en Informatica, Amsterdam, XG, The Netherlands","institution_ids":["https://openalex.org/I1341640284"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078443823","display_name":"Shashwat Silas","orcid":"https://orcid.org/0000-0002-1742-7137"},"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":"Shashwat Silas","raw_affiliation_strings":["Computer Science Department, Stanford University, Stanford, CA, USA"],"affiliations":[{"raw_affiliation_string":"Computer Science Department, Stanford University, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022963784","display_name":"Mary Wootters","orcid":"https://orcid.org/0000-0002-2345-2531"},"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":"Mary Wootters","raw_affiliation_strings":["Computer Science Department and the Department of Electrical Engineering, Stanford University, Stanford, CA, USA"],"affiliations":[{"raw_affiliation_string":"Computer Science Department and the Department of Electrical Engineering, Stanford University, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5068388812"],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":null,"apc_paid":null,"fwci":0.42,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.70190297,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"68","issue":"2","first_page":"905","last_page":"922"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9986000061035156,"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"}},"topics":[{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9986000061035156,"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/T11130","display_name":"Coding theory and cryptography","score":0.9977999925613403,"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/T11567","display_name":"semigroups and automata theory","score":0.9977999925613403,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.6832876205444336},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4659629166126251},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3534439206123352},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3301948308944702},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.12939882278442383}],"concepts":[{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.6832876205444336},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4659629166126251},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3534439206123352},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3301948308944702},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.12939882278442383}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2021.3123497","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2021.3123497","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:arXiv.org:2009.04553","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2009.04553","pdf_url":"https://arxiv.org/pdf/2009.04553","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":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2009.04553","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2009.04553","pdf_url":"https://arxiv.org/pdf/2009.04553","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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1740449593","display_name":null,"funder_award_id":"CCF-1563742","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6751408502","display_name":null,"funder_award_id":"CCF-1814603","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G677682426","display_name":null,"funder_award_id":"74079","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W390146837","https://openalex.org/W1510599311","https://openalex.org/W1559492868","https://openalex.org/W1580365030","https://openalex.org/W2029773437","https://openalex.org/W2053816258","https://openalex.org/W2055309977","https://openalex.org/W2056884477","https://openalex.org/W2072942107","https://openalex.org/W2090418561","https://openalex.org/W2162725776","https://openalex.org/W2168365126","https://openalex.org/W2543082256","https://openalex.org/W2775887812","https://openalex.org/W2963480797","https://openalex.org/W2964303929","https://openalex.org/W2982506607","https://openalex.org/W3108728869","https://openalex.org/W3149161352","https://openalex.org/W3195642419","https://openalex.org/W3214532196","https://openalex.org/W4205759049","https://openalex.org/W4293052541","https://openalex.org/W4367669913","https://openalex.org/W6767071336","https://openalex.org/W6805571428"],"related_works":["https://openalex.org/W1978042415","https://openalex.org/W3086542228","https://openalex.org/W2017331178","https://openalex.org/W2976797620","https://openalex.org/W2334965593","https://openalex.org/W1978225469","https://openalex.org/W2567026640","https://openalex.org/W3103555317","https://openalex.org/W1978588354","https://openalex.org/W1412164264"],"abstract_inverted_index":{"Suppose":[0],"that":[1,12,54,66,83,222,236],"<inline-formula":[2,20,34,43,60,74,84,97,110,124,138,152,254],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[3,21,35,44,61,75,85,93,98,111,125,139,153,230,255,289],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[4,22,36,45,62,76,86,99,112,126,140,154,256],"<tex-math":[5,23,37,46,63,77,87,100,113,127,141,155,257],"notation=\"LaTeX\">$\\mathcal":[6,47,101,128,156,258],"{P}$":[7,48,102,129,157,259],"</tex-math></inline-formula>":[8,28,41,49,65,79,89,103,118,130,146,158,260],"is":[9,90,119,147,226],"a":[10,17,105,133,189,237],"property":[11,53,253],"may":[13],"be":[14,51],"satisfied":[15],"by":[16,202],"random":[18,106,134,161],"code":[19,107,135],"notation=\"LaTeX\">$C":[24],"\\subset":[25],"\\Sigma":[26],"^{n}$":[27],".":[29,80,159],"For":[30,215],"example,":[31],"for":[32,96,172,188,251,270,282,287],"some":[33,69],"notation=\"LaTeX\">$p":[38],"\\in":[39],"(0,1)$":[40],",":[42,131],"might":[50],"the":[52,91,169,177,197,203,223,233,248,252,267,284],"there":[55],"exist":[56],"three":[57],"elements":[58],"of":[59,72,108,136,192,205,208],"notation=\"LaTeX\">$C$":[64],"lie":[67],"in":[68,165,217,227,272,291],"Hamming":[70],"ball":[71],"radius":[73],"notation=\"LaTeX\">$pn$":[78],"We":[81,184],"say":[82],"notation=\"LaTeX\">$R^{\\ast}$":[88],"<italic":[92,229,288],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">threshold":[94],"rate</i>":[95],"if":[104],"rate":[109,137,225,250,269],"notation=\"LaTeX\">$R^{\\ast}":[114,142],"+":[115],"\\varepsilon":[116,144],"$":[117,145],"very":[120,148],"likely":[121],"to":[122,150,232],"satisfy":[123,151],"while":[132],"-":[143],"unlikely":[149],"While":[160],"codes":[162],"are":[163,180,200,211],"well-studied":[164],"coding":[166],"theory,":[167],"even":[168],"threshold":[170,186,224,249,268,285],"rates":[171,187,286],"relatively":[173],"simple":[174,238],"properties":[175,216],"like":[176,196],"one":[178],"above":[179],"not":[181,244],"well":[182,277],"understood.":[183],"characterize":[185],"rich":[190],"class":[191],"properties.":[193],"These":[194],"properties,":[195],"example":[198],"above,":[199,261],"defined":[201],"inclusion":[204],"specific":[206],"sets":[207],"codewords":[209],"which":[210],"also":[212],"suitably":[213],"\u201csymmetric.\u201d":[214],"this":[218],"class,":[219],"we":[220],"show":[221],"fact":[228],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">equal</i>":[231],"lower":[234],"bound":[235],"first-moment":[239],"calculation":[240],"obtains.":[241],"Our":[242],"techniques":[243],"only":[245],"pin":[246],"down":[247],"they":[262],"give":[263],"sharp":[264],"bounds":[265],"on":[266],"list-recovery":[271],"several":[273],"parameter":[274],"regimes,":[275],"as":[276,278],"an":[279],"efficient":[280],"algorithm":[281],"estimating":[283],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">list-recovery</i>":[290],"general.":[292]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
