{"id":"https://openalex.org/W2268439312","doi":"https://doi.org/10.1109/isit.2010.5513337","title":"Error rates of capacity-achieving codes are convex","display_name":"Error rates of capacity-achieving codes are convex","publication_year":2010,"publication_date":"2010-06-01","ids":{"openalex":"https://openalex.org/W2268439312","doi":"https://doi.org/10.1109/isit.2010.5513337","mag":"2268439312"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2010.5513337","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2010.5513337","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 IEEE International Symposium on Information Theory","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/A5065761968","display_name":"Sergey Loyka","orcid":"https://orcid.org/0000-0002-6405-5524"},"institutions":[{"id":"https://openalex.org/I153718931","display_name":"University of Ottawa","ror":"https://ror.org/03c4mmv16","country_code":"CA","type":"education","lineage":["https://openalex.org/I153718931"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Sergey Loyka","raw_affiliation_strings":["SITE, University of Ottawa, Ottawa, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"SITE, University of Ottawa, Ottawa, Canada","institution_ids":["https://openalex.org/I153718931"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021397477","display_name":"Fran\u00e7ois Gagnon","orcid":"https://orcid.org/0000-0002-4558-3401"},"institutions":[{"id":"https://openalex.org/I9736820","display_name":"\u00c9cole de Technologie Sup\u00e9rieure","ror":"https://ror.org/0020snb74","country_code":"CA","type":"education","lineage":["https://openalex.org/I49663120","https://openalex.org/I9736820"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Francois Gagnon","raw_affiliation_strings":["Department of Electrical Engineering, Ecole de Technologie Sup\u00e9rieure, Montreal, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Ecole de Technologie Sup\u00e9rieure, Montreal, Canada","institution_ids":["https://openalex.org/I9736820"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001633086","display_name":"Victoria Kostina","orcid":"https://orcid.org/0000-0002-2406-7440"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Victoria Kostina","raw_affiliation_strings":["Department of Electrical Engineering, Princeton University, Princeton, NJ, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Princeton University, Princeton, NJ, USA","institution_ids":["https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.4713,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.84857986,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"325","last_page":"329"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10964","display_name":"Wireless Communication Security Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.9987000226974487,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/decoding-methods","display_name":"Decoding methods","score":0.5629211664199829},{"id":"https://openalex.org/keywords/additive-white-gaussian-noise","display_name":"Additive white Gaussian noise","score":0.5607213377952576},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5578763484954834},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5109331011772156},{"id":"https://openalex.org/keywords/noise-power","display_name":"Noise power","score":0.4800789952278137},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.44971194863319397},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.44875040650367737},{"id":"https://openalex.org/keywords/channel-capacity","display_name":"Channel capacity","score":0.44683530926704407},{"id":"https://openalex.org/keywords/bit-error-rate","display_name":"Bit error rate","score":0.43561357259750366},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3718050718307495},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.363059401512146},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3583177626132965},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.32185035943984985},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.29256588220596313},{"id":"https://openalex.org/keywords/white-noise","display_name":"White noise","score":0.2574697732925415},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.24895158410072327},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09007644653320312}],"concepts":[{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.5629211664199829},{"id":"https://openalex.org/C169334058","wikidata":"https://www.wikidata.org/wiki/Q353292","display_name":"Additive white Gaussian noise","level":3,"score":0.5607213377952576},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5578763484954834},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5109331011772156},{"id":"https://openalex.org/C203234222","wikidata":"https://www.wikidata.org/wiki/Q2133519","display_name":"Noise power","level":3,"score":0.4800789952278137},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.44971194863319397},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.44875040650367737},{"id":"https://openalex.org/C97744766","wikidata":"https://www.wikidata.org/wiki/Q870845","display_name":"Channel capacity","level":3,"score":0.44683530926704407},{"id":"https://openalex.org/C56296756","wikidata":"https://www.wikidata.org/wiki/Q840922","display_name":"Bit error rate","level":3,"score":0.43561357259750366},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3718050718307495},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.363059401512146},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3583177626132965},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.32185035943984985},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.29256588220596313},{"id":"https://openalex.org/C112633086","wikidata":"https://www.wikidata.org/wiki/Q381287","display_name":"White noise","level":2,"score":0.2574697732925415},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.24895158410072327},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09007644653320312},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit.2010.5513337","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2010.5513337","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 IEEE International Symposium on Information Theory","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.7900000214576721}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1503221585","https://openalex.org/W1568307856","https://openalex.org/W1577906631","https://openalex.org/W1629679131","https://openalex.org/W1979931516","https://openalex.org/W2101362947","https://openalex.org/W2106464481","https://openalex.org/W2111357004","https://openalex.org/W2113165941","https://openalex.org/W2115040155","https://openalex.org/W2129015875","https://openalex.org/W2135479785","https://openalex.org/W2165350939","https://openalex.org/W2296319761","https://openalex.org/W2547954945","https://openalex.org/W3103148956","https://openalex.org/W4250589301","https://openalex.org/W4252713891"],"related_works":["https://openalex.org/W3090071501","https://openalex.org/W2165991268","https://openalex.org/W2015705343","https://openalex.org/W2371289173","https://openalex.org/W4244093570","https://openalex.org/W2301162158","https://openalex.org/W1682736069","https://openalex.org/W2015579740","https://openalex.org/W2155687826","https://openalex.org/W2170302359"],"abstract_inverted_index":{"Motivated":[0],"by":[1],"a":[2],"wide-spread":[3],"use":[4],"of":[5,11,15,47,59],"convex":[6,57,106,122],"optimization":[7],"techniques,":[8],"convexity":[9],"properties":[10],"bit":[12,31,50],"error":[13,48,51,107,123],"rate":[14,52],"the":[16,22,44,60,66,83,88,94],"maximum":[17],"likelihood":[18],"detector":[19],"operating":[20],"in":[21,65,93,109],"AWGN":[23],"channel":[24,95],"are":[25,53],"studied":[26],"for":[27],"arbitrary":[28],"constellations":[29],"and":[30,49,62,103,112],"mappings,":[32],"which":[33],"also":[34],"includes":[35],"coding":[36,96],"under":[37],"maximum-likelihood":[38],"decoding.":[39],"Under":[40],"this":[41,99],"generic":[42],"setting,":[43],"pairwise":[45],"probability":[46],"shown":[54],"to":[55],"be":[56],"functions":[58],"SNR":[61,101,111],"noise":[63,69,85,89,113],"power":[64],"high":[67,100],"SNR/low":[68],"regime":[70],"with":[71],"explicitly-determined":[72],"boundary.":[73],"Any":[74],"code,":[75],"including":[76],"capacity-achieving":[77,119],"ones,":[78],"whose":[79],"decision":[80],"regions":[81],"include":[82],"hardened":[84],"spheres":[86],"(from":[87],"sphere":[90],"hardening":[91],"argument":[92],"theorem)":[97],"satisfies":[98],"requirement":[102],"thus":[104],"has":[105],"rates":[108],"both":[110],"power.":[114],"We":[115],"conjecture":[116],"that":[117],"all":[118],"codes":[120],"have":[121],"rates.":[124]},"counts_by_year":[{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}