{"id":"https://openalex.org/W3197187995","doi":"https://doi.org/10.1109/isit45174.2021.9517756","title":"Soft Minoration: Solution to Cover's Problem In the Original Discrete Memoryless Setting","display_name":"Soft Minoration: Solution to Cover's Problem In the Original Discrete Memoryless Setting","publication_year":2021,"publication_date":"2021-07-12","ids":{"openalex":"https://openalex.org/W3197187995","doi":"https://doi.org/10.1109/isit45174.2021.9517756","mag":"3197187995"},"language":"en","primary_location":{"id":"doi:10.1109/isit45174.2021.9517756","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit45174.2021.9517756","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2021 IEEE International Symposium on Information Theory (ISIT)","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/A5100383868","display_name":"Jingbo Liu","orcid":"https://orcid.org/0000-0001-5637-5264"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jingbo Liu","raw_affiliation_strings":["University of Illinois,Department of Statistics and Department of Electrical and Computer Engineering,Urbana-Champaign","Department of Statistics and Department of Electrical and Computer Engineering, University of Illinois, Urbana-Champaign"],"affiliations":[{"raw_affiliation_string":"University of Illinois,Department of Statistics and Department of Electrical and Computer Engineering,Urbana-Champaign","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"Department of Statistics and Department of Electrical and Computer Engineering, University of Illinois, Urbana-Champaign","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5100383868"],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":null,"apc_paid":null,"fwci":0.1012,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.43482204,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"1648","last_page":"1652"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10964","display_name":"Wireless Communication Security Techniques","score":0.9991999864578247,"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":0.9991999864578247,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9983000159263611,"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"}},{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9031000137329102,"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/cover","display_name":"Cover (algebra)","score":0.6514514684677124},{"id":"https://openalex.org/keywords/infimum-and-supremum","display_name":"Infimum and supremum","score":0.6347827911376953},{"id":"https://openalex.org/keywords/bounding-overwatch","display_name":"Bounding overwatch","score":0.6339623332023621},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5940835475921631},{"id":"https://openalex.org/keywords/relay","display_name":"Relay","score":0.5142409205436707},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4987180233001709},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.45346084237098694},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.4489884376525879},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.44849419593811035},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4271456003189087},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4246664047241211},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4109515845775604},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35480958223342896},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2862616181373596},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12537908554077148},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10648581385612488}],"concepts":[{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.6514514684677124},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.6347827911376953},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.6339623332023621},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5940835475921631},{"id":"https://openalex.org/C2778156585","wikidata":"https://www.wikidata.org/wiki/Q174053","display_name":"Relay","level":3,"score":0.5142409205436707},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4987180233001709},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.45346084237098694},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4489884376525879},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.44849419593811035},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4271456003189087},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4246664047241211},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4109515845775604},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35480958223342896},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2862616181373596},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12537908554077148},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10648581385612488},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","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/isit45174.2021.9517756","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit45174.2021.9517756","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2021 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6100000143051147,"id":"https://metadata.un.org/sdg/9","display_name":"Industry, innovation and infrastructure"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W950997499","https://openalex.org/W1644323187","https://openalex.org/W2014031743","https://openalex.org/W2089555817","https://openalex.org/W2097854052","https://openalex.org/W2112743058","https://openalex.org/W2162635854","https://openalex.org/W2741290151","https://openalex.org/W2744192101","https://openalex.org/W2766775506","https://openalex.org/W2783136786","https://openalex.org/W2788914578","https://openalex.org/W2963368320","https://openalex.org/W3042411152","https://openalex.org/W3042939197","https://openalex.org/W3080447237","https://openalex.org/W3081123008","https://openalex.org/W3106552691","https://openalex.org/W3196984802","https://openalex.org/W4210783106","https://openalex.org/W6653922964"],"related_works":["https://openalex.org/W2953175190","https://openalex.org/W2257286100","https://openalex.org/W4288318511","https://openalex.org/W2562705109","https://openalex.org/W2099602951","https://openalex.org/W2098184873","https://openalex.org/W2950484692","https://openalex.org/W2030840627","https://openalex.org/W2117694977","https://openalex.org/W4288910996"],"abstract_inverted_index":{"In":[0,58,96],"1987,":[1],"Cover":[2],"raised":[3],"a":[4,18,89,109,121,145,151],"question":[5],"about":[6],"the":[7,14,24,28,40,45,66,80,86,101,117,127,138,141,163],"minimum":[8,102],"relay":[9,21,103,114],"rate":[10,104],"needed":[11],"for":[12,39,105],"achieving":[13],"maximum":[15,106],"capacity":[16,107],"in":[17,108],"symmetric":[19,42,113],"discrete-memoryless":[20],"channel.":[22],"Despite":[23],"many":[25],"efforts":[26],"over":[27],"past":[29],"and":[30,79,160],"recent":[31],"years,":[32],"this":[33,59],"problem":[34,78,82],"was":[35],"previously":[36],"only":[37],"solved":[38],"binary":[41],"case":[43],"or":[44],"Gaussian":[46],"counterpart,":[47],"where":[48],"arguments":[49],"specialized":[50],"to":[51,166],"these":[52],"particular":[53],"channel":[54,115],"distributions":[55],"were":[56],"used.":[57],"paper,":[60],"through":[61],"different":[62],"information-theoretic":[63],"expansions":[64],"highlighting":[65],"unique":[67],"capacity-achieving":[68,128],"output":[69,129],"distribution,":[70,130],"we":[71,98],"demonstrate":[72],"an":[73],"interesting":[74],"connection":[75],"between":[76],"Cover's":[77,134],"minoration":[81],"(i.e.,":[83],"lower":[84,149],"bounding":[85,150],"supremum":[87],"of":[88,120,148,162,168],"stochastic":[90],"process)":[91],"from":[92],"high":[93],"dimensional":[94],"probability.":[95],"particular,":[97],"show":[99],"that":[100],"general":[110],"discrete":[111],"memoryless":[112],"is":[116,144,155],"conditional":[118],"entropy":[119],"certain":[122],"equivalence":[123],"class":[124],"determined":[125],"by":[126],"thus":[131],"completely":[132],"resolving":[133],"original":[135],"problem.":[136],"On":[137],"probability":[139],"part,":[140],"main":[142],"innovation":[143],"robust":[146],"method":[147],"soft-max":[152],"(soft-minoration),":[153],"which":[154],"based":[156],"on":[157],"mixed-volume":[158],"inequalities":[159],"estimates":[161],"Banach-Mazur":[164],"distance":[165],"subspaces":[167],"<tex":[169],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[170],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$\\ell_{\\infty}$</tex>":[171],".":[172]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-03-25T13:04:00.132906","created_date":"2025-10-10T00:00:00"}
