{"id":"https://openalex.org/W1973578387","doi":"https://doi.org/10.1109/tit.2011.2173730","title":"Concavity of the Mutual Information Rate for Input-Restricted Memoryless Channels at High SNR","display_name":"Concavity of the Mutual Information Rate for Input-Restricted Memoryless Channels at High SNR","publication_year":2012,"publication_date":"2012-02-28","ids":{"openalex":"https://openalex.org/W1973578387","doi":"https://doi.org/10.1109/tit.2011.2173730","mag":"1973578387"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2011.2173730","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2011.2173730","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":["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/A5000081781","display_name":"Guangyue Han","orcid":"https://orcid.org/0000-0001-9895-5646"},"institutions":[{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["HK"],"is_corresponding":true,"raw_author_name":"Guangyue Han","raw_affiliation_strings":["Department of Mathematics, University of Hong Kong, Hong Kong, China","Dept. of Math., Univ. of Hong Kong, Hong Kong, , China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Hong Kong, Hong Kong, China","institution_ids":["https://openalex.org/I889458895"]},{"raw_affiliation_string":"Dept. of Math., Univ. of Hong Kong, Hong Kong, , China","institution_ids":["https://openalex.org/I889458895"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113544364","display_name":"Brian Marcus","orcid":null},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Brian H. Marcus","raw_affiliation_strings":["Department of Mathematics, University of British Columbia, Vancouver, BC, Canada","Dept. of Math., Univ. of British Columbia, Vancouver, BC, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of British Columbia, Vancouver, BC, Canada","institution_ids":["https://openalex.org/I141945490"]},{"raw_affiliation_string":"Dept. of Math., Univ. of British Columbia, Vancouver, BC, Canada","institution_ids":["https://openalex.org/I141945490"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5000081781"],"corresponding_institution_ids":["https://openalex.org/I889458895"],"apc_list":null,"apc_paid":null,"fwci":3.4612,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.9235031,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"58","issue":"3","first_page":"1534","last_page":"1548"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9998999834060669,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9998999834060669,"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/T12029","display_name":"DNA and Biological Computing","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":0.9987000226974487,"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/mutual-information","display_name":"Mutual information","score":0.8181630373001099},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.7374711036682129},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6713731288909912},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.6282766461372375},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5800215005874634},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.5548049807548523},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.5343702435493469},{"id":"https://openalex.org/keywords/channel-capacity","display_name":"Channel capacity","score":0.5253618955612183},{"id":"https://openalex.org/keywords/information-theory","display_name":"Information theory","score":0.523182213306427},{"id":"https://openalex.org/keywords/entropy-rate","display_name":"Entropy rate","score":0.5010054111480713},{"id":"https://openalex.org/keywords/mixing","display_name":"Mixing (physics)","score":0.4857964515686035},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36089766025543213},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35723528265953064},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3352305591106415},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.33415305614471436},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28866463899612427},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2454673945903778},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.198863685131073},{"id":"https://openalex.org/keywords/binary-entropy-function","display_name":"Binary entropy function","score":0.1461026966571808},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.13953718543052673},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.13522082567214966},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07259953022003174}],"concepts":[{"id":"https://openalex.org/C152139883","wikidata":"https://www.wikidata.org/wiki/Q252973","display_name":"Mutual information","level":2,"score":0.8181630373001099},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.7374711036682129},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6713731288909912},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.6282766461372375},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5800215005874634},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.5548049807548523},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5343702435493469},{"id":"https://openalex.org/C97744766","wikidata":"https://www.wikidata.org/wiki/Q870845","display_name":"Channel capacity","level":3,"score":0.5253618955612183},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.523182213306427},{"id":"https://openalex.org/C125252325","wikidata":"https://www.wikidata.org/wiki/Q1345213","display_name":"Entropy rate","level":4,"score":0.5010054111480713},{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.4857964515686035},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36089766025543213},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35723528265953064},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3352305591106415},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.33415305614471436},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28866463899612427},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2454673945903778},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.198863685131073},{"id":"https://openalex.org/C44415725","wikidata":"https://www.wikidata.org/wiki/Q4913893","display_name":"Binary entropy function","level":3,"score":0.1461026966571808},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.13953718543052673},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.13522082567214966},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07259953022003174},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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":3,"locations":[{"id":"doi:10.1109/tit.2011.2173730","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2011.2173730","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:CiteSeerX.psu:10.1.1.409.578","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.409.578","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ubc.ca/~marcus/pubs_electronic/Concavity_31.pdf","raw_type":"text"},{"id":"pmh:oai:hub.hku.hk:10722/156283","is_oa":false,"landing_page_url":"http://hdl.handle.net/10722/156283","pdf_url":null,"source":{"id":"https://openalex.org/S4377196271","display_name":"The HKU Scholars Hub (University of Hong Kong)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I889458895","host_organization_name":"University of Hong Kong","host_organization_lineage":["https://openalex.org/I889458895"],"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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1556443961","https://openalex.org/W1565611252","https://openalex.org/W1665243225","https://openalex.org/W1862031973","https://openalex.org/W2002912642","https://openalex.org/W2025503267","https://openalex.org/W2043591730","https://openalex.org/W2070432296","https://openalex.org/W2093897717","https://openalex.org/W2099111195","https://openalex.org/W2120636752","https://openalex.org/W2124330979","https://openalex.org/W2127323309","https://openalex.org/W2127434124","https://openalex.org/W2152773357","https://openalex.org/W2160304172","https://openalex.org/W2161037106","https://openalex.org/W2318260403","https://openalex.org/W2485984369","https://openalex.org/W2542539484","https://openalex.org/W3101598514","https://openalex.org/W4206252072"],"related_works":["https://openalex.org/W2121323749","https://openalex.org/W3124771927","https://openalex.org/W4225940264","https://openalex.org/W2750125254","https://openalex.org/W2057609120","https://openalex.org/W1801046103","https://openalex.org/W2889544313","https://openalex.org/W2111510771","https://openalex.org/W986037092","https://openalex.org/W2392704982"],"abstract_inverted_index":{"We":[0,16],"consider":[1],"a":[2,12,45,58],"memoryless":[3],"channel":[4,46],"with":[5,49],"an":[6],"input":[7,54],"Markov":[8,30,55],"process":[9],"supported":[10],"on":[11],"mixing":[13],"finite-type":[14],"constraint.":[15],"continue":[17],"the":[18,23,27,39],"development":[19],"of":[20,26,43,57],"asymptotics":[21],"for":[22],"entropy":[24],"rate":[25,42],"output":[28],"hidden":[29],"chain":[31],"and":[32],"deduce":[33],"that,":[34],"at":[35],"high":[36],"signal-to-noise":[37],"ratio,":[38],"mutual":[40],"information":[41],"such":[44],"is":[47],"concave":[48],"respect":[50],"to":[51],"\u201calmost\u201d":[52],"all":[53],"chains":[56],"given":[59],"order.":[60]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":6},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
