{"id":"https://openalex.org/W2975772810","doi":"https://doi.org/10.1109/isit.2019.8849415","title":"An Elementary Proof of a Classical Information-Theoretic Formula","display_name":"An Elementary Proof of a Classical Information-Theoretic Formula","publication_year":2019,"publication_date":"2019-07-01","ids":{"openalex":"https://openalex.org/W2975772810","doi":"https://doi.org/10.1109/isit.2019.8849415","mag":"2975772810"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2019.8849415","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2019.8849415","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 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/A5100654393","display_name":"Xianming Liu","orcid":"https://orcid.org/0000-0003-3440-628X"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xianming Liu","raw_affiliation_strings":["Huazhong University of Science and Technology"],"affiliations":[{"raw_affiliation_string":"Huazhong University of Science and Technology","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050186123","display_name":"Ronit Bustin","orcid":"https://orcid.org/0000-0002-0529-3485"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ronit Bustin","raw_affiliation_strings":["General Motors Advanced Technical Center - Israel"],"affiliations":[{"raw_affiliation_string":"General Motors Advanced Technical Center - Israel","institution_ids":[]}]},{"author_position":"middle","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":false,"raw_author_name":"Guangyue Han","raw_affiliation_strings":["The University of Hong Kong"],"affiliations":[{"raw_affiliation_string":"The University of Hong Kong","institution_ids":["https://openalex.org/I889458895"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025989795","display_name":"Shlomo Shamai","orcid":"https://orcid.org/0000-0002-6594-3371"},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Shlomo Shamai Shitz","raw_affiliation_strings":["Technion-Israel Institute of Technology"],"affiliations":[{"raw_affiliation_string":"Technion-Israel Institute of Technology","institution_ids":["https://openalex.org/I174306211"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100654393"],"corresponding_institution_ids":["https://openalex.org/I47720641"],"apc_list":null,"apc_paid":null,"fwci":0.2,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.56064242,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"1392","last_page":"1396"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9944000244140625,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9944000244140625,"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9587000012397766,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9297000169754028,"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/elementary-proof","display_name":"Elementary proof","score":0.6099952459335327},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.512915849685669},{"id":"https://openalex.org/keywords/proof-of-concept","display_name":"Proof of concept","score":0.4990851879119873},{"id":"https://openalex.org/keywords/proof-theory","display_name":"Proof theory","score":0.4908321499824524},{"id":"https://openalex.org/keywords/information-theory","display_name":"Information theory","score":0.4158734083175659},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.4066528081893921},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3583550453186035},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3366180658340454},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2356615960597992},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.18361619114875793},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.15085375308990479},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1126624047756195},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0889664888381958}],"concepts":[{"id":"https://openalex.org/C2777478746","wikidata":"https://www.wikidata.org/wiki/Q5358910","display_name":"Elementary proof","level":2,"score":0.6099952459335327},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.512915849685669},{"id":"https://openalex.org/C124978682","wikidata":"https://www.wikidata.org/wiki/Q1201019","display_name":"Proof of concept","level":2,"score":0.4990851879119873},{"id":"https://openalex.org/C2318724","wikidata":"https://www.wikidata.org/wiki/Q852732","display_name":"Proof theory","level":3,"score":0.4908321499824524},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.4158734083175659},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4066528081893921},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3583550453186035},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3366180658340454},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2356615960597992},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.18361619114875793},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.15085375308990479},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1126624047756195},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0889664888381958},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit.2019.8849415","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2019.8849415","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W33041645","https://openalex.org/W197497516","https://openalex.org/W1510355813","https://openalex.org/W1537932563","https://openalex.org/W1989008275","https://openalex.org/W2016119814","https://openalex.org/W2033079303","https://openalex.org/W2045463928","https://openalex.org/W2054243772","https://openalex.org/W2092841162","https://openalex.org/W2111616148","https://openalex.org/W2132105090","https://openalex.org/W2135479785","https://openalex.org/W2142901448","https://openalex.org/W2153634854","https://openalex.org/W2163258071","https://openalex.org/W2175624993","https://openalex.org/W2486222733","https://openalex.org/W2606034937","https://openalex.org/W2964320221","https://openalex.org/W3099354821","https://openalex.org/W4243833160","https://openalex.org/W4252713891","https://openalex.org/W4388534025","https://openalex.org/W6601357525","https://openalex.org/W6632108797","https://openalex.org/W6806823677"],"related_works":["https://openalex.org/W4312475206","https://openalex.org/W4387322292","https://openalex.org/W4295538670","https://openalex.org/W3120006117","https://openalex.org/W3189967158","https://openalex.org/W2151894250","https://openalex.org/W2263677784","https://openalex.org/W1530460876","https://openalex.org/W1491058778","https://openalex.org/W2162495973"],"abstract_inverted_index":{"A":[0],"renowned":[1],"information-theoretic":[2],"formula":[3],"by":[4],"Shannon":[5],"expresses":[6],"the":[7,29,34,55],"mutual":[8],"information":[9],"rate":[10],"of":[11,24,28,33,47],"a":[12,17,25,42,78],"white":[13],"Gaussian":[14,19],"channel":[15,35],"with":[16],"stationary":[18],"input":[20],"as":[21],"an":[22],"integral":[23],"simple":[26],"function":[27],"power":[30],"spectral":[31],"density":[32],"input.":[36],"We":[37],"give":[38],"in":[39],"this":[40,48],"paper":[41],"rigorous":[43],"yet":[44],"elementary":[45,84],"proof":[46],"classical":[49],"formula.":[50],"As":[51],"opposed":[52],"to":[53,67,69],"all":[54],"conventional":[56],"approaches,":[57],"which":[58,75],"either":[59],"rely":[60],"on":[61,77],"heavy":[62],"mathematical":[63],"machineries":[64],"or":[65],"have":[66],"resort":[68],"some":[70,90],"\"external\"":[71],"results,":[72],"our":[73],"proof,":[74],"hinges":[76],"recently":[79],"proven":[80],"sampling":[81],"theorem,":[82],"is":[83],"and":[85,96],"self-":[86],"contained,":[87],"only":[88],"using":[89],"well-known":[91],"facts":[92],"from":[93],"basic":[94],"calculus":[95],"matrix":[97],"theory.":[98]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-17T18:11:37.981687","created_date":"2025-10-10T00:00:00"}