{"id":"https://openalex.org/W2013528585","doi":"https://doi.org/10.1109/tit.1968.1054156","title":"Estimates ofepsiloncapacity for certain linear communication channels","display_name":"Estimates ofepsiloncapacity for certain linear communication channels","publication_year":1968,"publication_date":"1968-05-01","ids":{"openalex":"https://openalex.org/W2013528585","doi":"https://doi.org/10.1109/tit.1968.1054156","mag":"2013528585"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1968.1054156","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1968.1054156","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/A5038080014","display_name":"William L. Root","orcid":null},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"W. Root","raw_affiliation_strings":["Department of AeroSpace Engrg, University of Michigan, Ann Arbor, MI, USA"],"affiliations":[{"raw_affiliation_string":"Department of AeroSpace Engrg, University of Michigan, Ann Arbor, MI, USA","institution_ids":["https://openalex.org/I27837315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5038080014"],"corresponding_institution_ids":["https://openalex.org/I27837315"],"apc_list":null,"apc_paid":null,"fwci":1.6267,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.81998239,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"3","first_page":"361","last_page":"369"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41756972670555115},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3611326217651367},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34164535999298096}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41756972670555115},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3611326217651367},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34164535999298096}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1968.1054156","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1968.1054156","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W2035368262","https://openalex.org/W2064528533","https://openalex.org/W2092390447","https://openalex.org/W2331274018","https://openalex.org/W4239022279","https://openalex.org/W6702848602"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2003465964","https://openalex.org/W303980170","https://openalex.org/W2351491280","https://openalex.org/W2386767533","https://openalex.org/W2371447506","https://openalex.org/W2333698505","https://openalex.org/W2889453578","https://openalex.org/W3141679561"],"abstract_inverted_index":{"The":[0,117,156,218],"following":[1],"simple":[2],"abstract":[3],"model":[4,222],"for":[5],"a":[6,55],"class":[7],"of":[8,15,35,94,97,105,168,175,178,181,203,207,210,220,226],"communications":[9],"problems":[10],"is":[11,22,48,71,84,119],"adopted:":[12],"the":[13,26,30,45,63,139,166,173,176,179,185,204,208,211,221,224,227],"set":[14],"possible":[16],"transmitted":[17,46],"signals":[18,125,183],"<tex":[19,31,39,58,68,72,81,98,111,132,140,152,188,192,214],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[20,32,40,59,69,73,82,99,112,133,141,153,189,193,215],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">x</tex>":[21],"taken":[23],"to":[24,50,120,184],"be":[25,51,127],"unit":[27],"ball":[28],"in":[29,147,201],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">L_{2}</tex>":[33],"space":[34],"functions":[36],"defined":[37],"on":[38,53,165],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">[-T,":[41],"T]</tex>":[42],"(bounded":[43],"energy);":[44],"signal":[47,67],"assumed":[49],"operated":[52],"by":[54,90,149],"convolution":[56,212],"operator":[57,213],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">H</tex>":[60,100,216],";":[61],"and":[62,162,223],"final":[64],"observed":[65],"received":[66],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">z</tex>":[70],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">z":[74],"=":[75,143],"Hx":[76],"+":[77],"n</tex>":[78],",":[79,101],"where":[80],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</tex>":[83],"an":[85],"unknown":[86],"error,":[87],"caused":[88],"either":[89],"additive":[91],"noise,":[92],"lack":[93],"complete":[95],"knowledge":[96],"or":[102],"other":[103],"causes,":[104],"norm":[106,148],"less":[107],"than":[108],"some":[109],"specified":[110],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\\epsilon</tex>":[113,154],"(not":[114],"necessarily":[115],"small).":[116],"problem":[118],"determine":[121],"how":[122,130],"many":[123,131],"\"distinguishable\"":[124],"can":[126],"sent,":[128],"i.e.,":[129,172],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">x_{i}</tex>":[134],"there":[135],"are":[136,145,159,200,229],"such":[137],"that":[138],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">y_{i}":[142],"Hx_{i}</tex>":[144],"separated":[146],"at":[150],"least":[151],".":[155,197,217],"chief":[157],"results":[158,228],"asymptotic":[160],"upper":[161],"lower":[163],"bounds":[164],"rate":[167],"error-free":[169],"transmission":[170],"possible,":[171],"ratio":[174],"logarithm":[177],"number":[180],"distinguishable":[182],"time":[186],"interval":[187],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2T</tex>":[190],"as":[191],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">T":[194],"\\rightarrow":[195],"\\infty</tex>":[196],"These":[198],"estimates":[199],"terms":[202],"Fourier":[205],"transform":[206],"kernel":[209],"suitability":[219],"nature":[225],"discussed.":[230]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}
