{"id":"https://openalex.org/W2155075061","doi":"https://doi.org/10.1109/tit.1974.1055231","title":"An upper bound to the capacity of the band-limited Gaussian autoregressive channel with noiseless feedback","display_name":"An upper bound to the capacity of the band-limited Gaussian autoregressive channel with noiseless feedback","publication_year":1974,"publication_date":"1974-05-01","ids":{"openalex":"https://openalex.org/W2155075061","doi":"https://doi.org/10.1109/tit.1974.1055231","mag":"2155075061"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1974.1055231","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1974.1055231","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/A5022782681","display_name":"J. Tiernan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. Tiernan","raw_affiliation_strings":["Naval Electronics Laboratory Center, San Diego, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Naval Electronics Laboratory Center, San Diego, CA, USA","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010046653","display_name":"J. Schalkwijk","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. Schalkwijk","raw_affiliation_strings":["TechnischeHogeschool, Afdeling Elektrotechniek, Eindhoven, Noord-Brabant, Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"TechnischeHogeschool, Afdeling Elektrotechniek, Eindhoven, Noord-Brabant, Netherlands","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.7985,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.90266867,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"20","issue":"3","first_page":"311","last_page":"316"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10964","display_name":"Wireless Communication Security 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"}},"topics":[{"id":"https://openalex.org/T10964","display_name":"Wireless Communication Security 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/T12879","display_name":"Distributed Sensor Networks and Detection Algorithms","score":0.9969000220298767,"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/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.9490000009536743,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5329227447509766},{"id":"https://openalex.org/keywords/autoregressive-model","display_name":"Autoregressive model","score":0.4781154990196228},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.43517330288887024},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3861556351184845},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36152762174606323},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.31435346603393555},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.31297892332077026}],"concepts":[{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5329227447509766},{"id":"https://openalex.org/C159877910","wikidata":"https://www.wikidata.org/wiki/Q2202883","display_name":"Autoregressive model","level":2,"score":0.4781154990196228},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.43517330288887024},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3861556351184845},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36152762174606323},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31435346603393555},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.31297892332077026},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1974.1055231","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1974.1055231","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1590624540","https://openalex.org/W1989008275","https://openalex.org/W1999480374","https://openalex.org/W2063142364","https://openalex.org/W2114715837","https://openalex.org/W2119257920","https://openalex.org/W2129977719","https://openalex.org/W2142901448","https://openalex.org/W2158706756","https://openalex.org/W2164684058"],"related_works":["https://openalex.org/W2171218219","https://openalex.org/W2150410159","https://openalex.org/W1972271943","https://openalex.org/W3150905897","https://openalex.org/W4327525404","https://openalex.org/W4287185323","https://openalex.org/W1520183331","https://openalex.org/W2099889858","https://openalex.org/W2168175994","https://openalex.org/W2283583712"],"abstract_inverted_index":{"Upper":[0],"bounds":[1],"to":[2,133],"the":[3,27,44,48,59,65,71,87],"capacity":[4,89,134,153],"of":[5,37,73],"band-limited":[6],"Gaussian":[7],"<tex":[8,20,55,62,68,80,90,143],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[9,21,56,63,69,81,91,144],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">m</tex>":[10],"th-order":[11],"autoregressive":[12,35],"channels":[13,36],"with":[14],"feedback":[15,136],"and":[16,33,79,140,146],"average":[17],"energy":[18],"constraint":[19],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">E</tex>":[22],"are":[23,26,43],"derived.":[24],"These":[25],"only":[28],"known":[29,46],"hounds":[30],"on":[31],"one-":[32],"two-way":[34],"order":[38],"greater":[39],"than":[40,149],"one.":[41],"They":[42],"tightest":[45],"for":[47,137],"first-order":[49,88],"case.":[50],"In":[51],"this":[52,151],"case":[53],"let":[54],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\\alpha_1</tex>":[57],"be":[58],"regression":[60],"coefficient,":[61],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\\sigma^2</tex>":[64],"innovation":[66],"variance,":[67],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">N</tex>":[70],"number":[72],"channel":[74],"iterations":[75],"per":[76],"source":[77],"symbol,":[78],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">e":[82],"=":[83],"E/N</tex>":[84],";":[85],"then":[86],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">C^1</tex>":[92],"is":[93,131,147],"bounded":[94],"by":[95],"\\begin{equation}":[96],"C^1":[97],"\\leq":[98,112],"\\begin{cases}":[99],"\\frac{1}{2}":[100,116],"\\ln":[101,117],"[\\frac{e}{\\sigma^2}(1+":[102],"\\mid":[103,105],"\\alpha_1":[104,121],")":[106],"^":[107],"2":[108],"+1],":[109],"&":[110,126],"\\frac{e}{\\sigma^2}":[111],"\\frac{1}{1-":[113],"\\alpha_1^2}":[114],"\\\\":[115],"[\\frac{e}{\\sigma^2}":[118],"+":[119,124],"\\frac{2\\mid":[120],"\\mid}{\\sqrt{1-\\alpha_1^2}}":[122],"\\sqrt{\\frac{e}{\\simga^2}}":[123],"\\frac{1}{1-\\alpha_1^2}],":[125],"\\text{elsewhere}.\\\\":[127],"\\end{cases}":[128],"\\end{equation}":[129],"This":[130],"equal":[132],"without":[135],"very":[138,141],"low":[139],"high":[142],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">e/\\sigma^2</tex>":[145],"less":[148],"twice":[150],"one-way":[152],"everywhere.":[154]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
