{"id":"https://openalex.org/W2123095296","doi":"https://doi.org/10.1109/tit.1982.1056588","title":"Achievable rates for multiple descriptions","display_name":"Achievable rates for multiple descriptions","publication_year":1982,"publication_date":"1982-11-01","ids":{"openalex":"https://openalex.org/W2123095296","doi":"https://doi.org/10.1109/tit.1982.1056588","mag":"2123095296"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1982.1056588","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1982.1056588","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/A5078716556","display_name":"Abbas El Gamal","orcid":"https://orcid.org/0000-0002-0853-0415"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A.E. Gamal","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5055073921","display_name":"Thomas M. Cover","orcid":null},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"T. Cover","raw_affiliation_strings":["University of Stanford, Stanford, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Stanford, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8353,"has_fulltext":false,"cited_by_count":663,"citation_normalized_percentile":{"value":0.86982249,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"28","issue":"6","first_page":"851","last_page":"857"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9986000061035156,"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"}},"topics":[{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9986000061035156,"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/T10964","display_name":"Wireless Communication Security Techniques","score":0.9915000200271606,"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/T11716","display_name":"Random Matrices and Applications","score":0.9449999928474426,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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":0.34144461154937744}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34144461154937744}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.1982.1056588","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1982.1056588","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:10.1.1.205.4564","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.205.4564","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://isl.stanford.edu/groups/elgamal/abbas_publications/J014.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1989008275","https://openalex.org/W2011564903","https://openalex.org/W2042711474","https://openalex.org/W2062540956","https://openalex.org/W2138571053","https://openalex.org/W2142901448","https://openalex.org/W2157032401","https://openalex.org/W4230860499"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2382290278","https://openalex.org/W2350741829","https://openalex.org/W2130043461","https://openalex.org/W2530322880","https://openalex.org/W1596801655"],"abstract_inverted_index":{"Consider":[0],"a":[1,16,104],"sequence":[2,51],"of":[3,28,49],"independent":[4],"identically":[5],"distributed":[6],"(i.i.d.)":[7],"random":[8],"variables":[9],"<tex":[10,19,25,29,35,42,52,65,71,80,94,108,112,118,121,125],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[11,20,26,30,36,43,53,66,72,81,95,109,113,119,122,126],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">X_{l},X_{2},":[12],"\\cdots,":[13],"X_{n}</tex>":[14],"and":[15,41,70],"distortion":[17,92,141],"measure":[18],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">d(X_{i},X\u0302_{i})</tex>":[21],"on":[22],"the":[23,50,91],"estimates":[24,64],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">X\u0302_{i}</tex>":[27],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">X_{i}</tex>":[31],".":[32,58],"Two":[33],"descriptions":[34],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">i(X)\\in":[37],"\\{1,2,":[38,45],"\\cdots":[39,56],",2^{nR_{1}\\}</tex>":[40],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">j(X)\\in":[44],"\\cdots,2^{nR_{2}\\}</tex>":[46],"are":[47,74,99,134],"given":[48],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">X=(X_{1},":[54],"X_{2},":[55],",X_{n})</tex>":[57],"From":[59],"these":[60],"two":[61],"descriptions,":[62],"three":[63],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">(i(X)),":[67],"X2(j(X))</tex>":[68],",":[69],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\\hat{X}_{O}(i(X),j(X))</tex>":[73],"formed,":[75],"with":[76,111],"resulting":[77],"expected":[78],"distortions":[79],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">E":[82],"\\frac{1/n}":[83],"\\sum^{n}_{k=1}":[84],"d(X_{k},":[85],"\\hat{X}_{mk})=D_{m},":[86],"m=0,1,2.</tex>":[87],"We":[88],"find":[89],"that":[90,117],"constraints":[93],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">D_{0},":[96],"D_{1},":[97],"D_{2}</tex>":[98],"achievable":[100],"if":[101],"there":[102],"exists":[103],"probability":[105],"mass":[106],"distribution":[107],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">p(x)p(\\hat{x}_{1},\\hat{x}_{2},\\hat{x}_{0}|x)</tex>":[110],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">Ed(X,\\hat{x}_{m})\\leq":[114],"D_{m}</tex>":[115],"such":[116],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">R_{1}&gt;I(X;\\hat{X}_{1}),</tex>":[120],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">R_{2}&gt;I(X;\\hat{X}_{2}),</tex>":[123],"where":[124],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">I(\\cdot)</tex>":[127],"denotes":[128],"Shannon":[129],"mutual":[130],"information.":[131],"These":[132],"rates":[133],"shown":[135],"to":[136],"be":[137],"optimal":[138],"for":[139],"deterministic":[140],"measures.":[142]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":18},{"year":2017,"cited_by_count":14},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":15},{"year":2014,"cited_by_count":22},{"year":2013,"cited_by_count":20},{"year":2012,"cited_by_count":31}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}