{"id":"https://openalex.org/W3204439019","doi":"https://doi.org/10.1109/tit.2021.3116926","title":"Fundamental Limits of Distributed Linear Encoding","display_name":"Fundamental Limits of Distributed Linear Encoding","publication_year":2021,"publication_date":"2021-10-05","ids":{"openalex":"https://openalex.org/W3204439019","doi":"https://doi.org/10.1109/tit.2021.3116926","mag":"3204439019"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2021.3116926","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2021.3116926","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/A5062557745","display_name":"Nastaran Abadi Khooshemehr","orcid":"https://orcid.org/0000-0002-3962-9100"},"institutions":[{"id":"https://openalex.org/I133529467","display_name":"Sharif University of Technology","ror":"https://ror.org/024c2fq17","country_code":"IR","type":"education","lineage":["https://openalex.org/I133529467"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Nastaran Abadi Khooshemehr","raw_affiliation_strings":["Department of Electrical Engineering, Sharif University of Technology, Tehran, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Sharif University of Technology, Tehran, Iran","institution_ids":["https://openalex.org/I133529467"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113662214","display_name":"Mohammad Ali Maddah-Ali","orcid":null},"institutions":[{"id":"https://openalex.org/I133529467","display_name":"Sharif University of Technology","ror":"https://ror.org/024c2fq17","country_code":"IR","type":"education","lineage":["https://openalex.org/I133529467"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Mohammad Ali Maddah-Ali","raw_affiliation_strings":["Department of Electrical Engineering, Sharif University of Technology, Tehran, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Sharif University of Technology, Tehran, Iran","institution_ids":["https://openalex.org/I133529467"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5062557745"],"corresponding_institution_ids":["https://openalex.org/I133529467"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.17178827,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"67","issue":"12","first_page":"7985","last_page":"7998"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11181","display_name":"Advanced Data Storage Technologies","score":0.9998000264167786,"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/T11181","display_name":"Advanced Data Storage Technologies","score":0.9998000264167786,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9965999722480774,"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/T10237","display_name":"Cryptography and Data Security","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/cardinality","display_name":"Cardinality (data modeling)","score":0.585659921169281},{"id":"https://openalex.org/keywords/encoding","display_name":"Encoding (memory)","score":0.5534868836402893},{"id":"https://openalex.org/keywords/node","display_name":"Node (physics)","score":0.5487880110740662},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.5437605977058411},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.5078592896461487},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4748513996601105},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.44741007685661316},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4304000735282898},{"id":"https://openalex.org/keywords/coding-theory","display_name":"Coding theory","score":0.41598182916641235},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3921131491661072},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.366946816444397},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.34902340173721313},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.17799678444862366},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15810364484786987},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.11913365125656128},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.09735250473022461}],"concepts":[{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.585659921169281},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.5534868836402893},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.5487880110740662},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.5437605977058411},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.5078592896461487},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4748513996601105},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.44741007685661316},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4304000735282898},{"id":"https://openalex.org/C113709454","wikidata":"https://www.wikidata.org/wiki/Q602136","display_name":"Coding theory","level":2,"score":0.41598182916641235},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3921131491661072},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.366946816444397},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.34902340173721313},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.17799678444862366},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15810364484786987},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.11913365125656128},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.09735250473022461},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2021.3116926","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2021.3116926","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":22,"referenced_works":["https://openalex.org/W1565060721","https://openalex.org/W1584781809","https://openalex.org/W1979205928","https://openalex.org/W2014554046","https://openalex.org/W2042694970","https://openalex.org/W2048218060","https://openalex.org/W2058863419","https://openalex.org/W2083270107","https://openalex.org/W2118925326","https://openalex.org/W2136237463","https://openalex.org/W2137928654","https://openalex.org/W2156663229","https://openalex.org/W2414673748","https://openalex.org/W2488849407","https://openalex.org/W2551526409","https://openalex.org/W2604218357","https://openalex.org/W2949333674","https://openalex.org/W2964073244","https://openalex.org/W3080494535","https://openalex.org/W4211068006","https://openalex.org/W4248175462","https://openalex.org/W4248289108"],"related_works":["https://openalex.org/W1847915440","https://openalex.org/W2020567882","https://openalex.org/W3013412531","https://openalex.org/W2739495308","https://openalex.org/W2947386998","https://openalex.org/W2922502643","https://openalex.org/W24519920","https://openalex.org/W3013502888","https://openalex.org/W2528333032","https://openalex.org/W3135460134"],"abstract_inverted_index":{"In":[0,305,366,403],"general":[1],"coding":[2,30,382],"theory,":[3,31],"we":[4,35,308,378,413],"often":[5],"assume":[6],"that":[7,171,199,327,385,390,415,434],"error":[8],"is":[9,23,44,97,248,271],"observed":[10],"in":[11,32,317,386,420,436],"transferring":[12],"or":[13],"storing":[14],"encoded":[15,110,193],"symbols,":[16],"while":[17],"the":[18,37,40,52,102,113,120,126,132,145,148,164,167,187,192,223,226,233,259,310,319,391,394,397,407,410,417,428,437],"process":[19,41,188],"of":[20,29,42,54,58,61,101,119,125,147,166,169,189,207,225,235,243,261,274,396,409,439],"encoding":[21,43,84,103,106,141,217,246,313,320],"itself":[22],"error-free.":[24],"Motivated":[25],"by":[26,131,152,176],"recent":[27],"applications":[28],"this":[33,306],"paper,":[34,307],"consider":[36],"case":[38],"where":[39],"distributed":[45,55,245,311],"and":[46,74,134,163,219,237,297,347,383],"prone":[47],"to":[48,99,139,203,221,368,405],"error.":[49],"We":[50,325],"introduce":[51],"problem":[53],"encoding,":[56],"comprised":[57],"a":[59,93,117,200,244,272,421],"set":[60,168],"<inline-formula":[62,75,153,177,208,249,263,275,282,289,298,328,338,348,357,370],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[63,76,154,178,209,250,264,276,283,290,299,329,339,349,358,371],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[64,77,155,179,210,251,265,277,284,291,300,330,340,350,359,372],"<tex-math":[65,78,156,180,211,252,266,278,285,292,301,331,341,351,360,373],"notation=\"LaTeX\">$K":[66],"\\in":[67,80,158,182,213,254],"\\mathbb":[68,81,159,183,214,255],"{N}$":[69,82,160,184,215,256],"</tex-math></inline-formula>":[70,83,161,185,216,257,268,280,287,295,303,335,345,354,364,376],"isolated":[71],"source":[72,87,127],"nodes":[73,128,218,228,321,399],"notation=\"LaTeX\">$N":[79],"nodes.":[85,104,142,239],"Each":[86,105],"node":[88,107],"has":[89],"one":[90,173,316,442],"symbol":[91,111],"from":[92,112,191],"finite":[94],"field,":[95,115],"which":[96,270,318],"sent":[98],"each":[100,172],"stores":[108],"an":[109,204],"same":[114],"as":[116],"function":[118,273],"received":[121],"symbols.":[122],"However,":[123],"some":[124],"are":[129,400],"controlled":[130],"adversary":[133,418],"may":[135],"send":[136],"different":[137,140],"symbols":[138,170,194,224],"Depending":[143],"on":[144],"number":[146],"adversarial":[149,238],"nodes,":[150],"denoted":[151,175],"notation=\"LaTeX\">$\\beta":[157,293],",":[162,186,258,269,281,288,296,336,346,355,377],"cardinality":[165],"generates,":[174],"notation=\"LaTeX\">$v":[181],"decoding":[190],"could":[195],"be":[196],"impossible.":[197],"Assume":[198],"decoder":[201,392,429],"connects":[202],"arbitrary":[205],"subset":[206],"notation=\"LaTeX\">$t":[212],"wants":[220],"decode":[222],"honest":[227,236,398,443],"correctly,":[229],"without":[230],"necessarily":[231],"identifying":[232],"sets":[234],"An":[240],"important":[241],"characteristic":[242],"system":[247],"notation=\"LaTeX\">$t^{*}":[253],"minimum":[260],"such":[262],"notation=\"LaTeX\">$t$":[267],"notation=\"LaTeX\">$K$":[279],"notation=\"LaTeX\">$N$":[286],"$":[294],"notation=\"LaTeX\">$v$":[302],".":[304,365],"study":[309],"linear":[312,323,381],"system,":[314],"i.e.":[315],"use":[322,379],"coding.":[324],"show":[326,384,414],"notation=\"LaTeX\">$t^{*}_{\\textrm":[332,352,374],"{Linear}}=K+2\\beta":[333],"(v-1)$":[334,344,363],"if":[337,356],"notation=\"LaTeX\">$N\\ge":[342],"K+2\\beta":[343,362],"{Linear}}=N$":[353],"notation=\"LaTeX\">$N\\le":[361],"order":[367,404],"achieve":[369],"{Linear}}$":[375],"random":[380],"any":[387],"feasible":[388,432],"solution":[389],"finds,":[393],"messages":[395],"decoded":[401],"correctly.":[402],"prove":[406],"converse":[408],"fundamental":[411],"limit,":[412],"when":[416],"behaves":[419],"particular":[422],"way,":[423],"it":[424],"can":[425],"always":[426],"confuse":[427],"between":[430],"two":[431],"solutions":[433],"differ":[435],"message":[438],"at":[440],"least":[441],"node.":[444]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
