{"id":"https://openalex.org/W2035908129","doi":"https://doi.org/10.1109/tit.2011.2169532","title":"On Network Coding for Sum-Networks","display_name":"On Network Coding for Sum-Networks","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2035908129","doi":"https://doi.org/10.1109/tit.2011.2169532","mag":"2035908129"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2011.2169532","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2011.2169532","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0906.0695","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Brijesh Kumar Rai","orcid":null},"institutions":[{"id":"https://openalex.org/I1317621060","display_name":"Indian Institute of Technology Guwahati","ror":"https://ror.org/0022nd079","country_code":"IN","type":"education","lineage":["https://openalex.org/I1317621060"]},{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Brijesh Kumar Rai","raw_affiliation_strings":["Department of Electrical Engineering, Indian Institute of Technology Bombay, India","Department of Electronics and Electrical Engineering, Indian Institute of Technology Guwahati, India"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Indian Institute of Technology Bombay, India","institution_ids":["https://openalex.org/I162827531"]},{"raw_affiliation_string":"Department of Electronics and Electrical Engineering, Indian Institute of Technology Guwahati, India","institution_ids":["https://openalex.org/I1317621060"]}]},{"author_position":"last","author":{"id":null,"display_name":"Bikash Kumar Dey","orcid":null},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Bikash Kumar Dey","raw_affiliation_strings":["Department of Electrical Engineering, Indian Institute of Technology Bombay, India"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Indian Institute of Technology Bombay, India","institution_ids":["https://openalex.org/I162827531"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I1317621060","https://openalex.org/I162827531"],"apc_list":null,"apc_paid":null,"fwci":8.1961,"has_fulltext":false,"cited_by_count":68,"citation_normalized_percentile":{"value":0.97737772,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"58","issue":"1","first_page":"50","last_page":"63"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9699000120162964,"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":0.9699000120162964,"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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.008100000210106373,"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/T10148","display_name":"Advanced MIMO Systems Optimization","score":0.0032999999821186066,"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/linear-network-coding","display_name":"Linear network coding","score":0.7918000221252441},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.7330999970436096},{"id":"https://openalex.org/keywords/existential-quantification","display_name":"Existential quantification","score":0.5863999724388123},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.4629000127315521},{"id":"https://openalex.org/keywords/directed-acyclic-graph","display_name":"Directed acyclic graph","score":0.4196000099182129},{"id":"https://openalex.org/keywords/alphabet","display_name":"Alphabet","score":0.37770000100135803},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.36660000681877136},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.3605000078678131},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.335999995470047}],"concepts":[{"id":"https://openalex.org/C138293262","wikidata":"https://www.wikidata.org/wiki/Q1089578","display_name":"Linear network coding","level":3,"score":0.7918000221252441},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7487000226974487},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.7330999970436096},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.6085000038146973},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.5863999724388123},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.4629000127315521},{"id":"https://openalex.org/C74197172","wikidata":"https://www.wikidata.org/wiki/Q1195339","display_name":"Directed acyclic graph","level":2,"score":0.4196000099182129},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.41370001435279846},{"id":"https://openalex.org/C112876837","wikidata":"https://www.wikidata.org/wiki/Q837518","display_name":"Alphabet","level":2,"score":0.37770000100135803},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.36660000681877136},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3605000078678131},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.335999995470047},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.31859999895095825},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.3116999864578247},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3093000054359436},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.30059999227523804},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28870001435279846},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.2802000045776367},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.2777000069618225},{"id":"https://openalex.org/C20050597","wikidata":"https://www.wikidata.org/wiki/Q261527","display_name":"Linear form","level":2,"score":0.2759999930858612},{"id":"https://openalex.org/C113709454","wikidata":"https://www.wikidata.org/wiki/Q602136","display_name":"Coding theory","level":2,"score":0.27489998936653137},{"id":"https://openalex.org/C32946077","wikidata":"https://www.wikidata.org/wiki/Q618079","display_name":"Network analysis","level":2,"score":0.27320000529289246},{"id":"https://openalex.org/C60603091","wikidata":"https://www.wikidata.org/wiki/Q2981616","display_name":"Variable-length code","level":3,"score":0.26579999923706055},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.26510000228881836},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.25619998574256897},{"id":"https://openalex.org/C3020028006","wikidata":"https://www.wikidata.org/wiki/Q9158","display_name":"Electronic mail","level":2,"score":0.25600001215934753}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tit.2011.2169532","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2011.2169532","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:arXiv.org:0906.0695","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0906.0695","pdf_url":"https://arxiv.org/pdf/0906.0695","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:dsapce.library.iitb.ac.in:100/14904","is_oa":false,"landing_page_url":"http://dspace.library.iitb.ac.in/jspui/handle/100/14904","pdf_url":null,"source":{"id":"https://openalex.org/S4306400899","display_name":"DSpace (IIT Bombay)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I162827531","host_organization_name":"Indian Institute of Technology Bombay","host_organization_lineage":["https://openalex.org/I162827531"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:0906.0695","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0906.0695","pdf_url":"https://arxiv.org/pdf/0906.0695","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1971506714","https://openalex.org/W2019307453","https://openalex.org/W2022456395","https://openalex.org/W2045603582","https://openalex.org/W2048235391","https://openalex.org/W2053269541","https://openalex.org/W2096342910","https://openalex.org/W2098674643","https://openalex.org/W2101517602","https://openalex.org/W2102801035","https://openalex.org/W2102931639","https://openalex.org/W2103320637","https://openalex.org/W2104973644","https://openalex.org/W2105831729","https://openalex.org/W2106403318","https://openalex.org/W2110540512","https://openalex.org/W2114578240","https://openalex.org/W2119442443","https://openalex.org/W2123562143","https://openalex.org/W2123976939","https://openalex.org/W2132123317","https://openalex.org/W2133338663","https://openalex.org/W2138928022","https://openalex.org/W2150284816","https://openalex.org/W2153242915","https://openalex.org/W2164651000","https://openalex.org/W2209179758","https://openalex.org/W2539443493","https://openalex.org/W6654396071","https://openalex.org/W6782648086"],"related_works":[],"abstract_inverted_index":{"A":[0],"directed":[1,51],"acyclic":[2,52],"network":[3,27,67,119,157,176,183,204],"is":[4,31,56,72,88,120,141,194,205],"considered":[5],"where":[6],"all":[7,20],"the":[8,13,16,21,101,135,138,143,156],"terminals":[9],"need":[10],"to":[11,186],"recover":[12],"sum":[14],"of":[15,78,115,128,137,148,155],"symbols":[17],"generated":[18],"at":[19],"sources.":[22],"We":[23],"call":[24],"such":[25],"a":[26,28,36,62,85,93,104,118,124,178,199],"sum-network.":[29,70],"It":[30,55,71],"shown":[32,58,73,185,195],"that":[33,59,74,196],"there":[34,60,83,197],"exists":[35,61,84,198],"solvably":[37,64],"(and":[38],"linear":[39,63,90,126,149,175],"solvably)":[40],"equivalent":[41,65],"sum-network":[42,86,179,201],"for":[43,49,68,75,162,169],"any":[44,50,76,110,129],"multiple-unicast":[45,66],"network,":[46],"and":[47,98,132,153,180],"thus":[48],"communication":[53,170],"network.":[54],"also":[57],"every":[69],"set":[77,114],"polynomials":[79,102],"having":[80],"integer":[81],"coefficients,":[82],"which":[87,122],"scalar":[89],"solvable":[91,200],"over":[92],"finite":[94,111],"field":[95,140],"F":[96],"if":[97,100,131,134],"only":[99,133],"have":[103],"common":[105],"root":[106],"in":[107,142],"F.":[108],"For":[109],"or":[112],"cofinite":[113],"prime":[116],"numbers,":[117],"constructed":[121],"has":[123],"vector":[125,174],"solution":[127],"length":[130],"characteristic":[136],"alphabet":[139],"given":[144],"set.":[145],"The":[146],"insufficiency":[147],"net-":[150],"work":[151],"coding":[152,158],"unachievability":[154],"capacity":[159],"are":[160,184],"proved":[161],"sum-networks":[163],"by":[164],"using":[165],"similar":[166],"known":[167],"results":[168],"networks.":[171],"Under":[172],"fractional":[173],"coding,":[177,192],"its":[181],"reverse":[182,203],"be":[187],"equivalent.":[188],"However,":[189],"under":[190],"nonlinear":[191],"it":[193],"whose":[202],"not":[206],"solvable.":[207]},"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":12},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2016-06-24T00:00:00"}