{"id":"https://openalex.org/W2099755158","doi":"https://doi.org/10.1109/isit.2009.5205943","title":"Network coding capacity: A functional dependence bound","display_name":"Network coding capacity: A functional dependence bound","publication_year":2009,"publication_date":"2009-06-01","ids":{"openalex":"https://openalex.org/W2099755158","doi":"https://doi.org/10.1109/isit.2009.5205943","mag":"2099755158"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2009.5205943","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2009.5205943","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE International Symposium on Information Theory","raw_type":"proceedings-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/A5052643871","display_name":"Satyajit Thakor","orcid":"https://orcid.org/0000-0001-9527-0975"},"institutions":[{"id":"https://openalex.org/I170239107","display_name":"University of South Australia","ror":"https://ror.org/01p93h210","country_code":"AU","type":"education","lineage":["https://openalex.org/I170239107"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Satyajit Thakor","raw_affiliation_strings":["Institute of Telecommunications Research, University of South Australia, Australia","Institute for Telecommunications Research, University of South Australia, Australia#TAB#"],"affiliations":[{"raw_affiliation_string":"Institute of Telecommunications Research, University of South Australia, Australia","institution_ids":["https://openalex.org/I170239107"]},{"raw_affiliation_string":"Institute for Telecommunications Research, University of South Australia, Australia#TAB#","institution_ids":["https://openalex.org/I170239107"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072485708","display_name":"Alex Grant","orcid":"https://orcid.org/0000-0002-5345-7771"},"institutions":[{"id":"https://openalex.org/I170239107","display_name":"University of South Australia","ror":"https://ror.org/01p93h210","country_code":"AU","type":"education","lineage":["https://openalex.org/I170239107"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Alex Grant","raw_affiliation_strings":["Institute of Telecommunications Research, University of South Australia, Australia","Institute for Telecommunications Research, University of South Australia, Australia#TAB#"],"affiliations":[{"raw_affiliation_string":"Institute of Telecommunications Research, University of South Australia, Australia","institution_ids":["https://openalex.org/I170239107"]},{"raw_affiliation_string":"Institute for Telecommunications Research, University of South Australia, Australia#TAB#","institution_ids":["https://openalex.org/I170239107"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010336848","display_name":"Terence Chan","orcid":"https://orcid.org/0000-0002-6550-7203"},"institutions":[{"id":"https://openalex.org/I170239107","display_name":"University of South Australia","ror":"https://ror.org/01p93h210","country_code":"AU","type":"education","lineage":["https://openalex.org/I170239107"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Terence Chan","raw_affiliation_strings":["Institute of Telecommunications Research, University of South Australia, Australia","Institute for Telecommunications Research, University of South Australia, Australia#TAB#"],"affiliations":[{"raw_affiliation_string":"Institute of Telecommunications Research, University of South Australia, Australia","institution_ids":["https://openalex.org/I170239107"]},{"raw_affiliation_string":"Institute for Telecommunications Research, University of South Australia, Australia#TAB#","institution_ids":["https://openalex.org/I170239107"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5052643871"],"corresponding_institution_ids":["https://openalex.org/I170239107"],"apc_list":null,"apc_paid":null,"fwci":3.9836,"has_fulltext":false,"cited_by_count":36,"citation_normalized_percentile":{"value":0.93919812,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"263","last_page":"267"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":1.0,"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":1.0,"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/T12791","display_name":"Full-Duplex Wireless Communications","score":0.9753000140190125,"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/T10964","display_name":"Wireless Communication Security Techniques","score":0.9653000235557556,"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/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6840196251869202},{"id":"https://openalex.org/keywords/linear-network-coding","display_name":"Linear network coding","score":0.6280309557914734},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.6078523397445679},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.5553156137466431},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5547606945037842},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5238081216812134},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.5194520354270935},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.49223366379737854},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4256194531917572},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4235420823097229},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3957342505455017},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3871116042137146},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.345639169216156},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33939987421035767},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06949728727340698}],"concepts":[{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6840196251869202},{"id":"https://openalex.org/C138293262","wikidata":"https://www.wikidata.org/wiki/Q1089578","display_name":"Linear network coding","level":3,"score":0.6280309557914734},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.6078523397445679},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.5553156137466431},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5547606945037842},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5238081216812134},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.5194520354270935},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.49223366379737854},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4256194531917572},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4235420823097229},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3957342505455017},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3871116042137146},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.345639169216156},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33939987421035767},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06949728727340698},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C158379750","wikidata":"https://www.wikidata.org/wiki/Q214111","display_name":"Network packet","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/isit.2009.5205943","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2009.5205943","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE International Symposium on Information Theory","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.243.4748","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.243.4748","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0901.4612v1.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320315885","display_name":"Australian Government","ror":"https://ror.org/0314h5y94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W176089054","https://openalex.org/W177399933","https://openalex.org/W646142101","https://openalex.org/W1489262227","https://openalex.org/W1515040589","https://openalex.org/W1965124840","https://openalex.org/W1976329386","https://openalex.org/W2026482663","https://openalex.org/W2028792902","https://openalex.org/W2080663793","https://openalex.org/W2099111195","https://openalex.org/W2103320637","https://openalex.org/W2105831729","https://openalex.org/W2106403318","https://openalex.org/W2121205191","https://openalex.org/W2140785822","https://openalex.org/W2147101953","https://openalex.org/W2147681281","https://openalex.org/W2152093244","https://openalex.org/W2167614100","https://openalex.org/W2478708596","https://openalex.org/W4205523767","https://openalex.org/W4205946516","https://openalex.org/W4212896000"],"related_works":["https://openalex.org/W2212571888","https://openalex.org/W2139379087","https://openalex.org/W2020805386","https://openalex.org/W2285288187","https://openalex.org/W2411336269","https://openalex.org/W2124128583","https://openalex.org/W2489403550","https://openalex.org/W2079655802","https://openalex.org/W2581667880","https://openalex.org/W2096444692"],"abstract_inverted_index":{"Explicit":[0],"characterization":[1,83],"and":[2],"computation":[3],"of":[4,27,30,70,84],"the":[5,22,28,45,49,94],"multi-source":[6],"network":[7,71],"coding":[8],"capacity":[9,23],"region":[10,24],"(or":[11],"even":[12],"bounds)":[13],"is":[14,36,55,97],"long":[15],"standing":[16],"open":[17],"problem.":[18,43],"In":[19],"fact,":[20],"finding":[21],"requires":[25],"determination":[26],"set":[29],"all":[31,85],"entropic":[32],"vectors":[33],"Gamma*,":[34],"which":[35],"known":[37,51,101],"to":[38,61],"be":[39],"an":[40,62],"extremely":[41],"hard":[42,57],"On":[44],"other":[46],"hand,":[47],"calculating":[48],"explicitly":[50],"linear":[52],"programming":[53],"bound":[54,96],"very":[56],"in":[58,65,88],"practice":[59],"due":[60],"exponential":[63],"growth":[64],"complexity":[66],"as":[67],"a":[68,75],"function":[69],"size.":[72],"We":[73,90],"give":[74],"new,":[76],"easily":[77],"computable":[78],"outer":[79],"bound,":[80],"based":[81],"on":[82],"functional":[86],"dependencies":[87],"networks.":[89],"also":[91],"show":[92],"that":[93],"proposed":[95],"tighter":[98],"than":[99],"some":[100],"bounds.":[102]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}