{"id":"https://openalex.org/W4409013612","doi":"https://doi.org/10.1109/tit.2025.3556551","title":"Edge-Subset Lattice and Its Application to Linear Network Error Correction Coding","display_name":"Edge-Subset Lattice and Its Application to Linear Network Error Correction Coding","publication_year":2025,"publication_date":"2025-03-31","ids":{"openalex":"https://openalex.org/W4409013612","doi":"https://doi.org/10.1109/tit.2025.3556551"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2025.3556551","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2025.3556551","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/A5027528912","display_name":"Xuan Guang","orcid":"https://orcid.org/0000-0002-0928-421X"},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xuan Guang","raw_affiliation_strings":["School of Mathematical Sciences and the Key Laboratory of Pure Mathematics and Combinatorics (LPMC), Nankai University, Tianjin, China"],"raw_orcid":"https://orcid.org/0000-0002-0928-421X","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences and the Key Laboratory of Pure Mathematics and Combinatorics (LPMC), Nankai University, Tianjin, China","institution_ids":["https://openalex.org/I205237279"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Ruopu Cui","orcid":"https://orcid.org/0009-0008-9658-3226"},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ruopu Cui","raw_affiliation_strings":["School of Mathematical Sciences and the Key Laboratory of Pure Mathematics and Combinatorics (LPMC), Nankai University, Tianjin, China"],"raw_orcid":"https://orcid.org/0009-0008-9658-3226","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences and the Key Laboratory of Pure Mathematics and Combinatorics (LPMC), Nankai University, Tianjin, China","institution_ids":["https://openalex.org/I205237279"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038760786","display_name":"Raymond W. Yeung","orcid":"https://orcid.org/0000-0001-7386-4027"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Raymond W. Yeung","raw_affiliation_strings":["Department of Information Engineering, Institute of Network Coding, The Chinese University of Hong Kong, Hong Kong, SAR, China","Institute of Network Coding and Department of Information Engineering, The Chinese University of Hong Kong, Hong Kong SAR, China"],"raw_orcid":"https://orcid.org/0000-0001-7386-4027","affiliations":[{"raw_affiliation_string":"Department of Information Engineering, Institute of Network Coding, The Chinese University of Hong Kong, Hong Kong, SAR, China","institution_ids":["https://openalex.org/I177725633"]},{"raw_affiliation_string":"Institute of Network Coding and Department of Information Engineering, The Chinese University of Hong Kong, Hong Kong SAR, China","institution_ids":["https://openalex.org/I177725633"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0513775,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"71","issue":"7","first_page":"5700","last_page":"5719"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9973999857902527,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9973999857902527,"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/T11130","display_name":"Coding theory and cryptography","score":0.9882000088691711,"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"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9876999855041504,"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/computer-science","display_name":"Computer science","score":0.5002961158752441},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.47450774908065796},{"id":"https://openalex.org/keywords/linear-network-coding","display_name":"Linear network coding","score":0.4609890580177307},{"id":"https://openalex.org/keywords/variable-length-code","display_name":"Variable-length code","score":0.44723960757255554},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.44643110036849976},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.44472819566726685},{"id":"https://openalex.org/keywords/shannon\u2013fano-coding","display_name":"Shannon\u2013Fano coding","score":0.442124605178833},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4126572906970978},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.32757842540740967},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.2773164212703705},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.24196207523345947},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.11596190929412842},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10644277930259705}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5002961158752441},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.47450774908065796},{"id":"https://openalex.org/C138293262","wikidata":"https://www.wikidata.org/wiki/Q1089578","display_name":"Linear network coding","level":3,"score":0.4609890580177307},{"id":"https://openalex.org/C60603091","wikidata":"https://www.wikidata.org/wiki/Q2981616","display_name":"Variable-length code","level":3,"score":0.44723960757255554},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.44643110036849976},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.44472819566726685},{"id":"https://openalex.org/C130811719","wikidata":"https://www.wikidata.org/wiki/Q2645","display_name":"Shannon\u2013Fano coding","level":4,"score":0.442124605178833},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4126572906970978},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.32757842540740967},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.2773164212703705},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.24196207523345947},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.11596190929412842},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10644277930259705},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2025.3556551","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2025.3556551","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":[{"id":"https://openalex.org/G1579949423","display_name":null,"funder_award_id":"14207219","funder_id":"https://openalex.org/F4320322887","funder_display_name":"The Research Council"},{"id":"https://openalex.org/G3490976664","display_name":null,"funder_award_id":"2023YFA1009604","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G4610906710","display_name":null,"funder_award_id":"62461160306","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6901315762","display_name":null,"funder_award_id":"NKU 050-63253087","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G6984540029","display_name":null,"funder_award_id":"62171238","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8890425352","display_name":null,"funder_award_id":"2022YFA1005000","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322887","display_name":"The Research Council","ror":"https://ror.org/03tcppy59"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W108696806","https://openalex.org/W1606480398","https://openalex.org/W1995875735","https://openalex.org/W2014554046","https://openalex.org/W2042474604","https://openalex.org/W2055060019","https://openalex.org/W2078535861","https://openalex.org/W2083270107","https://openalex.org/W2083315413","https://openalex.org/W2093397547","https://openalex.org/W2105831729","https://openalex.org/W2115602633","https://openalex.org/W2118456153","https://openalex.org/W2119856092","https://openalex.org/W2139416652","https://openalex.org/W2149286354","https://openalex.org/W2149342630","https://openalex.org/W2154501376","https://openalex.org/W2157328738","https://openalex.org/W2172117832","https://openalex.org/W2404362146","https://openalex.org/W2534491645","https://openalex.org/W2557793327","https://openalex.org/W2964269129","https://openalex.org/W3045242109","https://openalex.org/W4206775542","https://openalex.org/W4213060883","https://openalex.org/W4232896595","https://openalex.org/W4233580922","https://openalex.org/W4386918884"],"related_works":["https://openalex.org/W4312628177","https://openalex.org/W2123072960","https://openalex.org/W2213686625","https://openalex.org/W2262362834","https://openalex.org/W1485515172","https://openalex.org/W2104750217","https://openalex.org/W2548599468","https://openalex.org/W1997045285","https://openalex.org/W2109115525","https://openalex.org/W2365030987"],"abstract_inverted_index":{"In":[0,129,155],"this":[1],"paper,":[2],"we":[3,76,131,211],"first":[4],"explore":[5],"the":[6,40,61,64,82,89,151,158,164,204,207,218,224,232,235,249,265,271,291,298],"underlying":[7],"mathematical":[8],"structure":[9],"of":[10,29,63,85,118,145,149,166,185,194,199,206,226,270,297,300],"edge":[11,30],"subsets":[12],"on":[13,33,143,217,264,277],"a":[14,21,27,47,49,52,78,106,146,181,278,294],"finite":[15],"directed":[16],"acyclic":[17],"graph":[18,109,122],"in":[19,121,169,252,293],"using":[20],"lattice-theoretic":[22,83],"approach.":[23],"We":[24,230,282],"prove":[25],"that":[26,248,288],"collection":[28],"subsets,":[31],"depending":[32],"different":[34],"conditions":[35],"it":[36],"satisfies,":[37],"together":[38],"with":[39],"corresponding":[41],"\u201ccut-separating\u201d":[42],"partial":[43],"order,":[44],"can":[45,289],"form":[46],"meet-semilattice,":[48],"join-semilattice":[50],"or":[51],"lattice.":[53],"The":[54,98,255],"bottom":[55],"and":[56,71,74,93,96,101,111,126,242,245,268],"top":[57],"thus":[58,246],"derived":[59],"generalize":[60],"concept":[62],"primary":[65,90],"minimum":[66,91,159,219],"cut":[67,92],"introduced":[68,99],"by":[69,238],"Guang":[70],"Yeung":[72],"(2018)":[73],"hence":[75],"provide":[77],"new":[79],"way":[80],"from":[81],"point":[84],"view":[86],"to":[87,116],"understand":[88],"its":[94],"existence":[95,165,225],"uniqueness.":[97],"concepts":[100],"obtained":[102],"results":[103,237],"regarded":[104,179],"as":[105,180],"bridge":[107],"connect":[108],"theory":[110],"lattice":[112,124],"theory,":[113,123,125],"which":[114,150,177,259],"appear":[115],"be":[117],"fundamental":[119],"interest":[120,196],"even":[127],"beyond.":[128],"addition,":[130],"consider":[132],"linear":[133,295],"network":[134,148,266],"error":[135,272],"correction":[136,273],"(LNEC)":[137],"coding":[138],"when":[139],"errors":[140],"may":[141],"occur":[142],"edges":[144],"communication":[147],"topology":[152,267],"is":[153,188,251,260],"known.":[154],"LNEC":[156,167,171,227],"coding,":[157],"required":[160,220],"field":[161,221],"size":[162,222],"for":[163,223],"codes,":[168,187],"particular":[170],"maximum":[172],"distance":[173],"separable":[174],"(MDS)":[175,228],"codes":[176],"are":[178],"most":[182],"important":[183],"type":[184],"optimal":[186],"an":[189,213,285],"open":[190],"problem":[191],"not":[192,276],"only":[193,263],"theoretical":[195,240],"but":[197,275],"also":[198,283],"practical":[200],"importance.":[201],"By":[202],"applying":[203],"approach":[205],"above":[208],"edge-subset":[209],"(semi-)lattice,":[210],"obtain":[212],"improved":[214,256],"upper":[215,257],"bound":[216,292],"codes.":[229],"quantify":[231],"improvement":[233,250],"over":[234],"existing":[236],"both":[239],"analysis":[241],"numerical":[243],"simulations":[244],"show":[247],"general":[253],"significant.":[254],"bound,":[258],"graph-theoretic,":[261],"depends":[262],"requirement":[269],"capability":[274],"specific":[279],"code":[280],"construction.":[281],"develop":[284],"efficient":[286],"algorithm":[287],"compute":[290],"time":[296],"number":[299],"edges.":[301]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
