{"id":"https://openalex.org/W2964269129","doi":"https://doi.org/10.1109/tit.2016.2550522","title":"Variable-Rate Linear Network Error Correction MDS Codes","display_name":"Variable-Rate Linear Network Error Correction MDS Codes","publication_year":2016,"publication_date":"2016-04-05","ids":{"openalex":"https://openalex.org/W2964269129","doi":"https://doi.org/10.1109/tit.2016.2550522","mag":"2964269129"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2016.2550522","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2016.2550522","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"]},{"id":"https://openalex.org/I4401200345","display_name":"Laboratoire de physique de la mati\u00e8re condens\u00e9e","ror":"https://ror.org/05brss208","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4401200345","https://openalex.org/I4647051"]}],"countries":["CN","FR"],"is_corresponding":true,"raw_author_name":"Xuan Guang","raw_affiliation_strings":["School of Mathematical Sciences and LPMC, Nankai University, Tianjin, China","School of Mathematical Sciences and LPMC, Nankai University, Tianjin. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences and LPMC, Nankai University, Tianjin, China","institution_ids":["https://openalex.org/I205237279","https://openalex.org/I4401200345"]},{"raw_affiliation_string":"School of Mathematical Sciences and LPMC, Nankai University, Tianjin. China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063946169","display_name":"Fang\u2010Wei Fu","orcid":"https://orcid.org/0000-0002-9696-8977"},"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"]},{"id":"https://openalex.org/I4401200345","display_name":"Laboratoire de physique de la mati\u00e8re condens\u00e9e","ror":"https://ror.org/05brss208","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4401200345","https://openalex.org/I4647051"]}],"countries":["CN","FR"],"is_corresponding":false,"raw_author_name":"Fang-Wei Fu","raw_affiliation_strings":["Chern Institute of Mathematics and LPMC, Nankai University, Tianjin, China","Chern Institute of Mathematics and LPMC , Nankai University , Tianjin, China"],"affiliations":[{"raw_affiliation_string":"Chern Institute of Mathematics and LPMC, Nankai University, Tianjin, China","institution_ids":["https://openalex.org/I205237279","https://openalex.org/I4401200345"]},{"raw_affiliation_string":"Chern Institute of Mathematics and LPMC , Nankai University , Tianjin, China","institution_ids":["https://openalex.org/I205237279"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000511351","display_name":"Zhen Zhang","orcid":"https://orcid.org/0000-0003-1559-625X"},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhen Zhang","raw_affiliation_strings":["Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, CA, USA","Ming Hsieh Department of Electrical EngineeringCommunication Sciences Institute, University of Southern California, Los Angeles, CA, USA"],"affiliations":[{"raw_affiliation_string":"Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I1174212"]},{"raw_affiliation_string":"Ming Hsieh Department of Electrical EngineeringCommunication Sciences Institute, University of Southern California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I1174212"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5027528912"],"corresponding_institution_ids":["https://openalex.org/I205237279","https://openalex.org/I4401200345"],"apc_list":null,"apc_paid":null,"fwci":1.1581,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.83020061,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"62","issue":"6","first_page":"3147","last_page":"3164"},"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/T11130","display_name":"Coding theory and cryptography","score":0.9937000274658203,"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/T11458","display_name":"Advanced Wireless Communication Technologies","score":0.9919000267982483,"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":0.6425275206565857},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6143991947174072},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.5756635069847107},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5577808618545532},{"id":"https://openalex.org/keywords/error-detection-and-correction","display_name":"Error detection and correction","score":0.522063672542572},{"id":"https://openalex.org/keywords/node","display_name":"Node (physics)","score":0.5115569233894348},{"id":"https://openalex.org/keywords/code-rate","display_name":"Code rate","score":0.4984297752380371},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.43982064723968506},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.42241528630256653},{"id":"https://openalex.org/keywords/fountain-code","display_name":"Fountain code","score":0.4140978157520294},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.35966742038726807},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3280560374259949},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.1370392143726349},{"id":"https://openalex.org/keywords/network-packet","display_name":"Network packet","score":0.1306852400302887},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.12361985445022583}],"concepts":[{"id":"https://openalex.org/C138293262","wikidata":"https://www.wikidata.org/wiki/Q1089578","display_name":"Linear network coding","level":3,"score":0.6425275206565857},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6143991947174072},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.5756635069847107},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5577808618545532},{"id":"https://openalex.org/C103088060","wikidata":"https://www.wikidata.org/wiki/Q1062839","display_name":"Error detection and correction","level":2,"score":0.522063672542572},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.5115569233894348},{"id":"https://openalex.org/C206468330","wikidata":"https://www.wikidata.org/wiki/Q834373","display_name":"Code rate","level":3,"score":0.4984297752380371},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.43982064723968506},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.42241528630256653},{"id":"https://openalex.org/C76132124","wikidata":"https://www.wikidata.org/wiki/Q5474786","display_name":"Fountain code","level":5,"score":0.4140978157520294},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.35966742038726807},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3280560374259949},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.1370392143726349},{"id":"https://openalex.org/C158379750","wikidata":"https://www.wikidata.org/wiki/Q214111","display_name":"Network packet","level":2,"score":0.1306852400302887},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.12361985445022583},{"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2016.2550522","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2016.2550522","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/G1292825847","display_name":null,"funder_award_id":"61171082","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1686089283","display_name":null,"funder_award_id":"61301137","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2301527561","display_name":null,"funder_award_id":"61571243","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W108696806","https://openalex.org/W177399933","https://openalex.org/W1988752113","https://openalex.org/W2005581645","https://openalex.org/W2012291662","https://openalex.org/W2014554046","https://openalex.org/W2026288260","https://openalex.org/W2042474604","https://openalex.org/W2048235391","https://openalex.org/W2055060019","https://openalex.org/W2075714087","https://openalex.org/W2083270107","https://openalex.org/W2083315413","https://openalex.org/W2105831729","https://openalex.org/W2106403318","https://openalex.org/W2106831077","https://openalex.org/W2109831419","https://openalex.org/W2110065573","https://openalex.org/W2115602633","https://openalex.org/W2118456153","https://openalex.org/W2119856092","https://openalex.org/W2123562143","https://openalex.org/W2128555802","https://openalex.org/W2130093830","https://openalex.org/W2136237463","https://openalex.org/W2138928022","https://openalex.org/W2139379087","https://openalex.org/W2139416652","https://openalex.org/W2152303628","https://openalex.org/W2153098283","https://openalex.org/W2157328738","https://openalex.org/W2162219773","https://openalex.org/W2167614100","https://openalex.org/W2170184107","https://openalex.org/W2404362146","https://openalex.org/W2534491645","https://openalex.org/W2563871604","https://openalex.org/W3101008197","https://openalex.org/W4205946516","https://openalex.org/W4212896000","https://openalex.org/W6680766608","https://openalex.org/W6728374566"],"related_works":["https://openalex.org/W135568846","https://openalex.org/W2460434904","https://openalex.org/W1789159349","https://openalex.org/W832867880","https://openalex.org/W2147254059","https://openalex.org/W2151857680","https://openalex.org/W4386066307","https://openalex.org/W917159298","https://openalex.org/W1975697476","https://openalex.org/W2113911300"],"abstract_inverted_index":{"In":[0,99],"network":[1,23,38,44,72,114,127,175,244],"communication,":[2],"the":[3,62,79,103,109,136,151,160,188,205,214,217,220,224,228,252,271],"source":[4,225],"often":[5],"transmits":[6],"messages":[7],"at":[8,141,223],"several":[9],"different":[10,28,59,133],"information":[11,20,84],"rates":[12,29,60,134],"within":[13],"a":[14,36,70,171,232,240,248],"session.":[15],"How":[16],"to":[17,54,95,101,168,268,276],"deal":[18],"with":[19],"transmission":[21],"and":[22,178,195,198,227,247],"error":[24,39,45,73,115,128],"correction":[25,40,46,74,116,129],"simultaneously":[26],"under":[27],"is":[30,86,92,211,235,259],"introduced":[31,236],"in":[32],"this":[33,67,256,264],"paper":[34],"as":[35,270],"variable-rate":[37,112,174,243],"problem.":[41],"Apparently,":[42],"linear":[43,71,113,126],"maximum":[47],"distance":[48],"separable":[49],"(MDS)":[50],"codes":[51,118,131,177],"are":[52],"expected":[53],"be":[55],"used":[56],"for":[57,82,155,182,191,200,237],"these":[58,125],"guaranteeing":[61],"maximal":[63],"error-correcting":[64],"capability.":[65],"For":[66],"purpose,":[68],"designing":[69],"MDS":[75,117,130,176,245],"code":[76],"based":[77],"on":[78,202,251],"existing":[80],"results":[81],"each":[83,142,146,192],"rate":[85,161],"an":[87,166,180],"alternative":[88],"solution,":[89],"but":[90],"it":[91],"inefficient":[93],"due":[94],"its":[96],"high":[97],"complexity.":[98],"order":[100],"solve":[102],"problem":[104],"more":[105],"efficiently,":[106],"we":[107,164],"present":[108],"concept":[110],"of":[111,132,173,207,242,255],"preserving":[119],"local":[120,138,153],"encoding":[121,139,221],"kernels,":[122],"that":[123,263],"is,":[124],"have":[135],"same":[137,152],"kernel":[140,154],"internal":[143,193],"node.":[144],"Thus,":[145],"nonsource":[147],"node":[148],"always":[149],"uses":[150],"coding,":[156],"no":[157],"matter":[158],"what":[159],"is.":[162],"Furthermore,":[163],"propose":[165],"approach":[167,186,267],"construct":[169],"such":[170,239],"family":[172,241],"give":[179],"algorithm":[181,210],"efficient":[183],"implementation.":[184],"This":[185],"economizes":[187],"storage":[189],"space":[190],"node,":[194,226],"saves":[196],"resources":[197],"time":[199,218],"transmissions":[201],"networks.":[203],"Moreover,":[204],"performance":[206],"our":[208],"proposed":[209],"analyzed,":[212],"including":[213],"field":[215,273],"size,":[216],"complexity,":[219],"complexity":[222],"decoding":[229],"methods.":[230],"Finally,":[231],"random":[233,257],"method":[234,258],"constructing":[238],"codes,":[246],"lower":[249],"bound":[250],"success":[253],"probability":[254,265],"given,":[260],"which":[261],"shows":[262],"will":[266],"one":[269],"base":[272],"size":[274],"goes":[275],"infinity.":[277]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}