{"id":"https://openalex.org/W3197712426","doi":"https://doi.org/10.1109/isit45174.2021.9518084","title":"Solving Monoshift Systems and Applications in Random Coding","display_name":"Solving Monoshift Systems and Applications in Random Coding","publication_year":2021,"publication_date":"2021-07-12","ids":{"openalex":"https://openalex.org/W3197712426","doi":"https://doi.org/10.1109/isit45174.2021.9518084","mag":"3197712426"},"language":"en","primary_location":{"id":"doi:10.1109/isit45174.2021.9518084","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit45174.2021.9518084","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2021 IEEE International Symposium on Information Theory (ISIT)","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/A5101624432","display_name":"Yiheng Zhang","orcid":"https://orcid.org/0000-0002-1940-6137"},"institutions":[{"id":"https://openalex.org/I4210116924","display_name":"Chinese University of Hong Kong, Shenzhen","ror":"https://ror.org/02d5ks197","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633","https://openalex.org/I180726961","https://openalex.org/I4210116924"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yiheng Zhang","raw_affiliation_strings":["The Chinese University of Hong Kong,Shenzhen","The Chinese University of Hong Kong, Shenzhen"],"affiliations":[{"raw_affiliation_string":"The Chinese University of Hong Kong,Shenzhen","institution_ids":["https://openalex.org/I4210116924"]},{"raw_affiliation_string":"The Chinese University of Hong Kong, Shenzhen","institution_ids":["https://openalex.org/I4210116924"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076731706","display_name":"Ximing Fu","orcid":"https://orcid.org/0000-0001-7058-2091"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210116924","display_name":"Chinese University of Hong Kong, Shenzhen","ror":"https://ror.org/02d5ks197","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633","https://openalex.org/I180726961","https://openalex.org/I4210116924"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ximing Fu","raw_affiliation_strings":["The Chinese University of Hong Kong,Shenzhen","The Chinese University of Hong Kong, Shenzhen","University of Science and Technology of China"],"affiliations":[{"raw_affiliation_string":"The Chinese University of Hong Kong,Shenzhen","institution_ids":["https://openalex.org/I4210116924"]},{"raw_affiliation_string":"The Chinese University of Hong Kong, Shenzhen","institution_ids":["https://openalex.org/I4210116924"]},{"raw_affiliation_string":"University of Science and Technology of China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003554167","display_name":"Xuanchen Wu","orcid":null},"institutions":[{"id":"https://openalex.org/I4210116924","display_name":"Chinese University of Hong Kong, Shenzhen","ror":"https://ror.org/02d5ks197","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633","https://openalex.org/I180726961","https://openalex.org/I4210116924"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xuanchen Wu","raw_affiliation_strings":["The Chinese University of Hong Kong,Shenzhen","The Chinese University of Hong Kong, Shenzhen"],"affiliations":[{"raw_affiliation_string":"The Chinese University of Hong Kong,Shenzhen","institution_ids":["https://openalex.org/I4210116924"]},{"raw_affiliation_string":"The Chinese University of Hong Kong, Shenzhen","institution_ids":["https://openalex.org/I4210116924"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054079306","display_name":"Shenghao Yang","orcid":"https://orcid.org/0000-0003-1987-5643"},"institutions":[{"id":"https://openalex.org/I4210099586","display_name":"Shenzhen Research Institute of Big Data","ror":"https://ror.org/00z1gwf89","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210099586"]},{"id":"https://openalex.org/I4210116924","display_name":"Chinese University of Hong Kong, Shenzhen","ror":"https://ror.org/02d5ks197","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633","https://openalex.org/I180726961","https://openalex.org/I4210116924"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shenghao Yang","raw_affiliation_strings":["The Chinese University of Hong Kong,Shenzhen","The Chinese University of Hong Kong, Shenzhen","Shenzhen Research Institute of Big Data, Shenzhen, China","Shenzhen Key Laboratory of IoT Intelligent Systems and Wireless Network Technology"],"affiliations":[{"raw_affiliation_string":"The Chinese University of Hong Kong,Shenzhen","institution_ids":["https://openalex.org/I4210116924"]},{"raw_affiliation_string":"The Chinese University of Hong Kong, Shenzhen","institution_ids":["https://openalex.org/I4210116924"]},{"raw_affiliation_string":"Shenzhen Research Institute of Big Data, Shenzhen, China","institution_ids":["https://openalex.org/I4210099586"]},{"raw_affiliation_string":"Shenzhen Key Laboratory of IoT Intelligent Systems and Wireless Network Technology","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103017634","display_name":"Kenneth W. Shum","orcid":"https://orcid.org/0000-0001-6505-6177"},"institutions":[{"id":"https://openalex.org/I4210116924","display_name":"Chinese University of Hong Kong, Shenzhen","ror":"https://ror.org/02d5ks197","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633","https://openalex.org/I180726961","https://openalex.org/I4210116924"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kenneth W. Shum","raw_affiliation_strings":["The Chinese University of Hong Kong,Shenzhen","The Chinese University of Hong Kong, Shenzhen"],"affiliations":[{"raw_affiliation_string":"The Chinese University of Hong Kong,Shenzhen","institution_ids":["https://openalex.org/I4210116924"]},{"raw_affiliation_string":"The Chinese University of Hong Kong, Shenzhen","institution_ids":["https://openalex.org/I4210116924"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5101624432"],"corresponding_institution_ids":["https://openalex.org/I4210116924"],"apc_list":null,"apc_paid":null,"fwci":0.1593,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.5267095,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"1296","last_page":"1301"},"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/T10964","display_name":"Wireless Communication Security Techniques","score":0.996399998664856,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/augmented-matrix","display_name":"Augmented matrix","score":0.6148344874382019},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5859942436218262},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5641266107559204},{"id":"https://openalex.org/keywords/linear-network-coding","display_name":"Linear network coding","score":0.5566295385360718},{"id":"https://openalex.org/keywords/square-matrix","display_name":"Square matrix","score":0.5420598983764648},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5377178192138672},{"id":"https://openalex.org/keywords/random-matrix","display_name":"Random matrix","score":0.4649200737476349},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.42489057779312134},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4235474467277527},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.41802069544792175},{"id":"https://openalex.org/keywords/coefficient-matrix","display_name":"Coefficient matrix","score":0.4139154851436615},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3687919080257416},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.36758172512054443},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3669939637184143},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3056914806365967},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1485343873500824}],"concepts":[{"id":"https://openalex.org/C105129939","wikidata":"https://www.wikidata.org/wiki/Q2750301","display_name":"Augmented matrix","level":5,"score":0.6148344874382019},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5859942436218262},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5641266107559204},{"id":"https://openalex.org/C138293262","wikidata":"https://www.wikidata.org/wiki/Q1089578","display_name":"Linear network coding","level":3,"score":0.5566295385360718},{"id":"https://openalex.org/C69044650","wikidata":"https://www.wikidata.org/wiki/Q2739329","display_name":"Square matrix","level":4,"score":0.5420598983764648},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5377178192138672},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.4649200737476349},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.42489057779312134},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4235474467277527},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.41802069544792175},{"id":"https://openalex.org/C60866291","wikidata":"https://www.wikidata.org/wiki/Q5140577","display_name":"Coefficient matrix","level":3,"score":0.4139154851436615},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3687919080257416},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.36758172512054443},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3669939637184143},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3056914806365967},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1485343873500824},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"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/isit45174.2021.9518084","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit45174.2021.9518084","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2021 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W2757614","https://openalex.org/W1588709134","https://openalex.org/W1606480398","https://openalex.org/W1607153847","https://openalex.org/W1966612101","https://openalex.org/W1995416687","https://openalex.org/W2009136691","https://openalex.org/W2012957959","https://openalex.org/W2027413053","https://openalex.org/W2048235391","https://openalex.org/W2072841021","https://openalex.org/W2097764899","https://openalex.org/W2135386172","https://openalex.org/W2138928022","https://openalex.org/W2148575324","https://openalex.org/W2159416784","https://openalex.org/W2338815034","https://openalex.org/W2618071666","https://openalex.org/W2732892807","https://openalex.org/W2758707306","https://openalex.org/W2782632095","https://openalex.org/W2951327528","https://openalex.org/W2963513015","https://openalex.org/W3080168964","https://openalex.org/W3098978149","https://openalex.org/W3106493979","https://openalex.org/W3148585635","https://openalex.org/W4301902258"],"related_works":["https://openalex.org/W2355478383","https://openalex.org/W2370263758","https://openalex.org/W2026020054","https://openalex.org/W4255252257","https://openalex.org/W2657588900","https://openalex.org/W2506892714","https://openalex.org/W2355201024","https://openalex.org/W2349379571","https://openalex.org/W2385851794","https://openalex.org/W2166083100"],"abstract_inverted_index":{"A":[0],"monoshift":[1,19,31,44,59,86,93,144],"matrix":[2,5,45,106,131],"is":[3,21,110],"a":[4,18,22,30,43,47,75,83,89,120],"that":[6],"has":[7],"binary":[8],"polynomials":[9,28],"of":[10,24,53,78,82,143],"degree":[11,54],"at":[12,55],"most":[13,56],"1":[14],"as":[15,104,146],"entries,":[16],"and":[17,158],"system":[20,23,60],"linear":[25],"equations":[26],"over":[27,119],"with":[29,114,155],"coefficient":[32],"matrix.":[33,87],"We":[34,72],"propose":[35],"an":[36],"algorithm":[37],"called":[38,49],"augmented":[39,50,62],"elimination":[40],"to":[41,46,99],"reduce":[42],"form":[48,52,64],"echelon":[51,63],"1.":[57],"The":[58],"in":[61,151,159],"can":[65,137],"be":[66],"solved":[67],"efficiently":[68],"by":[69,148],"successive":[70],"cancellation.":[71],"further":[73],"derive":[74],"recursive":[76],"formula":[77],"the":[79,95,105,115,125,130,149],"rank":[80],"distribution":[81],"uniformly":[84,91],"random":[85,92,117],"For":[88],"square":[90,116],"matrix,":[94],"deficient-rank":[96,126],"probability":[97,127],"decreases":[98],"0":[100],"almost":[101],"exponentially":[102],"fast":[103],"size":[107,132],"increases.":[108,133],"This":[109],"quite":[111],"different":[112],"compared":[113],"matrices":[118],"fixed":[121],"finite":[122],"field,":[123],"where":[124],"increases":[128],"when":[129],"Certain":[134],"coding":[135],"problems":[136],"benefit":[138],"from":[139],"this":[140],"special":[141],"property":[142],"systems,":[145],"demonstrated":[147],"applications":[150],"distributed":[152],"storage":[153],"systems":[154],"decentralized":[156],"encoding":[157],"batched":[160],"network":[161],"coding.":[162]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-03-25T13:04:00.132906","created_date":"2025-10-10T00:00:00"}