{"id":"https://openalex.org/W4289655306","doi":"https://doi.org/10.1109/isit50566.2022.9834862","title":"Using Minors to Construct Generator Matrices for Quasi-Cyclic LDPC Codes","display_name":"Using Minors to Construct Generator Matrices for Quasi-Cyclic LDPC Codes","publication_year":2022,"publication_date":"2022-06-26","ids":{"openalex":"https://openalex.org/W4289655306","doi":"https://doi.org/10.1109/isit50566.2022.9834862"},"language":"en","primary_location":{"id":"doi:10.1109/isit50566.2022.9834862","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit50566.2022.9834862","pdf_url":null,"source":{"id":"https://openalex.org/S4363604560","display_name":"2022 IEEE International Symposium on Information Theory (ISIT)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2022 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/A5061445419","display_name":"Roxana Smarandache","orcid":"https://orcid.org/0000-0001-9085-5974"},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Roxana Smarandache","raw_affiliation_strings":["University of Notre Dame,Departments of Mathematics,Notre Dame,USA,IN 46556","Departments of Electrical Engineering, University of Notre Dame, Notre Dame, USA"],"affiliations":[{"raw_affiliation_string":"University of Notre Dame,Departments of Mathematics,Notre Dame,USA,IN 46556","institution_ids":["https://openalex.org/I107639228"]},{"raw_affiliation_string":"Departments of Electrical Engineering, University of Notre Dame, Notre Dame, USA","institution_ids":["https://openalex.org/I107639228"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012571757","display_name":"Anthony G\u00f3mez-Fonseca","orcid":"https://orcid.org/0000-0002-3569-9304"},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Anthony G\u00f3mez-Fonseca","raw_affiliation_strings":["University of Notre Dame,Departments of Mathematics,Notre Dame,USA,IN 46556"],"affiliations":[{"raw_affiliation_string":"University of Notre Dame,Departments of Mathematics,Notre Dame,USA,IN 46556","institution_ids":["https://openalex.org/I107639228"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076523933","display_name":"David G. M. Mitchell","orcid":"https://orcid.org/0000-0002-3544-9225"},"institutions":[{"id":"https://openalex.org/I10052268","display_name":"New Mexico State University","ror":"https://ror.org/00hpz7z43","country_code":"US","type":"education","lineage":["https://openalex.org/I10052268"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David G. M. Mitchell","raw_affiliation_strings":["New Mexico State University,Klipsch School of Electrical and Computer Engineering,Las Cruces,USA,NM 88003"],"affiliations":[{"raw_affiliation_string":"New Mexico State University,Klipsch School of Electrical and Computer Engineering,Las Cruces,USA,NM 88003","institution_ids":["https://openalex.org/I10052268"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5061445419"],"corresponding_institution_ids":["https://openalex.org/I107639228"],"apc_list":null,"apc_paid":null,"fwci":0.8642,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.6659289,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"548","last_page":"553"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":0.9998999834060669,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9998999834060669,"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/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.9991999864578247,"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/T10796","display_name":"Cooperative Communication and Network Coding","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"}}],"keywords":[{"id":"https://openalex.org/keywords/parity-check-matrix","display_name":"Parity-check matrix","score":0.8323186635971069},{"id":"https://openalex.org/keywords/low-density-parity-check-code","display_name":"Low-density parity-check code","score":0.8203017711639404},{"id":"https://openalex.org/keywords/generator-matrix","display_name":"Generator matrix","score":0.7893475294113159},{"id":"https://openalex.org/keywords/parity","display_name":"Parity (physics)","score":0.5803998708724976},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5431138873100281},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.502495288848877},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4821988642215729},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44225209951400757},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.43828529119491577},{"id":"https://openalex.org/keywords/polynomial-code","display_name":"Polynomial code","score":0.41489145159721375},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.4129319190979004},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.4095745384693146},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.360351026058197},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.2922555208206177},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.28710681200027466},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.2165791392326355},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.054099470376968384}],"concepts":[{"id":"https://openalex.org/C95925971","wikidata":"https://www.wikidata.org/wiki/Q3100414","display_name":"Parity-check matrix","level":4,"score":0.8323186635971069},{"id":"https://openalex.org/C67692717","wikidata":"https://www.wikidata.org/wiki/Q187444","display_name":"Low-density parity-check code","level":3,"score":0.8203017711639404},{"id":"https://openalex.org/C1842014","wikidata":"https://www.wikidata.org/wiki/Q1502046","display_name":"Generator matrix","level":3,"score":0.7893475294113159},{"id":"https://openalex.org/C2777151079","wikidata":"https://www.wikidata.org/wiki/Q141160","display_name":"Parity (physics)","level":2,"score":0.5803998708724976},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5431138873100281},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.502495288848877},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4821988642215729},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44225209951400757},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.43828529119491577},{"id":"https://openalex.org/C39635130","wikidata":"https://www.wikidata.org/wiki/Q7226636","display_name":"Polynomial code","level":5,"score":0.41489145159721375},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.4129319190979004},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.4095745384693146},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.360351026058197},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.2922555208206177},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28710681200027466},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.2165791392326355},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.054099470376968384},{"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/C109214941","wikidata":"https://www.wikidata.org/wiki/Q18334","display_name":"Particle physics","level":1,"score":0.0},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit50566.2022.9834862","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit50566.2022.9834862","pdf_url":null,"source":{"id":"https://openalex.org/S4363604560","display_name":"2022 IEEE International Symposium on Information Theory (ISIT)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2022 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.4300000071525574}],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W91277888","https://openalex.org/W1571565904","https://openalex.org/W1667880265","https://openalex.org/W2044078862","https://openalex.org/W2062642782","https://openalex.org/W2071304218","https://openalex.org/W2073843305","https://openalex.org/W2107621627","https://openalex.org/W2114869758","https://openalex.org/W2119604283","https://openalex.org/W2133068391","https://openalex.org/W2136923821","https://openalex.org/W2139645268","https://openalex.org/W2147776616","https://openalex.org/W2160065222","https://openalex.org/W2564319974","https://openalex.org/W2885415681","https://openalex.org/W6603727012"],"related_works":["https://openalex.org/W2537009867","https://openalex.org/W4289655306","https://openalex.org/W2121834236","https://openalex.org/W2150670983","https://openalex.org/W2557689695","https://openalex.org/W2148483316","https://openalex.org/W102425876","https://openalex.org/W2578769334","https://openalex.org/W2171322836","https://openalex.org/W2045231468"],"abstract_inverted_index":{"This":[0],"paper":[1],"gives":[2],"a":[3,45,93,104],"simple":[4],"method":[5,19,64,94],"to":[6,20,95],"construct":[7],"generator":[8],"matrices":[9],"with":[10,49],"polynomial":[11,121],"entries":[12],"(and":[13],"hence":[14,108],"offers":[15],"an":[16],"alternative":[17],"encoding":[18],"the":[21,50,58,63,74,77,80,84,97,109,112,116,119],"one":[22],"commonly":[23],"used)":[24],"for":[25,33],"all":[26],"quasi-cyclic":[27],"low-density":[28],"parity-check":[29,59,81,101,122],"(QC-LDPC)":[30],"codes,":[31],"even":[32],"those":[34],"that":[35],"are":[36],"rank":[37,53,98],"deficient.":[38],"The":[39],"approach":[40],"is":[41],"based":[42],"on":[43,65,88],"constructing":[44],"set":[46],"of":[47,57,79,99,111,118],"codewords":[48],"desired":[51],"total":[52],"by":[54,114],"using":[55,115],"minors":[56,78,117],"matrix.":[60,123],"We":[61],"exemplify":[62],"several":[66],"well-known":[67],"and":[68,83,91,107],"standard":[69],"codes.":[70],"Moreover,":[71],"we":[72],"explore":[73],"connections":[75],"between":[76],"matrix":[82,102],"known":[85],"upper":[86],"bound":[87],"minimum":[89],"distance":[90],"provide":[92],"compute":[96],"any":[100],"representing":[103],"QC-LDPC":[105],"code,":[106,113],"dimension":[110],"corresponding":[120]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2}],"updated_date":"2026-03-14T06:41:57.775601","created_date":"2025-10-10T00:00:00"}