{"id":"https://openalex.org/W4386736719","doi":"https://doi.org/10.1109/jsait.2023.3315585","title":"An Efficient Strategy to Count Cycles in the Tanner Graph of Quasi-Cyclic LDPC Codes","display_name":"An Efficient Strategy to Count Cycles in the Tanner Graph of Quasi-Cyclic LDPC Codes","publication_year":2023,"publication_date":"2023-01-01","ids":{"openalex":"https://openalex.org/W4386736719","doi":"https://doi.org/10.1109/jsait.2023.3315585"},"language":"en","primary_location":{"id":"doi:10.1109/jsait.2023.3315585","is_oa":false,"landing_page_url":"https://doi.org/10.1109/jsait.2023.3315585","pdf_url":null,"source":{"id":"https://openalex.org/S4210211895","display_name":"IEEE Journal on Selected Areas in Information Theory","issn_l":"2641-8770","issn":["2641-8770"],"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 Journal on Selected Areas in 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/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":true,"raw_author_name":"Anthony G\u00f3mez-Fonseca","raw_affiliation_strings":["Department of Mathematics, University of Notre Dame, Notre Dame, IN, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Notre Dame, Notre Dame, IN, USA","institution_ids":["https://openalex.org/I107639228"]}]},{"author_position":"middle","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":false,"raw_author_name":"Roxana Smarandache","raw_affiliation_strings":["Department of Mathematics and the Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and the Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, USA","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":["Klipsch School of Electrical and Computer Engineering, New Mexico State University, Las Cruces, NM, USA"],"affiliations":[{"raw_affiliation_string":"Klipsch School of Electrical and Computer Engineering, New Mexico State University, Las Cruces, NM, USA","institution_ids":["https://openalex.org/I10052268"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5012571757"],"corresponding_institution_ids":["https://openalex.org/I107639228"],"apc_list":null,"apc_paid":null,"fwci":1.4064,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.82584462,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"4","issue":null,"first_page":"499","last_page":"513"},"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":0.9979000091552734,"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":0.9976999759674072,"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/low-density-parity-check-code","display_name":"Low-density parity-check code","score":0.8053028583526611},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6645401120185852},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6341143846511841},{"id":"https://openalex.org/keywords/girth","display_name":"Girth (graph theory)","score":0.6211659908294678},{"id":"https://openalex.org/keywords/parity-check-matrix","display_name":"Parity-check matrix","score":0.5841532349586487},{"id":"https://openalex.org/keywords/adjacency-matrix","display_name":"Adjacency matrix","score":0.5681731700897217},{"id":"https://openalex.org/keywords/tanner-graph","display_name":"Tanner graph","score":0.5331277847290039},{"id":"https://openalex.org/keywords/parity","display_name":"Parity (physics)","score":0.47406691312789917},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4628424346446991},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.42116886377334595},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.28749582171440125},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1727411448955536},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11548727750778198},{"id":"https://openalex.org/keywords/error-floor","display_name":"Error floor","score":0.10145607590675354}],"concepts":[{"id":"https://openalex.org/C67692717","wikidata":"https://www.wikidata.org/wiki/Q187444","display_name":"Low-density parity-check code","level":3,"score":0.8053028583526611},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6645401120185852},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6341143846511841},{"id":"https://openalex.org/C2777434295","wikidata":"https://www.wikidata.org/wiki/Q959831","display_name":"Girth (graph theory)","level":2,"score":0.6211659908294678},{"id":"https://openalex.org/C95925971","wikidata":"https://www.wikidata.org/wiki/Q3100414","display_name":"Parity-check matrix","level":4,"score":0.5841532349586487},{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.5681731700897217},{"id":"https://openalex.org/C87117866","wikidata":"https://www.wikidata.org/wiki/Q7683664","display_name":"Tanner graph","level":5,"score":0.5331277847290039},{"id":"https://openalex.org/C2777151079","wikidata":"https://www.wikidata.org/wiki/Q141160","display_name":"Parity (physics)","level":2,"score":0.47406691312789917},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4628424346446991},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.42116886377334595},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.28749582171440125},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1727411448955536},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11548727750778198},{"id":"https://openalex.org/C46462455","wikidata":"https://www.wikidata.org/wiki/Q5395712","display_name":"Error floor","level":4,"score":0.10145607590675354},{"id":"https://openalex.org/C109214941","wikidata":"https://www.wikidata.org/wiki/Q18334","display_name":"Particle physics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/jsait.2023.3315585","is_oa":false,"landing_page_url":"https://doi.org/10.1109/jsait.2023.3315585","pdf_url":null,"source":{"id":"https://openalex.org/S4210211895","display_name":"IEEE Journal on Selected Areas in Information Theory","issn_l":"2641-8770","issn":["2641-8770"],"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 Journal on Selected Areas in Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7141613691","display_name":null,"funder_award_id":"CNS-2148358","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8530647473","display_name":null,"funder_award_id":"CCF-2145917","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G989716124","display_name":null,"funder_award_id":"HRD-1914635","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"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":35,"referenced_works":["https://openalex.org/W91277888","https://openalex.org/W1558273801","https://openalex.org/W1667880265","https://openalex.org/W1813544306","https://openalex.org/W1973712217","https://openalex.org/W1991921359","https://openalex.org/W2008209264","https://openalex.org/W2052423140","https://openalex.org/W2083342911","https://openalex.org/W2108136433","https://openalex.org/W2109383536","https://openalex.org/W2119017156","https://openalex.org/W2128765501","https://openalex.org/W2133068391","https://openalex.org/W2133339613","https://openalex.org/W2134523634","https://openalex.org/W2137874581","https://openalex.org/W2147776616","https://openalex.org/W2148317974","https://openalex.org/W2152165958","https://openalex.org/W2154297943","https://openalex.org/W2154993501","https://openalex.org/W2160065222","https://openalex.org/W2163532780","https://openalex.org/W2281218127","https://openalex.org/W2574730918","https://openalex.org/W2962845578","https://openalex.org/W2962883682","https://openalex.org/W2998239782","https://openalex.org/W3192350410","https://openalex.org/W4213281018","https://openalex.org/W4385234149","https://openalex.org/W6603727012","https://openalex.org/W6638490971","https://openalex.org/W6679489882"],"related_works":["https://openalex.org/W2090897912","https://openalex.org/W2602611185","https://openalex.org/W2150639697","https://openalex.org/W3212819824","https://openalex.org/W3167562836","https://openalex.org/W4297803167","https://openalex.org/W1526609637","https://openalex.org/W2122913048","https://openalex.org/W2996745071","https://openalex.org/W2163532780"],"abstract_inverted_index":{"In":[0,45],"this":[1,46],"paper,":[2],"we":[3,48],"present":[4],"an":[5],"efficient":[6],"strategy":[7,36],"to":[8,62,110,157],"enumerate":[9],"the":[10,16,51,55,69,78,87,103,117,124,128,150,158,170],"number":[11,88],"of":[12,19,54,65,89,119,130,160,173],"k-cycles,":[13,90],"g\u2264k<2g,":[14],"in":[15,68,98,116],"Tanner":[17],"graph":[18],"a":[20,163],"quasi-cyclic":[21],"low-density":[22],"parity-check":[23,32],"(QC-LDPC)":[24],"code":[25],"with":[26],"girth":[27],"g":[28],"using":[29],"its":[30],"polynomial":[31,56],"matrix":[33,58],"H.":[34],"This":[35,106],"works":[37,168],"for":[38,86,133],"both":[39],"(dv,dc)-regular":[40],"and":[41,71,135,142],"irregular":[42],"QC-LDPC":[43,120,174],"codes.":[44,175],"approach,":[47,156],"note":[49],"that":[50],"mth":[52],"power":[53],"adjacency":[57],"can":[59,72],"be":[60,74],"used":[61],"describe":[63],"walks":[64],"length":[66],"m":[67],"protograph":[70],"therefore":[73],"sufficiently":[75],"described":[76],"by":[77,92],"matrices":[79,104],"Bm(H)(HHT)m/2H(m2),":[80],"where":[81],"m\u22650.":[82],"We":[83],"provide":[84],"formulas":[85],"Nk,":[91,132],"just":[93],"taking":[94],"into":[95],"account":[96],"repetitions":[97],"some":[99],"multisets":[100],"constructed":[101],"from":[102],"Bm(H).":[105],"approach":[107],"is":[108,137],"shown":[109],"have":[111],"low":[112],"complexity.":[113],"For":[114],"example,":[115],"case":[118],"codes":[121],"based":[122],"on":[123,149,169],"3\u00d7nv":[125],"fully-connected":[126],"protograph,":[127],"complexity":[129],"determining":[131],"k=4,6,8,10":[134],"12,":[136],"O(nv2log(N)),":[138],"O(nv2log(nv)log(N)),":[139],"O(nv4log4(nv)log(N)),":[140],"O(nv4log(nv)log(N))":[141],"O(nv6log6(nv)log(N)),":[143],"respectively.":[144],"The":[145],"complexity,":[146],"depending":[147],"logarithmically":[148],"lifting":[151],"factor":[152],"N,":[153],"gives":[154],"our":[155,161],"best":[159],"knowledge,":[162],"significant":[164],"advantage":[165],"over":[166],"previous":[167],"cycle":[171],"distribution":[172]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}