{"id":"https://openalex.org/W4415084588","doi":"https://doi.org/10.1109/tit.2025.3631564","title":"The Impact of the Distance Between Cycles on Elementary Trapping Sets","display_name":"The Impact of the Distance Between Cycles on Elementary Trapping Sets","publication_year":2025,"publication_date":"2025-11-11","ids":{"openalex":"https://openalex.org/W4415084588","doi":"https://doi.org/10.1109/tit.2025.3631564"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2025.3631564","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2025.3631564","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":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2503.01341","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111005807","display_name":"Haoran Xiong","orcid":"https://orcid.org/0009-0007-4174-5112"},"institutions":[{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haoran Xiong","raw_affiliation_strings":["School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China"],"raw_orcid":"https://orcid.org/0009-0007-4174-5112","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100399476","display_name":"Guanghui Wang","orcid":"https://orcid.org/0000-0002-3730-5575"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guanghui Wang","raw_affiliation_strings":["School of Mathematics, Shandong University, Jinan, China"],"raw_orcid":"https://orcid.org/0000-0002-3730-5575","affiliations":[{"raw_affiliation_string":"School of Mathematics, Shandong University, Jinan, China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5104108916","display_name":"Zhiming Ma","orcid":null},"institutions":[{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhiming Ma","raw_affiliation_strings":["School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0003-1169-7627","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"last","author":{"id":null,"display_name":"Guiying Yan","orcid":"https://orcid.org/0000-0002-1736-5482"},"institutions":[{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guiying Yan","raw_affiliation_strings":["School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-1736-5482","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"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":0.2547113,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"72","issue":"1","first_page":"298","last_page":"314"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9269999861717224,"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"}},"topics":[{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9269999861717224,"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/minimum-distance","display_name":"Minimum distance","score":0.6359999775886536},{"id":"https://openalex.org/keywords/spectral-radius","display_name":"Spectral radius","score":0.576200008392334},{"id":"https://openalex.org/keywords/radius","display_name":"RADIUS","score":0.5091000199317932},{"id":"https://openalex.org/keywords/low-density-parity-check-code","display_name":"Low-density parity-check code","score":0.45719999074935913},{"id":"https://openalex.org/keywords/probability-of-error","display_name":"Probability of error","score":0.39820000529289246},{"id":"https://openalex.org/keywords/critical-distance","display_name":"Critical distance","score":0.3939000070095062},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.38670000433921814},{"id":"https://openalex.org/keywords/trapping","display_name":"Trapping","score":0.3529999852180481}],"concepts":[{"id":"https://openalex.org/C3018063660","wikidata":"https://www.wikidata.org/wiki/Q6865448","display_name":"Minimum distance","level":2,"score":0.6359999775886536},{"id":"https://openalex.org/C140532419","wikidata":"https://www.wikidata.org/wiki/Q249748","display_name":"Spectral radius","level":3,"score":0.576200008392334},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.5091000199317932},{"id":"https://openalex.org/C67692717","wikidata":"https://www.wikidata.org/wiki/Q187444","display_name":"Low-density parity-check code","level":3,"score":0.45719999074935913},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43380001187324524},{"id":"https://openalex.org/C92224547","wikidata":"https://www.wikidata.org/wiki/Q1673216","display_name":"Probability of error","level":2,"score":0.39820000529289246},{"id":"https://openalex.org/C24723263","wikidata":"https://www.wikidata.org/wiki/Q1571884","display_name":"Critical distance","level":4,"score":0.3939000070095062},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.38670000433921814},{"id":"https://openalex.org/C2777924906","wikidata":"https://www.wikidata.org/wiki/Q34168","display_name":"Trapping","level":2,"score":0.3529999852180481},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.349700003862381},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.3352000117301941},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.32429999113082886},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3149999976158142},{"id":"https://openalex.org/C2986158284","wikidata":"https://www.wikidata.org/wiki/Q6522493","display_name":"Distance measurement","level":2,"score":0.3149000108242035},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3089999854564667},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.30799999833106995},{"id":"https://openalex.org/C87117866","wikidata":"https://www.wikidata.org/wiki/Q7683664","display_name":"Tanner graph","level":5,"score":0.28380000591278076},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.27129998803138733},{"id":"https://openalex.org/C500300565","wikidata":"https://www.wikidata.org/wiki/Q925667","display_name":"Computer simulation","level":2,"score":0.2705000042915344},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.26510000228881836},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.26260000467300415},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.26030001044273376},{"id":"https://openalex.org/C46462455","wikidata":"https://www.wikidata.org/wiki/Q5395712","display_name":"Error floor","level":4,"score":0.2596000134944916}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tit.2025.3631564","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2025.3631564","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"},{"id":"pmh:oai:arXiv.org:2503.01341","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2503.01341","pdf_url":"https://arxiv.org/pdf/2503.01341","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2503.01341","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2503.01341","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2503.01341","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2503.01341","pdf_url":"https://arxiv.org/pdf/2503.01341","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3015776869","display_name":null,"funder_award_id":"No. 2023YFA1009602","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G5647958688","display_name":null,"funder_award_id":"2023YFA1009602","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"}],"funders":[{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Elementary":[0],"trapping":[1],"sets":[2],"(ETSs)":[3],"are":[4,30],"the":[5,9,17,37,40,69,79,89,100,109,113,118,126,149,162,169,177,183,188,195],"main":[6],"culprits":[7],"of":[8,11,39,72,102,112,120,141,156,164],"performance":[10,163,203],"low-density":[12],"parity-check":[13],"(LDPC)":[14],"codes":[15,166,197],"in":[16,187],"error":[18,154],"floor":[19],"region.":[20],"Due":[21],"to":[22,32,59,205,209],"their":[23],"large":[24],"quantities":[25],"and":[26,54,63,75,93,144,153],"complex":[27],"structures,":[28],"ETSs":[29],"difficult":[31],"analyze.":[33],"This":[34,122],"paper":[35],"studies":[36],"impact":[38],"distance":[41,80,105,140,170,184],"between":[42,81,106,171,185],"cycles":[43,60,82,103,107,172,186],"on":[44,47],"ETSs,":[45],"focusing":[46],"two":[48,137],"special":[49],"graph":[50],"classes:":[51],"theta":[52],"graphs":[53,74],"dumbbell":[55],"graphs,":[56],"which":[57,180],"correspond":[58],"with":[61,125,139],"negative":[62],"non-negative":[64],"distances,":[65],"respectively.":[66],"We":[67],"determine":[68],"Tur\u00e1n":[70,130],"numbers":[71],"these":[73],"prove":[76,97],"that":[77,98,161,194],"increasing":[78,99],"can":[83],"eliminate":[84],"more":[85],"ETSs.":[86,121,157],"Additionally,":[87],"using":[88,129],"linear":[90],"state-space":[91],"model":[92],"spectral":[94,110,151],"theory,":[95],"we":[96,147,175],"length":[101],"or":[104,206],"decreases":[108],"radius":[111],"system":[114],"matrix,":[115],"thereby":[116],"reducing":[117],"harmfulness":[119],"is":[123],"consistent":[124],"conclusion":[127],"obtained":[128],"numbers.":[131],"For":[132],"specific":[133],"cases":[134],"when":[135],"removing":[136],"6-cycles":[138],"-1,":[142],"0":[143],"1,":[145],"respectively,":[146],"calculate":[148],"sizes,":[150],"radii,":[152],"probabilities":[155],"These":[158],"results":[159,192],"confirm":[160],"LDPC":[165],"improves":[167],"as":[168],"increases.":[173],"Furthermore,":[174],"design":[176],"PEG-CYCLE":[178],"algorithm,":[179],"greedily":[181],"maximizes":[182],"Tanner":[189],"graph.":[190],"Numerical":[191],"show":[193],"QC-LDPC":[196],"constructed":[198],"by":[199],"our":[200],"method":[201],"achieve":[202],"comparable":[204],"even":[207],"superior":[208],"state-of-the-art":[210],"construction":[211],"methods.":[212]},"counts_by_year":[],"updated_date":"2026-07-19T07:52:34.831488","created_date":"2025-10-12T00:00:00"}