{"id":"https://openalex.org/W4405909024","doi":"https://doi.org/10.1109/itw61385.2024.10806922","title":"Theoretical Bounds for the Size of Elementary Trapping Sets by Graph Theory Methods","display_name":"Theoretical Bounds for the Size of Elementary Trapping Sets by Graph Theory Methods","publication_year":2024,"publication_date":"2024-11-24","ids":{"openalex":"https://openalex.org/W4405909024","doi":"https://doi.org/10.1109/itw61385.2024.10806922"},"language":"en","primary_location":{"id":"doi:10.1109/itw61385.2024.10806922","is_oa":false,"landing_page_url":"https://doi.org/10.1109/itw61385.2024.10806922","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2024 IEEE Information Theory Workshop (ITW)","raw_type":"proceedings-article"},"type":"conference-paper","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/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":["University of Chinese Academy of Sciences"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Chinese Academy of Sciences","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034323222","display_name":"Zicheng Ye","orcid":"https://orcid.org/0009-0005-8160-9698"},"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":"Zicheng Ye","raw_affiliation_strings":["University of Chinese Academy of Sciences"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Chinese Academy of Sciences","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090005179","display_name":"Huazi Zhang","orcid":null},"institutions":[{"id":"https://openalex.org/I4210160618","display_name":"Huawei Technologies (United Kingdom)","ror":"https://ror.org/056gzgs71","country_code":"GB","type":"company","lineage":["https://openalex.org/I2250955327","https://openalex.org/I4210160618"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Huazi Zhang","raw_affiliation_strings":["Huawei Technologies Co. Ltd"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Huawei Technologies Co. Ltd","institution_ids":["https://openalex.org/I4210160618"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100384800","display_name":"Jun Wang","orcid":"https://orcid.org/0000-0002-7884-6714"},"institutions":[{"id":"https://openalex.org/I4210160618","display_name":"Huawei Technologies (United Kingdom)","ror":"https://ror.org/056gzgs71","country_code":"GB","type":"company","lineage":["https://openalex.org/I2250955327","https://openalex.org/I4210160618"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Jun Wang","raw_affiliation_strings":["Huawei Technologies Co. Ltd"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Huawei Technologies Co. Ltd","institution_ids":["https://openalex.org/I4210160618"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100349873","display_name":"Ke Liu","orcid":"https://orcid.org/0000-0003-4668-2126"},"institutions":[{"id":"https://openalex.org/I4210160618","display_name":"Huawei Technologies (United Kingdom)","ror":"https://ror.org/056gzgs71","country_code":"GB","type":"company","lineage":["https://openalex.org/I2250955327","https://openalex.org/I4210160618"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Ke Liu","raw_affiliation_strings":["Huawei Technologies Co. Ltd"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Huawei Technologies Co. Ltd","institution_ids":["https://openalex.org/I4210160618"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054482111","display_name":"Dawei Yin","orcid":"https://orcid.org/0000-0002-8846-2001"},"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":"Dawei Yin","raw_affiliation_strings":["School of Mathematics, Shandong University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Shandong University","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100399482","display_name":"Guanghui Wang","orcid":"https://orcid.org/0000-0002-9275-8323"},"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"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Shandong University","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108430975","display_name":"Guiying Yan","orcid":"https://orcid.org/0000-0002-4477-824X"},"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":["University of Chinese Academy of Sciences"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Chinese Academy of Sciences","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"last","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":["University of Chinese Academy of Sciences"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Chinese Academy of Sciences","institution_ids":["https://openalex.org/I4210165038"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"193","last_page":"198"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9907000064849854,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9907000064849854,"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"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9722999930381775,"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"}},{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9563999772071838,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/graph-theory","display_name":"Graph theory","score":0.650646984577179},{"id":"https://openalex.org/keywords/trapping","display_name":"Trapping","score":0.5730310082435608},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5187554359436035},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4555876851081848},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3640788793563843},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3393342196941376},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.31687670946121216},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3028292655944824}],"concepts":[{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.650646984577179},{"id":"https://openalex.org/C2777924906","wikidata":"https://www.wikidata.org/wiki/Q34168","display_name":"Trapping","level":2,"score":0.5730310082435608},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5187554359436035},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4555876851081848},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3640788793563843},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3393342196941376},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.31687670946121216},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3028292655944824},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/itw61385.2024.10806922","is_oa":false,"landing_page_url":"https://doi.org/10.1109/itw61385.2024.10806922","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2024 IEEE Information Theory Workshop (ITW)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1964402820","https://openalex.org/W1973712217","https://openalex.org/W2021979706","https://openalex.org/W2119210254","https://openalex.org/W2126259959","https://openalex.org/W2128765501","https://openalex.org/W2133068391","https://openalex.org/W2151875415","https://openalex.org/W2153344955","https://openalex.org/W2155085924","https://openalex.org/W2155469840","https://openalex.org/W2157927886","https://openalex.org/W2170018710","https://openalex.org/W2579410364","https://openalex.org/W2592992924","https://openalex.org/W3171644859","https://openalex.org/W4285407565","https://openalex.org/W6628810906","https://openalex.org/W6638033105"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2007742350","https://openalex.org/W2394289659","https://openalex.org/W4296916267","https://openalex.org/W2051069894","https://openalex.org/W2532801570","https://openalex.org/W4385627933","https://openalex.org/W2480127678","https://openalex.org/W2806270048","https://openalex.org/W4310605282"],"abstract_inverted_index":{"Elementary":[0],"trapping":[1],"sets":[2],"(ETSs)":[3],"are":[4],"the":[5,9,15,37,72,96,124,133,141,150,157],"principal":[6],"culprits":[7],"for":[8,100],"performance":[10,181],"of":[11,39],"LDPC":[12,40],"codes":[13,41,174],"in":[14,36,47,71,87,112,156],"error":[16,49,185],"floor":[17,50,186],"region.":[18],"Due":[19],"to":[20,32,75],"their":[21],"large":[22],"quantity,":[23],"intricate":[24],"structures,":[25],"and":[26,67,104,182],"high":[27],"computational":[28],"complexity,":[29],"determining":[30],"how":[31],"eliminate":[33,76],"dominant":[34],"ETSs":[35],"design":[38],"has":[42],"become":[43],"a":[44,84,113,162,183],"critical":[45],"issue":[46],"improving":[48],"behavior.":[51],"In":[52],"this":[53,57],"paper,":[54],"we":[55,94,160],"address":[56],"problem":[58],"by":[59,83,138,148],"avoiding":[60],"particular":[61],"theta":[62],"graphs":[63],"<tex":[64,68,101,108,119,126,165],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[65,69,102,109,120,127,166],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$(\\theta(1,2,2)$</tex>":[66],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$\\theta(2,2,2))$</tex>":[70],"Tanner":[73,114,158],"graph":[74,88,115],"specific":[77],"ETSs.":[78],"These":[79],"can":[80],"be":[81],"characterized":[82],"pivotal":[85],"tool":[86],"theory":[89],"-":[90],"Tur\u00e1n":[91,98],"numbers.":[92],"Theoretically,":[93],"derive":[95],"exact":[97],"number":[99],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$\\theta(1,2,2)$</tex>":[103],"demonstrate":[105],"that":[106,173],"all":[107],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$(a,":[110],"b)$</tex>-ETSs":[111],"with":[116,176],"variable-reaular":[117],"degree":[118],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$d_{L}(v)=\\gamma$</tex>":[121],"must":[122],"satisfy":[123],"inequality":[125,164],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$b\\geq":[128,167],"a\\gamma-\\frac{1}{2}a^{2}$</tex>.":[129],"This":[130],"result":[131],"improves":[132],"lower":[134,184],"bound":[135],"previously":[136],"obtained":[137],"Amirzade":[139],"when":[140],"girth":[142,146],"is":[143],"6.":[144],"For":[145],"8,":[147],"constraining":[149],"relationship":[151],"between":[152],"any":[153],"two":[154],"8-cycles":[155],"graph,":[159],"establish":[161],"similar":[163],"a\\gamma-\\frac{a(\\sqrt{8a-7}-1)}{2}$</tex>.":[168],"Our":[169],"simulation":[170],"results":[171],"indicate":[172],"designed":[175],"these":[177],"considerations":[178],"exhibit":[179],"improved":[180],"over":[187],"additive":[188],"white":[189],"Gaussian":[190],"noise":[191],"channels.":[192]},"counts_by_year":[],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}