{"id":"https://openalex.org/W2079973940","doi":"https://doi.org/10.1109/tit.2012.2188272","title":"On the Smallest Absorbing Sets of LDPC Codes From Finite Planes","display_name":"On the Smallest Absorbing Sets of LDPC Codes From Finite Planes","publication_year":2012,"publication_date":"2012-03-09","ids":{"openalex":"https://openalex.org/W2079973940","doi":"https://doi.org/10.1109/tit.2012.2188272","mag":"2079973940"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2012.2188272","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2012.2188272","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":["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/A5100422467","display_name":"Haiyang Liu","orcid":"https://orcid.org/0000-0001-6567-8603"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210119392","display_name":"Institute of Microelectronics","ror":"https://ror.org/02s6gs133","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210119392"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haiyang Liu","raw_affiliation_strings":["Institute of Microelectronics, Chinese Academy of Sciences, Beijing, China","Inst. of Microelectron., Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Microelectronics, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210119392","https://openalex.org/I19820366"]},{"raw_affiliation_string":"Inst. of Microelectron., Beijing, China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071024482","display_name":"Yan Li","orcid":"https://orcid.org/0000-0002-0131-5720"},"institutions":[{"id":"https://openalex.org/I52158045","display_name":"China Agricultural University","ror":"https://ror.org/04v3ywz14","country_code":"CN","type":"education","lineage":["https://openalex.org/I52158045"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yan Li","raw_affiliation_strings":["Department of Applied Mathematics, China Agricultural University, Beijing, China","Dept. of Appl. Math., China Agric. Univ., Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, China Agricultural University, Beijing, China","institution_ids":["https://openalex.org/I52158045"]},{"raw_affiliation_string":"Dept. of Appl. Math., China Agric. Univ., Beijing, China","institution_ids":["https://openalex.org/I52158045"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003333304","display_name":"Lianrong Ma","orcid":null},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lianrong Ma","raw_affiliation_strings":["Department of Mathematical Sciences, Tsinghua University, Beijing, China","[Dept. of Math. Sci., Tsinghua Univ., Beijing, China]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"[Dept. of Math. Sci., Tsinghua Univ., Beijing, China]","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100428821","display_name":"Jie Chen","orcid":"https://orcid.org/0000-0003-3171-1887"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210119392","display_name":"Institute of Microelectronics","ror":"https://ror.org/02s6gs133","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210119392"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jie Chen","raw_affiliation_strings":["Institute of Microelectronics, Chinese Academy of Sciences, Beijing, China","Inst. of Microelectron., Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Microelectronics, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210119392","https://openalex.org/I19820366"]},{"raw_affiliation_string":"Inst. of Microelectron., Beijing, China","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7453,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.74793149,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"58","issue":"6","first_page":"4014","last_page":"4020"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","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/T11321","display_name":"Error Correcting Code Techniques","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/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.9983999729156494,"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":0.9965999722480774,"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":0.9085402488708496},{"id":"https://openalex.org/keywords/tanner-graph","display_name":"Tanner graph","score":0.8330607414245605},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.63919997215271},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.5619077086448669},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5294206738471985},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.5202152132987976},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4755958020687103},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4750494956970215},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.45493751764297485},{"id":"https://openalex.org/keywords/concatenated-error-correction-code","display_name":"Concatenated error correction code","score":0.4147277772426605},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.34608426690101624},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3027487099170685},{"id":"https://openalex.org/keywords/error-floor","display_name":"Error floor","score":0.24363082647323608},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2279651165008545}],"concepts":[{"id":"https://openalex.org/C67692717","wikidata":"https://www.wikidata.org/wiki/Q187444","display_name":"Low-density parity-check code","level":3,"score":0.9085402488708496},{"id":"https://openalex.org/C87117866","wikidata":"https://www.wikidata.org/wiki/Q7683664","display_name":"Tanner graph","level":5,"score":0.8330607414245605},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.63919997215271},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.5619077086448669},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5294206738471985},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.5202152132987976},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4755958020687103},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4750494956970215},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.45493751764297485},{"id":"https://openalex.org/C78944582","wikidata":"https://www.wikidata.org/wiki/Q5158264","display_name":"Concatenated error correction code","level":4,"score":0.4147277772426605},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.34608426690101624},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3027487099170685},{"id":"https://openalex.org/C46462455","wikidata":"https://www.wikidata.org/wiki/Q5395712","display_name":"Error floor","level":4,"score":0.24363082647323608},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2279651165008545},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2012.2188272","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2012.2188272","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"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5600000023841858,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W841358376","https://openalex.org/W1484692004","https://openalex.org/W1577660440","https://openalex.org/W1588943481","https://openalex.org/W1973053641","https://openalex.org/W2001732758","https://openalex.org/W2002667599","https://openalex.org/W2095882513","https://openalex.org/W2099940667","https://openalex.org/W2114074598","https://openalex.org/W2114869758","https://openalex.org/W2116726015","https://openalex.org/W2118324526","https://openalex.org/W2124113125","https://openalex.org/W2125836614","https://openalex.org/W2128765501","https://openalex.org/W2133945375","https://openalex.org/W2135573812","https://openalex.org/W2150972708","https://openalex.org/W2153049761","https://openalex.org/W2154287427","https://openalex.org/W2163055518","https://openalex.org/W2164592411","https://openalex.org/W2170998175","https://openalex.org/W4285719527","https://openalex.org/W4300188436","https://openalex.org/W6628810906","https://openalex.org/W6635197353","https://openalex.org/W6677658808"],"related_works":["https://openalex.org/W1968533815","https://openalex.org/W2808439818","https://openalex.org/W2126464345","https://openalex.org/W2150639697","https://openalex.org/W2090897912","https://openalex.org/W2351144917","https://openalex.org/W2142415334","https://openalex.org/W2996745071","https://openalex.org/W4386075075","https://openalex.org/W2071304218"],"abstract_inverted_index":{"Absorbing":[0],"sets,":[1],"a":[2,13,94,105,118,124,130],"class":[3],"of":[4,7,12,24,41,57,73,82,96,164,168],"combinatorial":[5,80],"structures":[6],"the":[8,22,25,37,55,79,83,100,153,159],"Tanner":[9,101],"graph":[10,102],"representation":[11],"low-density":[14],"parity-check":[15],"(LDPC)":[16],"code,":[17],"are":[18,64,143],"known":[19],"to":[20,66,103,128,150],"influence":[21],"performance":[23,155],"code":[26],"under":[27],"message":[28],"passing":[29],"iterative":[30],"decoding.":[31],"In":[32,134],"this":[33],"paper,":[34],"we":[35,115,136],"study":[36],"smallest":[38,58,84,106,125,140],"absorbing":[39,59,85,107,126,132,141],"sets":[40,60,86,142],"LDPC":[42,74,110,169],"codes":[43,111],"constructed":[44],"from":[45,112],"projective":[46,113],"planes":[47],"and":[48,87,91,121],"Euclidean":[49],"planes.":[50],"The":[51],"lower":[52],"bounds":[53],"on":[54],"parameters":[56],"given":[61],"by":[62],"Dolecek":[63],"proven":[65],"be":[67,104,129],"tight":[68],"for":[69,93,123],"these":[70,139,165],"two":[71,166],"families":[72,167],"codes.":[75,170],"We":[76],"also":[77],"analyze":[78],"properties":[81],"give":[88,117],"conditions":[89],"necessary":[90,120],"sufficient":[92,122],"set":[95,127],"bit":[97],"nodes":[98],"in":[99],"set.":[108,133],"For":[109],"planes,":[114],"further":[116],"condition":[119],"fully":[131],"addition,":[135],"show":[137],"that":[138],"asymptotically":[144],"not":[145],"stable,":[146],"which":[147],"may":[148],"explain":[149],"some":[151],"extent":[152],"good":[154],"as":[156,158],"well":[157],"low":[160],"error":[161],"floor":[162],"expectation":[163]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
