{"id":"https://openalex.org/W2077542512","doi":"https://doi.org/10.1109/tit.2014.2333519","title":"On the Minimum/Stopping Distance of Array Low-Density Parity-Check Codes","display_name":"On the Minimum/Stopping Distance of Array Low-Density Parity-Check Codes","publication_year":2014,"publication_date":"2014-07-11","ids":{"openalex":"https://openalex.org/W2077542512","doi":"https://doi.org/10.1109/tit.2014.2333519","mag":"2077542512"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2014.2333519","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2014.2333519","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"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1205.2590","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Eirik Rosnes","orcid":null},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":true,"raw_author_name":"Eirik Rosnes","raw_affiliation_strings":["Selmer Center, University of Bergen, Bergen, Norway"],"affiliations":[{"raw_affiliation_string":"Selmer Center, University of Bergen, Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Marcel Adrian Ambroze","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marcel Adrian Ambroze","raw_affiliation_strings":["Fixed and Mobile Communications Research Center, University of Plymouth, Plymouth, U.K"],"affiliations":[{"raw_affiliation_string":"Fixed and Mobile Communications Research Center, University of Plymouth, Plymouth, U.K","institution_ids":[]}]},{"author_position":"last","author":{"id":null,"display_name":"Martin Tomlinson","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Martin Tomlinson","raw_affiliation_strings":["Fixed and Mobile Communications Research Center, University of Plymouth, Plymouth, U.K"],"affiliations":[{"raw_affiliation_string":"Fixed and Mobile Communications Research Center, University of Plymouth, Plymouth, U.K","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4432739"],"apc_list":null,"apc_paid":null,"fwci":2.8778,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.91835872,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"60","issue":"9","first_page":"5204","last_page":"5214"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":0.9702000021934509,"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":0.9702000021934509,"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":0.008100000210106373,"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":0.005499999970197678,"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/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6736000180244446},{"id":"https://openalex.org/keywords/minimum-distance","display_name":"Minimum distance","score":0.6276999711990356},{"id":"https://openalex.org/keywords/low-density-parity-check-code","display_name":"Low-density parity-check code","score":0.5878999829292297},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.4643999934196472},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.41670000553131104},{"id":"https://openalex.org/keywords/coprime-integers","display_name":"Coprime integers","score":0.37059998512268066},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.35089999437332153},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.3492000102996826},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.3440000116825104}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6966999769210815},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6736000180244446},{"id":"https://openalex.org/C3018063660","wikidata":"https://www.wikidata.org/wiki/Q6865448","display_name":"Minimum distance","level":2,"score":0.6276999711990356},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5974000096321106},{"id":"https://openalex.org/C67692717","wikidata":"https://www.wikidata.org/wiki/Q187444","display_name":"Low-density parity-check code","level":3,"score":0.5878999829292297},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5831999778747559},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.4643999934196472},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.41670000553131104},{"id":"https://openalex.org/C23230895","wikidata":"https://www.wikidata.org/wiki/Q104752","display_name":"Coprime integers","level":2,"score":0.37059998512268066},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3517000079154968},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.35089999437332153},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.3492000102996826},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.3440000116825104},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.33180001378059387},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.3305000066757202},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.326200008392334},{"id":"https://openalex.org/C78944582","wikidata":"https://www.wikidata.org/wiki/Q5158264","display_name":"Concatenated error correction code","level":4,"score":0.3046000003814697},{"id":"https://openalex.org/C2778945305","wikidata":"https://www.wikidata.org/wiki/Q6865502","display_name":"Minimum weight","level":2,"score":0.29510000348091125},{"id":"https://openalex.org/C92224547","wikidata":"https://www.wikidata.org/wiki/Q1673216","display_name":"Probability of error","level":2,"score":0.2847999930381775},{"id":"https://openalex.org/C3020028006","wikidata":"https://www.wikidata.org/wiki/Q9158","display_name":"Electronic mail","level":2,"score":0.2815999984741211},{"id":"https://openalex.org/C114504821","wikidata":"https://www.wikidata.org/wiki/Q2164281","display_name":"Turbo code","level":3,"score":0.2809999883174896},{"id":"https://openalex.org/C111208986","wikidata":"https://www.wikidata.org/wiki/Q901698","display_name":"Distance matrix","level":2,"score":0.27300000190734863},{"id":"https://openalex.org/C169021753","wikidata":"https://www.wikidata.org/wiki/Q201972","display_name":"Reed\u2013Muller code","level":5,"score":0.26840001344680786},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.26420000195503235},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.25119999051094055}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tit.2014.2333519","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2014.2333519","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:1205.2590","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1205.2590","pdf_url":"https://arxiv.org/pdf/1205.2590","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":"pmh:oai:pearl.plymouth.ac.uk:10026.1/16179","is_oa":true,"landing_page_url":"http://hdl.handle.net/10026.1/16179","pdf_url":"http://hdl.handle.net/10026.1/16179","source":{"id":"https://openalex.org/S4306402507","display_name":"PEARL (University of Plymouth)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I897542642","host_organization_name":"University of Plymouth","host_organization_lineage":["https://openalex.org/I897542642"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"journal-article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1205.2590","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1205.2590","pdf_url":"https://arxiv.org/pdf/1205.2590","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/G4840547712","display_name":null,"funder_award_id":"183316","funder_id":"https://openalex.org/F4320323299","funder_display_name":"Norges Forskningsr\u00e5d"}],"funders":[{"id":"https://openalex.org/F4320323299","display_name":"Norges Forskningsr\u00e5d","ror":"https://ror.org/00epmv149"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1760355913","https://openalex.org/W2004036066","https://openalex.org/W2076838340","https://openalex.org/W2079767843","https://openalex.org/W2102105592","https://openalex.org/W2103495212","https://openalex.org/W2109491150","https://openalex.org/W2140276604","https://openalex.org/W2152956478","https://openalex.org/W2153292363","https://openalex.org/W2156660752","https://openalex.org/W2170998175"],"related_works":[],"abstract_inverted_index":{"In":[0,39,101],"this":[1,102],"paper,":[2,103],"we":[3,104,146,170],"study":[4],"the":[5,40,42,87,124,143],"minimum/stopping":[6,43,174],"distance":[7,44,91,166,175],"of":[8,45,69,77,110,126,131,154,161,183],"array":[9,15],"low-density":[10],"parity-check":[11],"(LDPC)":[12],"codes.":[13],"An":[14],"LDPC":[16,21],"code":[17,22],"is":[18,32,97],"a":[19,115,127,132,164],"quasi-cyclic":[20],"specified":[23],"by":[24,49,95,122],"two":[25],"integers":[26],"q":[27,31,70,162,184],"and":[28,36,52,71,73,114,180],"m,":[29,72],"where":[30],"an":[33,106],"odd":[34],"prime":[35],"m":[37,61,84,178],"q.":[38],"literature,":[41],"these":[46],"codes":[47],"(denoted":[48],"d(q,":[50,98,111,119],"m)":[51],"h(q,":[53],"m),":[54],"respectively)":[55],"has":[56],"been":[57,81,149],"thoroughly":[58],"studied":[59],"for":[60,66,158,177],"5.":[62],"Both":[63],"exact":[64],"results,":[65],"small":[67],"values":[68,160,182],"general":[74],"(i.e.,":[75],"independent":[76],"q)":[78],"bounds":[79,136],"have":[80,147],"established.":[82],"For":[83],"=":[85],"6,":[86],"best":[88],"known":[89],"minimum":[90,165],"upper":[92,108,117],"bound,":[93],"derived":[94],"Mittelholzer,":[96],"6)":[99,112],"32.":[100],"derive":[105],"improved":[107],"bound":[109,118],"20":[113],"new":[116,172],"7)":[120],"24":[121],"using":[123,163],"concept":[125],"template":[128],"support":[129],"matrix":[130],"codeword/stopping":[133],"set.":[134],"The":[135],"are":[137],"tight":[138],"with":[139],"high":[140],"probability":[141],"in":[142],"sense":[144],"that":[145],"not":[148],"able":[150],"to":[151],"find":[152],"codewords":[153],"strictly":[155],"lower":[156],"weight":[157],"several":[159],"probabilistic":[167],"algorithm.":[168],"Finally,":[169],"provide":[171],"specific":[173],"results":[176],"7":[179],"low-to-moderate":[181],"\u226479.":[185]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2016-06-24T00:00:00"}
