{"id":"https://openalex.org/W1667880265","doi":"https://doi.org/10.1109/tit.2011.2173244","title":"Quasi-Cyclic LDPC Codes: Influence of Proto- and Tanner-Graph Structure on Minimum Hamming Distance Upper Bounds","display_name":"Quasi-Cyclic LDPC Codes: Influence of Proto- and Tanner-Graph Structure on Minimum Hamming Distance Upper Bounds","publication_year":2012,"publication_date":"2012-02-01","ids":{"openalex":"https://openalex.org/W1667880265","doi":"https://doi.org/10.1109/tit.2011.2173244","mag":"1667880265"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2011.2173244","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2011.2173244","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/0901.4129","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Roxana Smarandache","orcid":null},"institutions":[{"id":"https://openalex.org/I26538001","display_name":"San Diego State University","ror":"https://ror.org/0264fdx42","country_code":"US","type":"education","lineage":["https://openalex.org/I26538001"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Roxana Smarandache","raw_affiliation_strings":["Department of Mathematics and Statistics, San Diego State University, San Diego, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, San Diego State University, San Diego, CA, USA","institution_ids":["https://openalex.org/I26538001"]}]},{"author_position":"last","author":{"id":null,"display_name":"Pascal O. Vontobel","orcid":null},"institutions":[{"id":"https://openalex.org/I1324840837","display_name":"Hewlett-Packard (United States)","ror":"https://ror.org/059rn9488","country_code":"US","type":"company","lineage":["https://openalex.org/I1324840837"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pascal O. Vontobel","raw_affiliation_strings":["Hewlett Packard Laboratories, Palo Alto, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hewlett Packard Laboratories, Palo Alto, CA, USA","institution_ids":["https://openalex.org/I1324840837"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":12.297,"has_fulltext":false,"cited_by_count":125,"citation_normalized_percentile":{"value":0.98829025,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"58","issue":"2","first_page":"585","last_page":"607"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":0.9779000282287598,"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":0.9779000282287598,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.002199999988079071,"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/T10878","display_name":"CRISPR and Genetic Engineering","score":0.0020000000949949026,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hamming-graph","display_name":"Hamming graph","score":0.7608000040054321},{"id":"https://openalex.org/keywords/hamming-code","display_name":"Hamming code","score":0.6875},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.6869000196456909},{"id":"https://openalex.org/keywords/convolutional-code","display_name":"Convolutional code","score":0.628000020980835},{"id":"https://openalex.org/keywords/hamming","display_name":"Hamming(7,4)","score":0.5982999801635742},{"id":"https://openalex.org/keywords/low-density-parity-check-code","display_name":"Low-density parity-check code","score":0.5637000203132629},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.5397999882698059},{"id":"https://openalex.org/keywords/hamming-weight","display_name":"Hamming weight","score":0.5194000005722046},{"id":"https://openalex.org/keywords/hamming-bound","display_name":"Hamming bound","score":0.512499988079071}],"concepts":[{"id":"https://openalex.org/C29696283","wikidata":"https://www.wikidata.org/wiki/Q369440","display_name":"Hamming graph","level":5,"score":0.7608000040054321},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.6875},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.6869000196456909},{"id":"https://openalex.org/C157899210","wikidata":"https://www.wikidata.org/wiki/Q1395022","display_name":"Convolutional code","level":3,"score":0.628000020980835},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6183000206947327},{"id":"https://openalex.org/C112932734","wikidata":"https://www.wikidata.org/wiki/Q2322550","display_name":"Hamming(7,4)","level":5,"score":0.5982999801635742},{"id":"https://openalex.org/C67692717","wikidata":"https://www.wikidata.org/wiki/Q187444","display_name":"Low-density parity-check code","level":3,"score":0.5637000203132629},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.5397999882698059},{"id":"https://openalex.org/C63361517","wikidata":"https://www.wikidata.org/wiki/Q5645805","display_name":"Hamming weight","level":5,"score":0.5194000005722046},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5138999819755554},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5135999917984009},{"id":"https://openalex.org/C166530166","wikidata":"https://www.wikidata.org/wiki/Q1970635","display_name":"Hamming bound","level":5,"score":0.512499988079071},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5026999711990356},{"id":"https://openalex.org/C33529081","wikidata":"https://www.wikidata.org/wiki/Q18378194","display_name":"Serial concatenated convolutional codes","level":5,"score":0.4146000146865845},{"id":"https://openalex.org/C78944582","wikidata":"https://www.wikidata.org/wiki/Q5158264","display_name":"Concatenated error correction code","level":4,"score":0.4101000130176544},{"id":"https://openalex.org/C2096984","wikidata":"https://www.wikidata.org/wiki/Q245464","display_name":"Cyclic code","level":5,"score":0.35659998655319214},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.35249999165534973},{"id":"https://openalex.org/C39635130","wikidata":"https://www.wikidata.org/wiki/Q7226636","display_name":"Polynomial code","level":5,"score":0.3499999940395355},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.34540000557899475},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33079999685287476},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3172000050544739},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.3160000145435333},{"id":"https://openalex.org/C114504821","wikidata":"https://www.wikidata.org/wiki/Q2164281","display_name":"Turbo code","level":3,"score":0.3140000104904175},{"id":"https://openalex.org/C169021753","wikidata":"https://www.wikidata.org/wiki/Q201972","display_name":"Reed\u2013Muller code","level":5,"score":0.31209999322891235},{"id":"https://openalex.org/C3018063660","wikidata":"https://www.wikidata.org/wiki/Q6865448","display_name":"Minimum distance","level":2,"score":0.29919999837875366},{"id":"https://openalex.org/C87117866","wikidata":"https://www.wikidata.org/wiki/Q7683664","display_name":"Tanner graph","level":5,"score":0.29829999804496765},{"id":"https://openalex.org/C197242373","wikidata":"https://www.wikidata.org/wiki/Q5163613","display_name":"Constant-weight code","level":5,"score":0.28209999203681946},{"id":"https://openalex.org/C202932441","wikidata":"https://www.wikidata.org/wiki/Q55611017","display_name":"Forward error correction","level":3,"score":0.2522999942302704}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2011.2173244","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2011.2173244","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:0901.4129","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0901.4129","pdf_url":"https://arxiv.org/pdf/0901.4129","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:0901.4129","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0901.4129","pdf_url":"https://arxiv.org/pdf/0901.4129","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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1571565904","https://openalex.org/W1595640491","https://openalex.org/W1973712217","https://openalex.org/W1976677460","https://openalex.org/W2035309551","https://openalex.org/W2062642782","https://openalex.org/W2078633872","https://openalex.org/W2081471788","https://openalex.org/W2089745384","https://openalex.org/W2103028698","https://openalex.org/W2110148463","https://openalex.org/W2116815462","https://openalex.org/W2119017156","https://openalex.org/W2121899554","https://openalex.org/W2122065823","https://openalex.org/W2125905426","https://openalex.org/W2128037788","https://openalex.org/W2133068391","https://openalex.org/W2135573812","https://openalex.org/W2137813581","https://openalex.org/W2141836583","https://openalex.org/W2142415334","https://openalex.org/W2144758604","https://openalex.org/W2147776616","https://openalex.org/W2150368154","https://openalex.org/W2157272487","https://openalex.org/W2162381958","https://openalex.org/W2167551988","https://openalex.org/W2169134868","https://openalex.org/W4213281018","https://openalex.org/W4214522349","https://openalex.org/W4300188436","https://openalex.org/W6606175091","https://openalex.org/W6606763497","https://openalex.org/W6635197353","https://openalex.org/W6638077476"],"related_works":[],"abstract_inverted_index":{"Quasi-cyclic":[0],"(QC)":[1],"low-density":[2],"parity-check":[3],"(LDPC)":[4],"codes":[5,29,91],"are":[6,114],"an":[7],"important":[8],"instance":[9],"of":[10,26,48,53,61,84,105,138,150],"proto-graph-based":[11],"LDPC":[12,28,67],"codes.":[13,107],"In":[14,108],"this":[15],"paper":[16],"we":[17,63,95],"present":[18,64],"upper":[19,34,81,143],"bounds":[20,35],"on":[21,37],"the":[22,49,54,76,85,101,119,134,146,151,159],"minimum":[23,78,135],"Hamming":[24,79,103,136,148],"distance":[25,80,104,137,149],"QC":[27,66,90,111,140,160],"and":[30,52,92,124],"study":[31],"how":[32],"these":[33],"depend":[36],"graph":[38,51],"structure":[39],"parameters":[40],"(like":[41],"variable":[42],"degrees,":[43,46],"check":[44],"node":[45],"girth)":[47],"Tanner":[50,130],"underlying":[55],"proto-graph.":[56],"Moreover,":[57],"for":[58,100],"several":[59],"classes":[60],"proto-graphs":[62],"explicit":[65],"code":[68,112,122,141,153],"constructions":[69],"that":[70,131,133,154],"achieve":[71],"(or":[72],"come":[73],"close":[74],"to)":[75],"respective":[77],"bounds.":[82],"Because":[83],"tight":[86],"algebraic":[87],"connection":[88],"between":[89],"convolutional":[93,106,121,152],"codes,":[94],"can":[96],"state":[97],"similar":[98],"results":[99],"free":[102,147],"fact,":[109],"some":[110],"statements":[113,123],"established":[115],"by":[116,129,145,157],"first":[117],"proving":[118],"corresponding":[120],"then":[125],"using":[126],"a":[127,139],"result":[128],"says":[132],"is":[142,155],"bounded":[144],"obtained":[156],"\u201cunwrapping\u201d":[158],"code.":[161]},"counts_by_year":[{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":11},{"year":2013,"cited_by_count":11},{"year":2012,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2016-06-24T00:00:00"}