{"id":"https://openalex.org/W2132963830","doi":"https://doi.org/10.1109/isit.2012.6284128","title":"On the girth of quasi cyclic protograph LDPC codes","display_name":"On the girth of quasi cyclic protograph LDPC codes","publication_year":2012,"publication_date":"2012-07-01","ids":{"openalex":"https://openalex.org/W2132963830","doi":"https://doi.org/10.1109/isit.2012.6284128","mag":"2132963830"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2012.6284128","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2012.6284128","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE International Symposium on Information Theory Proceedings","raw_type":"proceedings-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/A5076209108","display_name":"Mohammad M. Karimi","orcid":"https://orcid.org/0000-0001-5017-1252"},"institutions":[{"id":"https://openalex.org/I67031392","display_name":"Carleton University","ror":"https://ror.org/02qtvee93","country_code":"CA","type":"education","lineage":["https://openalex.org/I67031392"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Mehdi Karimi","raw_affiliation_strings":["Department of Systems and Computer Engineering, Carleton University, Ottawa, ONT, Canada","Dept. of Systems and Computer Eng., Carleton University, Ottawa, Ontario, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Systems and Computer Engineering, Carleton University, Ottawa, ONT, Canada","institution_ids":["https://openalex.org/I67031392"]},{"raw_affiliation_string":"Dept. of Systems and Computer Eng., Carleton University, Ottawa, Ontario, Canada","institution_ids":["https://openalex.org/I67031392"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046274917","display_name":"Amir H. Banihashemi","orcid":"https://orcid.org/0000-0003-0685-5256"},"institutions":[{"id":"https://openalex.org/I67031392","display_name":"Carleton University","ror":"https://ror.org/02qtvee93","country_code":"CA","type":"education","lineage":["https://openalex.org/I67031392"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Amir H. Banihashemi","raw_affiliation_strings":["Department of Systems and Computer Engineering, Carleton University, Ottawa, ONT, Canada","Dept. of Systems and Computer Eng., Carleton University, Ottawa, Ontario, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Systems and Computer Engineering, Carleton University, Ottawa, ONT, Canada","institution_ids":["https://openalex.org/I67031392"]},{"raw_affiliation_string":"Dept. of Systems and Computer Eng., Carleton University, Ottawa, Ontario, Canada","institution_ids":["https://openalex.org/I67031392"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5076209108"],"corresponding_institution_ids":["https://openalex.org/I67031392"],"apc_list":null,"apc_paid":null,"fwci":1.4184,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.83638185,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"1","issue":null,"first_page":"3078","last_page":"3082"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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/T12029","display_name":"DNA and Biological Computing","score":0.9902999997138977,"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"}},{"id":"https://openalex.org/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.9876000285148621,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/girth","display_name":"Girth (graph theory)","score":0.809503436088562},{"id":"https://openalex.org/keywords/low-density-parity-check-code","display_name":"Low-density parity-check code","score":0.7696714401245117},{"id":"https://openalex.org/keywords/tanner-graph","display_name":"Tanner graph","score":0.660293459892273},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6105037927627563},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5605719089508057},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5320758819580078},{"id":"https://openalex.org/keywords/base","display_name":"Base (topology)","score":0.5176637768745422},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5120623707771301},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5060016512870789},{"id":"https://openalex.org/keywords/odd-graph","display_name":"Odd graph","score":0.412160187959671},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.22943910956382751},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22464364767074585},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.21115097403526306},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.11976051330566406},{"id":"https://openalex.org/keywords/error-floor","display_name":"Error floor","score":0.10241159796714783}],"concepts":[{"id":"https://openalex.org/C2777434295","wikidata":"https://www.wikidata.org/wiki/Q959831","display_name":"Girth (graph theory)","level":2,"score":0.809503436088562},{"id":"https://openalex.org/C67692717","wikidata":"https://www.wikidata.org/wiki/Q187444","display_name":"Low-density parity-check code","level":3,"score":0.7696714401245117},{"id":"https://openalex.org/C87117866","wikidata":"https://www.wikidata.org/wiki/Q7683664","display_name":"Tanner graph","level":5,"score":0.660293459892273},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6105037927627563},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5605719089508057},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5320758819580078},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.5176637768745422},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5120623707771301},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5060016512870789},{"id":"https://openalex.org/C206815938","wikidata":"https://www.wikidata.org/wiki/Q7077445","display_name":"Odd graph","level":5,"score":0.412160187959671},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.22943910956382751},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22464364767074585},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.21115097403526306},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.11976051330566406},{"id":"https://openalex.org/C46462455","wikidata":"https://www.wikidata.org/wiki/Q5395712","display_name":"Error floor","level":4,"score":0.10241159796714783},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit.2012.6284128","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2012.6284128","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE International Symposium on Information Theory Proceedings","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":27,"referenced_works":["https://openalex.org/W152471750","https://openalex.org/W1558273801","https://openalex.org/W1568741201","https://openalex.org/W1813544306","https://openalex.org/W1973712217","https://openalex.org/W2042258047","https://openalex.org/W2071304218","https://openalex.org/W2107621627","https://openalex.org/W2107804146","https://openalex.org/W2109383536","https://openalex.org/W2114223390","https://openalex.org/W2117904894","https://openalex.org/W2119017156","https://openalex.org/W2127221638","https://openalex.org/W2128037788","https://openalex.org/W2128765501","https://openalex.org/W2137401802","https://openalex.org/W2143965786","https://openalex.org/W2152165958","https://openalex.org/W2313149118","https://openalex.org/W2963637485","https://openalex.org/W4285719527","https://openalex.org/W6606175091","https://openalex.org/W6633921854","https://openalex.org/W6638490971","https://openalex.org/W6680601974","https://openalex.org/W6698232065"],"related_works":["https://openalex.org/W2150639697","https://openalex.org/W2602611185","https://openalex.org/W3212819824","https://openalex.org/W3167562836","https://openalex.org/W4297803167","https://openalex.org/W2143011401","https://openalex.org/W4287029234","https://openalex.org/W2119604283","https://openalex.org/W2108474025","https://openalex.org/W2132963830"],"abstract_inverted_index":{"In":[0],"this":[1,88],"paper,":[2],"we":[3,58],"study":[4],"the":[5,8,11,28,32,35,38,42,64,67,81,125],"relationships":[6],"between":[7],"girth":[9,65],"of":[10,14,37,66],"Tanner":[12],"graph":[13,52],"a":[15,46,49,54,100,108],"quasi":[16],"cyclic":[17],"(QC)":[18],"protograph":[19],"low-density":[20],"parity-check":[21],"(LDPC)":[22],"code,":[23],"on":[24,41,63],"one":[25],"hand,":[26],"and":[27,31,34,53],"lifting":[29,56,97],"degree":[30,98],"size":[33],"structure":[36],"base":[39,51,102,119,126],"graph,":[40,103],"other":[43],"hand.":[44],"As":[45],"result,":[47],"for":[48,99],"given":[50,55,101],"degree,":[57],"derive":[59],"an":[60,95],"upper":[61,73],"bound":[62],"resulting":[68],"lifted":[69],"graphs":[70],"(codes).":[71],"The":[72,84],"bounds":[74],"derived":[75],"here":[76],"are":[77],"generally":[78],"tighter":[79],"than":[80],"existing":[82],"bounds.":[83],"results":[85],"presented":[86],"in":[87,104,116],"work":[89],"can":[90],"be":[91],"used":[92],"to":[93,106,112,122],"select":[94,124],"appropriate":[96],"order":[105],"have":[107],"desired":[109],"girth,":[110],"or":[111,121],"provide":[113],"some":[114],"insight":[115],"designing":[117],"good":[118],"graphs,":[120],"properly":[123],"graph's":[127],"edge":[128],"permutations.":[129]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2013,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}