{"id":"https://openalex.org/W2907468218","doi":"https://doi.org/10.1109/tcomm.2018.2890251","title":"Additive, Structural, and Multiplicative Transformations for the Construction of Quasi-Cyclic LDPC Matrices","display_name":"Additive, Structural, and Multiplicative Transformations for the Construction of Quasi-Cyclic LDPC Matrices","publication_year":2018,"publication_date":"2018-12-28","ids":{"openalex":"https://openalex.org/W2907468218","doi":"https://doi.org/10.1109/tcomm.2018.2890251","mag":"2907468218"},"language":"en","primary_location":{"id":"doi:10.1109/tcomm.2018.2890251","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcomm.2018.2890251","pdf_url":null,"source":{"id":"https://openalex.org/S196647941","display_name":"IEEE Transactions on Communications","issn_l":"0090-6778","issn":["0090-6778","1558-0857"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310316002","host_organization_name":"IEEE Communications Society","host_organization_lineage":["https://openalex.org/P4310316002","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Communications Society","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 Communications","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/A5055069847","display_name":"Alban Derrien","orcid":"https://orcid.org/0000-0001-8406-3487"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I161929037","display_name":"Universit\u00e9 de Bretagne Occidentale","ror":"https://ror.org/01b8h3982","country_code":"FR","type":"education","lineage":["https://openalex.org/I161929037"]},{"id":"https://openalex.org/I2802204017","display_name":"Universit\u00e9 de Bretagne Sud","ror":"https://ror.org/04ed7fw48","country_code":"FR","type":"education","lineage":["https://openalex.org/I2802204017"]},{"id":"https://openalex.org/I4210123702","display_name":"Laboratoire des Sciences et Techniques de l\u2019Information de la Communication et de la Connaissance","ror":"https://ror.org/0266kfd37","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I180375564","https://openalex.org/I201181511","https://openalex.org/I205703379","https://openalex.org/I2802204017","https://openalex.org/I4210123702","https://openalex.org/I4210127572","https://openalex.org/I4210145102","https://openalex.org/I4210148559","https://openalex.org/I4210159245","https://openalex.org/I4405260085"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Alban Derrien","raw_affiliation_strings":["Universit\u00e9 de Bretagne-Sud Lab-STICC, UMR 6285 CNRS, Lorient, France","UBS Lorient - Universit\u00e9 de Bretagne Sud - Lorient (Universit\u00e9 de Bretagne Sud - Centre Kerneur - BP92116 - 56321 Lorient Cedex - France)"],"raw_orcid":"https://orcid.org/0000-0001-8406-3487","affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Bretagne-Sud Lab-STICC, UMR 6285 CNRS, Lorient, France","institution_ids":["https://openalex.org/I2802204017","https://openalex.org/I1294671590","https://openalex.org/I161929037","https://openalex.org/I4210123702"]},{"raw_affiliation_string":"UBS Lorient - Universit\u00e9 de Bretagne Sud - Lorient (Universit\u00e9 de Bretagne Sud - Centre Kerneur - BP92116 - 56321 Lorient Cedex - France)","institution_ids":["https://openalex.org/I2802204017"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054060190","display_name":"Emmanuel Boutillon","orcid":"https://orcid.org/0000-0003-2124-0786"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I161929037","display_name":"Universit\u00e9 de Bretagne Occidentale","ror":"https://ror.org/01b8h3982","country_code":"FR","type":"education","lineage":["https://openalex.org/I161929037"]},{"id":"https://openalex.org/I2802204017","display_name":"Universit\u00e9 de Bretagne Sud","ror":"https://ror.org/04ed7fw48","country_code":"FR","type":"education","lineage":["https://openalex.org/I2802204017"]},{"id":"https://openalex.org/I4210123702","display_name":"Laboratoire des Sciences et Techniques de l\u2019Information de la Communication et de la Connaissance","ror":"https://ror.org/0266kfd37","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I180375564","https://openalex.org/I201181511","https://openalex.org/I205703379","https://openalex.org/I2802204017","https://openalex.org/I4210123702","https://openalex.org/I4210127572","https://openalex.org/I4210145102","https://openalex.org/I4210148559","https://openalex.org/I4210159245","https://openalex.org/I4405260085"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Emmanuel Boutillon","raw_affiliation_strings":["Universit\u00e9 de Bretagne-Sud Lab-STICC, UMR 6285 CNRS, Lorient, France","UBS - Universit\u00e9 de Bretagne Sud (BP 92116 - 56321 Lorient cedex - France)","Lab-STICC_UBS_CACS_IAS (France)"],"raw_orcid":"https://orcid.org/0000-0003-2124-0786","affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Bretagne-Sud Lab-STICC, UMR 6285 CNRS, Lorient, France","institution_ids":["https://openalex.org/I2802204017","https://openalex.org/I1294671590","https://openalex.org/I161929037","https://openalex.org/I4210123702"]},{"raw_affiliation_string":"UBS - Universit\u00e9 de Bretagne Sud (BP 92116 - 56321 Lorient cedex - France)","institution_ids":["https://openalex.org/I2802204017"]},{"raw_affiliation_string":"Lab-STICC_UBS_CACS_IAS (France)","institution_ids":["https://openalex.org/I161929037"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064937378","display_name":"Audrey Cerqueus","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I3019848993","display_name":"Mines Saint-\u00c9tienne","ror":"https://ror.org/05a1dws80","country_code":"FR","type":"education","lineage":["https://openalex.org/I203339264","https://openalex.org/I205703379","https://openalex.org/I3019848993"]},{"id":"https://openalex.org/I4210099416","display_name":"Laboratoire d'Informatique, de Mod\u00e9lisation et d'Optimisation des Syst\u00e8mes","ror":"https://ror.org/00t3fpp34","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I198244214","https://openalex.org/I198244214","https://openalex.org/I203339264","https://openalex.org/I205703379","https://openalex.org/I3019848993","https://openalex.org/I4210099416","https://openalex.org/I4210123221","https://openalex.org/I4210159245","https://openalex.org/I4387154249"]},{"id":"https://openalex.org/I4210103002","display_name":"University of Clermont Auvergne","ror":null,"country_code":"FR","type":null,"lineage":["https://openalex.org/I4210103002"]},{"id":"https://openalex.org/I4210134356","display_name":"Laboratoire G\u00e9nie Industriel","ror":"https://ror.org/0455wwj08","country_code":"FR","type":"facility","lineage":["https://openalex.org/I277688954","https://openalex.org/I277688954","https://openalex.org/I4210107720","https://openalex.org/I4210134356"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Audrey Cerqueus","raw_affiliation_strings":["Mines Saint-Etienne, Institut Henri Fayol, Universit\u00e9 Clermont Auvergne, CNRS, UMR 6158 LIMOS, Saint-Etienne, France","Mines Saint-\u00c9tienne MSE - \u00c9cole des Mines de Saint-\u00c9tienne (158, Cours Fauriel - 42023 Saint \u00c9tienne cedex 2 - France)","LIMOS - Laboratoire d'Informatique, de Mod\u00e9lisation et d'Optimisation des Syst\u00e8mes (Campus Universitaire des C\u00e9zeaux, 1 rue de la Chebarde, TSA 60125 / CS 60026, 63178 Aubi\u00e8re Cedex - France)","FAYOL-ENSMSE - D\u00e9partement G\u00e9nie math\u00e9matique et industriel (France)","FAYOL-ENSMSE - Institut Henri Fayol (158 cours Fauriel 42023 Saint-Etienne Cedex 2 - France)"],"raw_orcid":"https://orcid.org/0000-0003-0430-5971","affiliations":[{"raw_affiliation_string":"Mines Saint-Etienne, Institut Henri Fayol, Universit\u00e9 Clermont Auvergne, CNRS, UMR 6158 LIMOS, Saint-Etienne, France","institution_ids":["https://openalex.org/I3019848993","https://openalex.org/I4210103002","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"Mines Saint-\u00c9tienne MSE - \u00c9cole des Mines de Saint-\u00c9tienne (158, Cours Fauriel - 42023 Saint \u00c9tienne cedex 2 - France)","institution_ids":["https://openalex.org/I3019848993"]},{"raw_affiliation_string":"LIMOS - Laboratoire d'Informatique, de Mod\u00e9lisation et d'Optimisation des Syst\u00e8mes (Campus Universitaire des C\u00e9zeaux, 1 rue de la Chebarde, TSA 60125 / CS 60026, 63178 Aubi\u00e8re Cedex - France)","institution_ids":["https://openalex.org/I4210099416"]},{"raw_affiliation_string":"FAYOL-ENSMSE - D\u00e9partement G\u00e9nie math\u00e9matique et industriel (France)","institution_ids":["https://openalex.org/I4210134356","https://openalex.org/I3019848993"]},{"raw_affiliation_string":"FAYOL-ENSMSE - Institut Henri Fayol (158 cours Fauriel 42023 Saint-Etienne Cedex 2 - France)","institution_ids":["https://openalex.org/I3019848993"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5055069847"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I161929037","https://openalex.org/I2802204017","https://openalex.org/I4210123702"],"apc_list":null,"apc_paid":null,"fwci":0.7817,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.77183611,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"67","issue":"4","first_page":"2647","last_page":"2659"},"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":0.9972000122070312,"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":0.9886000156402588,"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/mathematics","display_name":"Mathematics","score":0.7582398653030396},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.7145066261291504},{"id":"https://openalex.org/keywords/low-density-parity-check-code","display_name":"Low-density parity-check code","score":0.5302947163581848},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5239118337631226},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.48367413878440857},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45838919281959534},{"id":"https://openalex.org/keywords/row","display_name":"Row","score":0.4411366581916809},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.41198021173477173},{"id":"https://openalex.org/keywords/equivalence-class","display_name":"Equivalence class (music)","score":0.4119721055030823},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.27785763144493103},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1564241349697113},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.13750669360160828}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7582398653030396},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.7145066261291504},{"id":"https://openalex.org/C67692717","wikidata":"https://www.wikidata.org/wiki/Q187444","display_name":"Low-density parity-check code","level":3,"score":0.5302947163581848},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5239118337631226},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.48367413878440857},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45838919281959534},{"id":"https://openalex.org/C135598885","wikidata":"https://www.wikidata.org/wiki/Q1366302","display_name":"Row","level":2,"score":0.4411366581916809},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.41198021173477173},{"id":"https://openalex.org/C2777044963","wikidata":"https://www.wikidata.org/wiki/Q5384707","display_name":"Equivalence class (music)","level":2,"score":0.4119721055030823},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27785763144493103},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1564241349697113},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.13750669360160828},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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":2,"locations":[{"id":"doi:10.1109/tcomm.2018.2890251","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcomm.2018.2890251","pdf_url":null,"source":{"id":"https://openalex.org/S196647941","display_name":"IEEE Transactions on Communications","issn_l":"0090-6778","issn":["0090-6778","1558-0857"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310316002","host_organization_name":"IEEE Communications Society","host_organization_lineage":["https://openalex.org/P4310316002","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Communications Society","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 Communications","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-01950474v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01950474","pdf_url":null,"source":{"id":"https://openalex.org/S4406922466","display_name":"SPIRE - Sciences Po Institutional REpository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Communications, 2019, 67 (4), pp.2647-2659. ⟨10.1109/TCOMM.2018.2890251⟩","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W91277888","https://openalex.org/W1673950838","https://openalex.org/W1715756787","https://openalex.org/W1966872244","https://openalex.org/W1968066836","https://openalex.org/W1973712217","https://openalex.org/W1988881747","https://openalex.org/W2015684392","https://openalex.org/W2024327134","https://openalex.org/W2073843305","https://openalex.org/W2083406405","https://openalex.org/W2119604283","https://openalex.org/W2128037788","https://openalex.org/W2128765501","https://openalex.org/W2136923821","https://openalex.org/W2137813581","https://openalex.org/W2141836583","https://openalex.org/W2143965786","https://openalex.org/W2144758604","https://openalex.org/W2156938362","https://openalex.org/W2157702143","https://openalex.org/W2166527432","https://openalex.org/W2166978909","https://openalex.org/W2167551988","https://openalex.org/W2173776306","https://openalex.org/W2299446443","https://openalex.org/W2531628009","https://openalex.org/W2535754933","https://openalex.org/W2564319974","https://openalex.org/W2781575254","https://openalex.org/W3098602947","https://openalex.org/W4232891256","https://openalex.org/W4256648168","https://openalex.org/W6603727012","https://openalex.org/W6681292908"],"related_works":["https://openalex.org/W2903058006","https://openalex.org/W2102374550","https://openalex.org/W2047069332","https://openalex.org/W2352157218","https://openalex.org/W4213381250","https://openalex.org/W2806845321","https://openalex.org/W4293418541","https://openalex.org/W2393084694","https://openalex.org/W4281971614","https://openalex.org/W2336709242"],"abstract_inverted_index":{"The":[0,40,75,84],"construction":[1],"of":[2,46,71,77,97,106,132,164,171,179,197],"a":[3,21,94,103,149,161,182,186],"quasi-cyclic":[4],"low":[5],"density":[6],"parity-check":[7],"(QC-LDPC)":[8],"matrix":[9,23,66],"is":[10,24,57,82,112,192],"usually":[11],"carried":[12],"out":[13],"in":[14,63,194],"two":[15],"steps.":[16],"In":[17,114],"the":[18,44,47,64,69,72,98,109,124,157,169,176,198,202],"first":[19],"step,":[20],"prototype":[22,48,65],"defined":[25],"according":[26],"to":[27,59,68,92,174,200],"certain":[28],"criteria":[29],"(size,":[30],"girth,":[31],"check":[32],"and":[33,37,138,144,185],"variable":[34],"node":[35],"degrees,":[36],"so":[38],"on).":[39],"second":[41],"step":[42],"involves":[43],"expansion":[45,188],"matrix.":[49,74],"During":[50],"this":[51,115],"last":[52],"phase,":[53],"an":[54,119],"integer":[55,80],"value":[56],"assigned":[58],"each":[60],"non-null":[61],"position":[62],"corresponding":[67],"right-rotation":[70],"identity":[73],"problem":[76],"determining":[78],"these":[79],"values":[81,107],"complex.":[83],"state-of-the-art":[85],"solutions":[86,180],"use":[87,168],"either":[88],"some":[89],"mathematical":[90],"constructions":[91],"guarantee":[93],"given":[95,183,187],"girth":[96,111,184],"final":[99],"QC-LDPC":[100],"code,":[101],"or":[102],"random":[104],"search":[105,125,158],"until":[108],"target":[110],"satisfied.":[113],"paper,":[116],"we":[117,167],"propose":[118],"alternative/complementary":[120],"method":[121],"that":[122],"reduces":[123],"space":[126,159],"by":[127,160],"defining":[128],"large":[129],"equivalence":[130,153],"classes":[131],"topologically":[133],"identical":[134],"matrices":[135],"through":[136],"row":[137],"column":[139],"permutations":[140],"using":[141],"additive,":[142],"structural,":[143],"multiplicative":[145],"transformations.":[146],"Selecting":[147],"only":[148],"single":[150],"element":[151],"per":[152],"class":[154],"can":[155],"reduce":[156],"few":[162],"orders":[163],"magnitude.":[165],"Then,":[166],"formalism":[170],"constraint":[172],"programming":[173],"list":[175],"exhaustive":[177],"sets":[178],"for":[181],"factor.":[189],"An":[190],"example":[191],"presented":[193],"all":[195],"sections":[196],"paper":[199],"illustrate":[201],"methodology.":[203]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}