{"id":"https://openalex.org/W2241439970","doi":"https://doi.org/10.1109/jsac.2015.2504281","title":"Distance Spectrum of Fixed-Rate Raptor Codes With Linear Random Precoders","display_name":"Distance Spectrum of Fixed-Rate Raptor Codes With Linear Random Precoders","publication_year":2015,"publication_date":"2015-11-26","ids":{"openalex":"https://openalex.org/W2241439970","doi":"https://doi.org/10.1109/jsac.2015.2504281","mag":"2241439970"},"language":"en","primary_location":{"id":"doi:10.1109/jsac.2015.2504281","is_oa":false,"landing_page_url":"https://doi.org/10.1109/jsac.2015.2504281","pdf_url":null,"source":{"id":"https://openalex.org/S90422530","display_name":"IEEE Journal on Selected Areas in Communications","issn_l":"0733-8716","issn":["0733-8716","1558-0008"],"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 Journal on Selected Areas in Communications","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1511.00562","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058256371","display_name":"Francisco L\u00e1zaro","orcid":"https://orcid.org/0000-0003-0761-7700"},"institutions":[{"id":"https://openalex.org/I2898391981","display_name":"Deutsches Zentrum f\u00fcr Luft- und Raumfahrt e. V. (DLR)","ror":"https://ror.org/04bwf3e34","country_code":"DE","type":"facility","lineage":["https://openalex.org/I1305996414","https://openalex.org/I2898391981"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Francisco Lazaro","raw_affiliation_strings":["Institute of Communications and Navigation, German Aerospace Center (DLR), Muenchner Strasse 20, Wessling, Germany","Institute of Communications and Navigation German Aerospace Center (DLR), Wessling, Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Communications and Navigation, German Aerospace Center (DLR), Muenchner Strasse 20, Wessling, Germany","institution_ids":["https://openalex.org/I2898391981"]},{"raw_affiliation_string":"Institute of Communications and Navigation German Aerospace Center (DLR), Wessling, Germany","institution_ids":["https://openalex.org/I2898391981"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012790875","display_name":"Enrico Paolini","orcid":"https://orcid.org/0000-0003-0781-531X"},"institutions":[{"id":"https://openalex.org/I9360294","display_name":"University of Bologna","ror":"https://ror.org/01111rn36","country_code":"IT","type":"education","lineage":["https://openalex.org/I9360294"]},{"id":"https://openalex.org/I2801039369","display_name":"Marconi University","ror":"https://ror.org/00j0rk173","country_code":"IT","type":"education","lineage":["https://openalex.org/I2801039369"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Enrico Paolini","raw_affiliation_strings":["Department of Electrical, Electronic, and Information Engineering \u201cG. Marconi\u201d, University of Bologna, via Venezia 52, Cesena, Italy","[Department of Electrical, Electronic, and Information Engineering \u201cG. Marconi\u201d, University of Bologna, via Venezia 52, Cesena, Italy]"],"affiliations":[{"raw_affiliation_string":"Department of Electrical, Electronic, and Information Engineering \u201cG. Marconi\u201d, University of Bologna, via Venezia 52, Cesena, Italy","institution_ids":["https://openalex.org/I9360294","https://openalex.org/I2801039369"]},{"raw_affiliation_string":"[Department of Electrical, Electronic, and Information Engineering \u201cG. Marconi\u201d, University of Bologna, via Venezia 52, Cesena, Italy]","institution_ids":["https://openalex.org/I2801039369","https://openalex.org/I9360294"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023681550","display_name":"Gianluigi Liva","orcid":"https://orcid.org/0000-0001-8657-2963"},"institutions":[{"id":"https://openalex.org/I2898391981","display_name":"Deutsches Zentrum f\u00fcr Luft- und Raumfahrt e. V. (DLR)","ror":"https://ror.org/04bwf3e34","country_code":"DE","type":"facility","lineage":["https://openalex.org/I1305996414","https://openalex.org/I2898391981"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Gianluigi Liva","raw_affiliation_strings":["Institute of Communications and Navigation, German Aerospace Center (DLR), Muenchner Strasse 20, Wessling, Germany","Institute of Communications and Navigation German Aerospace Center (DLR), Wessling, Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Communications and Navigation, German Aerospace Center (DLR), Muenchner Strasse 20, Wessling, Germany","institution_ids":["https://openalex.org/I2898391981"]},{"raw_affiliation_string":"Institute of Communications and Navigation German Aerospace Center (DLR), Wessling, Germany","institution_ids":["https://openalex.org/I2898391981"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091790848","display_name":"Gerhard Bauch","orcid":"https://orcid.org/0000-0002-0050-2604"},"institutions":[{"id":"https://openalex.org/I159176309","display_name":"Universit\u00e4t Hamburg","ror":"https://ror.org/00g30e956","country_code":"DE","type":"education","lineage":["https://openalex.org/I159176309"]},{"id":"https://openalex.org/I884043246","display_name":"Hamburg University of Technology","ror":"https://ror.org/04bs1pb34","country_code":"DE","type":"education","lineage":["https://openalex.org/I884043246"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Gerhard Bauch","raw_affiliation_strings":["Institute for Telecommunication, Hamburg University of Technology, Hamburg, Germany","[Institute for Telecommunication, Hamburg University of Technology, Hamburg, Germany]"],"affiliations":[{"raw_affiliation_string":"Institute for Telecommunication, Hamburg University of Technology, Hamburg, Germany","institution_ids":["https://openalex.org/I159176309","https://openalex.org/I884043246"]},{"raw_affiliation_string":"[Institute for Telecommunication, Hamburg University of Technology, Hamburg, Germany]","institution_ids":["https://openalex.org/I159176309","https://openalex.org/I884043246"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5058256371"],"corresponding_institution_ids":["https://openalex.org/I2898391981"],"apc_list":null,"apc_paid":null,"fwci":0.33346513,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.68820439,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"34","issue":"2","first_page":"422","last_page":"436"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9977999925613403,"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":0.9911999702453613,"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":0.6085208654403687},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.5675462484359741},{"id":"https://openalex.org/keywords/raptor-code","display_name":"Raptor code","score":0.5496925711631775},{"id":"https://openalex.org/keywords/code-rate","display_name":"Code rate","score":0.5124192833900452},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.49982500076293945},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.47918379306793213},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.47565290331840515},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.47364985942840576},{"id":"https://openalex.org/keywords/degree-distribution","display_name":"Degree distribution","score":0.465383917093277},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4428390860557556},{"id":"https://openalex.org/keywords/concatenated-error-correction-code","display_name":"Concatenated error correction code","score":0.4370356798171997},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.42069560289382935},{"id":"https://openalex.org/keywords/weight-distribution","display_name":"Weight distribution","score":0.41964399814605713},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.36147063970565796},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32787004113197327},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28003111481666565},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.16761070489883423},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09908714890480042}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6085208654403687},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.5675462484359741},{"id":"https://openalex.org/C101252705","wikidata":"https://www.wikidata.org/wiki/Q7294373","display_name":"Raptor code","level":5,"score":0.5496925711631775},{"id":"https://openalex.org/C206468330","wikidata":"https://www.wikidata.org/wiki/Q834373","display_name":"Code rate","level":3,"score":0.5124192833900452},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.49982500076293945},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.47918379306793213},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.47565290331840515},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.47364985942840576},{"id":"https://openalex.org/C87414783","wikidata":"https://www.wikidata.org/wiki/Q1002603","display_name":"Degree distribution","level":3,"score":0.465383917093277},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4428390860557556},{"id":"https://openalex.org/C78944582","wikidata":"https://www.wikidata.org/wiki/Q5158264","display_name":"Concatenated error correction code","level":4,"score":0.4370356798171997},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.42069560289382935},{"id":"https://openalex.org/C25432639","wikidata":"https://www.wikidata.org/wiki/Q3711790","display_name":"Weight distribution","level":2,"score":0.41964399814605713},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.36147063970565796},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32787004113197327},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28003111481666565},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.16761070489883423},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09908714890480042},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C34947359","wikidata":"https://www.wikidata.org/wiki/Q665189","display_name":"Complex network","level":2,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1109/jsac.2015.2504281","is_oa":false,"landing_page_url":"https://doi.org/10.1109/jsac.2015.2504281","pdf_url":null,"source":{"id":"https://openalex.org/S90422530","display_name":"IEEE Journal on Selected Areas in Communications","issn_l":"0733-8716","issn":["0733-8716","1558-0008"],"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 Journal on Selected Areas in Communications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1511.00562","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1511.00562","pdf_url":"https://arxiv.org/pdf/1511.00562","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":null},{"id":"mag:2241439970","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1511.00562","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:cris.unibo.it:11585/587506","is_oa":false,"landing_page_url":"http://hdl.handle.net/11585/587506","pdf_url":null,"source":{"id":"https://openalex.org/S4306402579","display_name":"Archivio istituzionale della ricerca (Alma Mater Studiorum Universit\u00e0 di Bologna)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210117483","host_organization_name":"Istituto di Ematologia di Bologna","host_organization_lineage":["https://openalex.org/I4210117483"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:tore.tuhh.de:11420/3380","is_oa":false,"landing_page_url":"http://hdl.handle.net/11420/3380","pdf_url":null,"source":{"id":"https://openalex.org/S4306401751","display_name":"tub.dok (Hamburg University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I884043246","host_organization_name":"Hamburg University of Technology","host_organization_lineage":["https://openalex.org/I884043246"],"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"},{"id":"doi:10.48550/arxiv.1511.00562","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1511.00562","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1511.00562","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1511.00562","pdf_url":"https://arxiv.org/pdf/1511.00562","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":null},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1758521522","https://openalex.org/W1968289971","https://openalex.org/W1982675367","https://openalex.org/W2007380483","https://openalex.org/W2012642489","https://openalex.org/W2026357470","https://openalex.org/W2029712200","https://openalex.org/W2049281372","https://openalex.org/W2095882513","https://openalex.org/W2098666072","https://openalex.org/W2105095541","https://openalex.org/W2113589487","https://openalex.org/W2115104320","https://openalex.org/W2128552304","https://openalex.org/W2134499105","https://openalex.org/W2138779134","https://openalex.org/W2165573107","https://openalex.org/W2167943285","https://openalex.org/W2282968627","https://openalex.org/W2296125569","https://openalex.org/W2914980053","https://openalex.org/W4229922087","https://openalex.org/W6678839936","https://openalex.org/W6733412889","https://openalex.org/W6763237538","https://openalex.org/W6983661625"],"related_works":["https://openalex.org/W2963072837","https://openalex.org/W2171337285","https://openalex.org/W3120441823","https://openalex.org/W2728668093","https://openalex.org/W2004376844","https://openalex.org/W2984050699","https://openalex.org/W2053009450","https://openalex.org/W1667524310","https://openalex.org/W2180891895","https://openalex.org/W2913363787","https://openalex.org/W2151292122","https://openalex.org/W2955767510","https://openalex.org/W850336655","https://openalex.org/W2109773707","https://openalex.org/W1652805857","https://openalex.org/W2074784752","https://openalex.org/W2155198039","https://openalex.org/W3102111690","https://openalex.org/W2137787303","https://openalex.org/W2750886954"],"abstract_inverted_index":{"Raptor":[0,56,136,145],"code":[1,57,84,88,106],"ensembles":[2,97],"with":[3,116],"linear":[4,114],"random":[5],"outer":[6,73],"codes":[7,146],"in":[8],"a":[9,47,60,105,113],"fixed-rate":[10,55,80,144],"setting":[11],"are":[12,140],"considered.":[13],"An":[14],"expression":[15,25],"for":[16,96,143],"the":[17,30,34,54,69,72,75,78,86,101,110,117,131],"average":[18],"distance":[19,103],"spectrum":[20],"is":[21,26,42,93,154],"derived":[22],"and":[23,49,85],"this":[24,99],"used":[27,125],"to":[28,45,126],"obtain":[29],"asymptotic":[31,38],"exponent":[32],"of":[33,71,77,104,130,133],"weight":[35,158],"distribution.":[36,90,159],"The":[37,66,120],"growth":[39,115],"rate":[40,70,76],"analysis":[41],"then":[43],"exploited":[44],"develop":[46],"necessary":[48],"sufficient":[50],"condition":[51,67],"under":[52,147],"which":[53],"ensemble":[58,111],"exhibits":[59],"strictly":[61],"positive":[62],"typical":[63],"minimum":[64,102],"distance.":[65],"involves":[68],"code,":[74],"inner":[79],"Luby":[81],"Transform":[82],"(LT)":[83],"LT":[87],"degree":[89],"Additionally,":[91],"it":[92],"shown":[94],"that":[95],"fulfilling":[98],"condition,":[100],"randomly":[107],"drawn":[108],"from":[109],"has":[112],"block":[118],"length.":[119],"analytical":[121],"results":[122,139],"can":[123],"be":[124],"make":[127],"accurate":[128],"predictions":[129],"performance":[132,153],"finite":[134],"length":[135],"codes.":[137],"These":[138],"particularly":[141],"useful":[142],"maximum":[148],"likelihood":[149],"erasure":[150],"decoding,":[151],"whose":[152],"driven":[155],"by":[156],"their":[157]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}
