{"id":"https://openalex.org/W2149724392","doi":"https://doi.org/10.1109/isit.2009.5205923","title":"Analytical solution of covariance evolution for regular LDPC codes","display_name":"Analytical solution of covariance evolution for regular LDPC codes","publication_year":2009,"publication_date":"2009-06-01","ids":{"openalex":"https://openalex.org/W2149724392","doi":"https://doi.org/10.1109/isit.2009.5205923","mag":"2149724392"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2009.5205923","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2009.5205923","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE International Symposium on Information Theory","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/A5011452126","display_name":"T. Nozaki","orcid":"https://orcid.org/0000-0003-3102-5764"},"institutions":[{"id":"https://openalex.org/I114531698","display_name":"Tokyo Institute of Technology","ror":"https://ror.org/0112mx960","country_code":"JP","type":"education","lineage":["https://openalex.org/I114531698"]},{"id":"https://openalex.org/I90023481","display_name":"National Institute of Information and Communications Technology","ror":"https://ror.org/016bgq349","country_code":"JP","type":"facility","lineage":["https://openalex.org/I90023481"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Takayuki Nozaki","raw_affiliation_strings":["Department of Communications and Integrated Systems, Tokyo Institute of Technology, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Communications and Integrated Systems, Tokyo Institute of Technology, Japan","institution_ids":["https://openalex.org/I90023481","https://openalex.org/I114531698"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109351206","display_name":"Kenta Kasai","orcid":null},"institutions":[{"id":"https://openalex.org/I114531698","display_name":"Tokyo Institute of Technology","ror":"https://ror.org/0112mx960","country_code":"JP","type":"education","lineage":["https://openalex.org/I114531698"]},{"id":"https://openalex.org/I90023481","display_name":"National Institute of Information and Communications Technology","ror":"https://ror.org/016bgq349","country_code":"JP","type":"facility","lineage":["https://openalex.org/I90023481"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Kenta Kasai","raw_affiliation_strings":["Department of Communications and Integrated Systems, Tokyo Institute of Technology, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Communications and Integrated Systems, Tokyo Institute of Technology, Japan","institution_ids":["https://openalex.org/I90023481","https://openalex.org/I114531698"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109935052","display_name":"Kohichi Sakaniwa","orcid":null},"institutions":[{"id":"https://openalex.org/I114531698","display_name":"Tokyo Institute of Technology","ror":"https://ror.org/0112mx960","country_code":"JP","type":"education","lineage":["https://openalex.org/I114531698"]},{"id":"https://openalex.org/I90023481","display_name":"National Institute of Information and Communications Technology","ror":"https://ror.org/016bgq349","country_code":"JP","type":"facility","lineage":["https://openalex.org/I90023481"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Kohichi Sakaniwa","raw_affiliation_strings":["Department of Communications and Integrated Systems, Tokyo Institute of Technology, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Communications and Integrated Systems, Tokyo Institute of Technology, Japan","institution_ids":["https://openalex.org/I90023481","https://openalex.org/I114531698"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3629,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.676093,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"2649","last_page":"2653"},"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/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.9980000257492065,"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/T11130","display_name":"Coding theory and cryptography","score":0.9898999929428101,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/covariance","display_name":"Covariance","score":0.852104663848877},{"id":"https://openalex.org/keywords/covariance-function","display_name":"Covariance function","score":0.6911560297012329},{"id":"https://openalex.org/keywords/rational-quadratic-covariance-function","display_name":"Rational quadratic covariance function","score":0.6087594032287598},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5973713994026184},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.583492636680603},{"id":"https://openalex.org/keywords/mat\u00e9rn-covariance-function","display_name":"Mat\u00e9rn covariance function","score":0.5689489245414734},{"id":"https://openalex.org/keywords/covariance-intersection","display_name":"Covariance intersection","score":0.5458422899246216},{"id":"https://openalex.org/keywords/low-density-parity-check-code","display_name":"Low-density parity-check code","score":0.5297003388404846},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5282151699066162},{"id":"https://openalex.org/keywords/cma-es","display_name":"CMA-ES","score":0.4784679114818573},{"id":"https://openalex.org/keywords/differential-evolution","display_name":"Differential evolution","score":0.41237252950668335},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41191205382347107},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33201128244400024},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.22226592898368835},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.18333345651626587}],"concepts":[{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.852104663848877},{"id":"https://openalex.org/C137250428","wikidata":"https://www.wikidata.org/wiki/Q5178897","display_name":"Covariance function","level":3,"score":0.6911560297012329},{"id":"https://openalex.org/C148893098","wikidata":"https://www.wikidata.org/wiki/Q7295778","display_name":"Rational quadratic covariance function","level":5,"score":0.6087594032287598},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5973713994026184},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.583492636680603},{"id":"https://openalex.org/C118006245","wikidata":"https://www.wikidata.org/wiki/Q6792079","display_name":"Mat\u00e9rn covariance function","level":5,"score":0.5689489245414734},{"id":"https://openalex.org/C83042196","wikidata":"https://www.wikidata.org/wiki/Q5178898","display_name":"Covariance intersection","level":4,"score":0.5458422899246216},{"id":"https://openalex.org/C67692717","wikidata":"https://www.wikidata.org/wiki/Q187444","display_name":"Low-density parity-check code","level":3,"score":0.5297003388404846},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5282151699066162},{"id":"https://openalex.org/C205555498","wikidata":"https://www.wikidata.org/wiki/Q505588","display_name":"CMA-ES","level":4,"score":0.4784679114818573},{"id":"https://openalex.org/C74750220","wikidata":"https://www.wikidata.org/wiki/Q2662197","display_name":"Differential evolution","level":2,"score":0.41237252950668335},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41191205382347107},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33201128244400024},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.22226592898368835},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.18333345651626587}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/isit.2009.5205923","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2009.5205923","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE International Symposium on Information Theory","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.243.5500","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.243.5500","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0901.2838v1.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1536930200","https://openalex.org/W2029712200","https://openalex.org/W2108957380","https://openalex.org/W2127490352","https://openalex.org/W2128765501","https://openalex.org/W2165259785","https://openalex.org/W4300188436","https://openalex.org/W6684412100"],"related_works":["https://openalex.org/W2022823194","https://openalex.org/W2110484224","https://openalex.org/W2046078371","https://openalex.org/W3128703436","https://openalex.org/W4315750325","https://openalex.org/W341081156","https://openalex.org/W2104432942","https://openalex.org/W2051502961","https://openalex.org/W3103531085","https://openalex.org/W2554071524"],"abstract_inverted_index":{"The":[0],"covariance":[1,13,29,68,80],"evolution":[2],"is":[3],"a":[4],"system":[5],"of":[6,14,17,23,35,38,41,78],"differential":[7],"equations":[8],"with":[9],"respect":[10],"to":[11,20,48,62,65],"the":[12,15,21,28,36,50,67,75,79],"number":[16,37],"edges":[18],"connecting":[19],"nodes":[22,40],"each":[24],"residual":[25,42],"degree.":[26],"Solving":[27],"evolution,":[30],"we":[31,73],"can":[32],"derive":[33],"distributions":[34],"check":[39],"degree":[43],"1,":[44],"which":[45],"helps":[46],"us":[47],"estimate":[49],"block":[51],"error":[52],"probability":[53],"for":[54],"finite-length":[55],"LDPC":[56],"code.":[57],"Amraoui":[58],"et":[59],"al.":[60],"resorted":[61],"numerical":[63],"computations":[64],"solve":[66],"evolution.":[69,81],"In":[70],"this":[71],"paper,":[72],"give":[74],"analytical":[76],"solution":[77]},"counts_by_year":[{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
