{"id":"https://openalex.org/W2121834236","doi":"https://doi.org/10.1109/isit.2011.6034185","title":"Block-triangularization of parity check matrices for efficient encoding of linear codes","display_name":"Block-triangularization of parity check matrices for efficient encoding of linear codes","publication_year":2011,"publication_date":"2011-07-01","ids":{"openalex":"https://openalex.org/W2121834236","doi":"https://doi.org/10.1109/isit.2011.6034185","mag":"2121834236"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2011.6034185","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2011.6034185","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 IEEE International Symposium on Information Theory Proceedings","raw_type":"proceedings-article"},"type":"conference-paper","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/A5110477800","display_name":"Tomoharu Shibuya","orcid":null},"institutions":[{"id":"https://openalex.org/I42999171","display_name":"Sophia University","ror":"https://ror.org/01nckkm68","country_code":"JP","type":"education","lineage":["https://openalex.org/I42999171"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Tomoharu Shibuya","raw_affiliation_strings":["Department of Information and Communication Sciences, Sophia University, Japan","Department of Information and Communication Sciences Sophia University, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Information and Communication Sciences, Sophia University, Japan","institution_ids":["https://openalex.org/I42999171"]},{"raw_affiliation_string":"Department of Information and Communication Sciences Sophia University, Japan","institution_ids":["https://openalex.org/I42999171"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5110477800"],"corresponding_institution_ids":["https://openalex.org/I42999171"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.19719377,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"533","last_page":"537"},"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":0.9983999729156494,"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":0.998199999332428,"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/parity-check-matrix","display_name":"Parity-check matrix","score":0.837792158126831},{"id":"https://openalex.org/keywords/low-density-parity-check-code","display_name":"Low-density parity-check code","score":0.7246062159538269},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.5822857618331909},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5401856303215027},{"id":"https://openalex.org/keywords/parity-bit","display_name":"Parity bit","score":0.5064917802810669},{"id":"https://openalex.org/keywords/parity","display_name":"Parity (physics)","score":0.5007853507995605},{"id":"https://openalex.org/keywords/raptor-code","display_name":"Raptor code","score":0.4954887628555298},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44901347160339355},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.44611552357673645},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.4460686445236206},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.4358947277069092},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.43451449275016785},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.418653279542923},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38353580236434937},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.377528578042984}],"concepts":[{"id":"https://openalex.org/C95925971","wikidata":"https://www.wikidata.org/wiki/Q3100414","display_name":"Parity-check matrix","level":4,"score":0.837792158126831},{"id":"https://openalex.org/C67692717","wikidata":"https://www.wikidata.org/wiki/Q187444","display_name":"Low-density parity-check code","level":3,"score":0.7246062159538269},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.5822857618331909},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5401856303215027},{"id":"https://openalex.org/C131521367","wikidata":"https://www.wikidata.org/wiki/Q625502","display_name":"Parity bit","level":2,"score":0.5064917802810669},{"id":"https://openalex.org/C2777151079","wikidata":"https://www.wikidata.org/wiki/Q141160","display_name":"Parity (physics)","level":2,"score":0.5007853507995605},{"id":"https://openalex.org/C101252705","wikidata":"https://www.wikidata.org/wiki/Q7294373","display_name":"Raptor code","level":5,"score":0.4954887628555298},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44901347160339355},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44611552357673645},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.4460686445236206},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4358947277069092},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.43451449275016785},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.418653279542923},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38353580236434937},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.377528578042984},{"id":"https://openalex.org/C109214941","wikidata":"https://www.wikidata.org/wiki/Q18334","display_name":"Particle physics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit.2011.6034185","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2011.6034185","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 IEEE International Symposium on Information Theory Proceedings","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1522351268","https://openalex.org/W1533712308","https://openalex.org/W2113498323","https://openalex.org/W2140655888","https://openalex.org/W2157145873","https://openalex.org/W3122510249"],"related_works":["https://openalex.org/W2141157615","https://openalex.org/W3105618276","https://openalex.org/W4384074457","https://openalex.org/W4247927056","https://openalex.org/W2083917443","https://openalex.org/W2164436933","https://openalex.org/W2596270314","https://openalex.org/W3045986722","https://openalex.org/W2534223869","https://openalex.org/W2100564368"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"propose":[4],"a":[5,26,32,48,55,59,70],"new":[6],"encoding":[7],"algorithm":[8,36,74],"for":[9],"linear":[10,51,78],"codes":[11,79],"whose":[12],"computational":[13],"complexity":[14,92],"is":[15,37],"O(w(H))":[16],"where":[17,93],"w(H)":[18],"denotes":[19,95],"the":[20,40,72,96],"number":[21],"of":[22,31,50,54,58],"non-zero":[23],"elements":[24],"in":[25],"parity":[27,56,60,83],"check":[28,61,84],"matrix":[29],"H":[30],"code.":[33],"The":[34],"proposed":[35,73],"based":[38],"on":[39],"block-triangularization":[41],"-":[42,53],"an":[43],"efficient":[44],"technique":[45],"to":[46],"solve":[47],"system":[49],"equations":[52],"part":[57],"matrix,":[62],"combining":[63],"additional":[64],"row":[65],"and":[66],"column":[67],"permutations.":[68],"As":[69],"result,":[71],"can":[75],"encode":[76],"any":[77],"defined":[80],"by":[81],"sparse":[82],"matrices,":[85],"such":[86],"as":[87],"LDPC":[88],"codes,":[89],"with":[90],"O(n)":[91],"n":[94],"code":[97],"length.":[98]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
