{"id":"https://openalex.org/W2164828669","doi":"https://doi.org/10.1109/tcomm.2014.2316174","title":"Low-Complexity Encoding of Quasi-Cyclic Codes Based on Galois Fourier Transform","display_name":"Low-Complexity Encoding of Quasi-Cyclic Codes Based on Galois Fourier Transform","publication_year":2014,"publication_date":"2014-04-08","ids":{"openalex":"https://openalex.org/W2164828669","doi":"https://doi.org/10.1109/tcomm.2014.2316174","mag":"2164828669"},"language":"en","primary_location":{"id":"doi:10.1109/tcomm.2014.2316174","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcomm.2014.2316174","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/A5013594198","display_name":"Qin Huang","orcid":"https://orcid.org/0000-0003-1621-6984"},"institutions":[{"id":"https://openalex.org/I194716290","display_name":"China Academy of Space Technology","ror":"https://ror.org/025397a59","country_code":"CN","type":"government","lineage":["https://openalex.org/I194716290","https://openalex.org/I2802615301"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qin Huang","raw_affiliation_strings":["School of Electronic and Information Engineering, China Academy of Space Technology, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electronic and Information Engineering, China Academy of Space Technology, Beijing, China","institution_ids":["https://openalex.org/I194716290"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074466108","display_name":"Li Tang","orcid":"https://orcid.org/0000-0003-0796-3160"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li Tang","raw_affiliation_strings":["School of Electronic and Information Engineering, Beihang University, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electronic and Information Engineering, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102295943","display_name":"Shanbao He","orcid":null},"institutions":[{"id":"https://openalex.org/I194716290","display_name":"China Academy of Space Technology","ror":"https://ror.org/025397a59","country_code":"CN","type":"government","lineage":["https://openalex.org/I194716290","https://openalex.org/I2802615301"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shanbao He","raw_affiliation_strings":["China Academy of Space Technology, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"China Academy of Space Technology, Beijing, China","institution_ids":["https://openalex.org/I194716290"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058154161","display_name":"Zixiang Xiong","orcid":"https://orcid.org/0000-0002-4714-3311"},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zixiang Xiong","raw_affiliation_strings":["Department of Electrical and Computer Engineering (ECE), Texas A&M University, College Station, TX, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering (ECE), Texas A&M University, College Station, TX, USA","institution_ids":["https://openalex.org/I91045830"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103046319","display_name":"Zulin Wang","orcid":"https://orcid.org/0000-0002-1328-7739"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zulin Wang","raw_affiliation_strings":["School of Electronic and Information Engineering, Beihang University, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electronic and Information Engineering, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.8694,"has_fulltext":false,"cited_by_count":55,"citation_normalized_percentile":{"value":0.97455805,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"62","issue":"6","first_page":"1757","last_page":"1767"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":0.9994000196456909,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/encoding","display_name":"Encoding (memory)","score":0.5437596440315247},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.5063673257827759},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4939616322517395},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.48473212122917175},{"id":"https://openalex.org/keywords/cyclic-code","display_name":"Cyclic code","score":0.4555148482322693},{"id":"https://openalex.org/keywords/galois-theory","display_name":"Galois theory","score":0.440085232257843},{"id":"https://openalex.org/keywords/discrete-fourier-transform","display_name":"Discrete Fourier transform (general)","score":0.419376939535141},{"id":"https://openalex.org/keywords/electronic-engineering","display_name":"Electronic engineering","score":0.37777066230773926},{"id":"https://openalex.org/keywords/concatenated-error-correction-code","display_name":"Concatenated error correction code","score":0.3736010789871216},{"id":"https://openalex.org/keywords/fractional-fourier-transform","display_name":"Fractional Fourier transform","score":0.3364117443561554},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.33003753423690796},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.29880839586257935},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2506028413772583},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.22853931784629822},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.15379923582077026},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.1263364553451538}],"concepts":[{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.5437596440315247},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.5063673257827759},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4939616322517395},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.48473212122917175},{"id":"https://openalex.org/C2096984","wikidata":"https://www.wikidata.org/wiki/Q245464","display_name":"Cyclic code","level":5,"score":0.4555148482322693},{"id":"https://openalex.org/C94398972","wikidata":"https://www.wikidata.org/wiki/Q92552","display_name":"Galois theory","level":2,"score":0.440085232257843},{"id":"https://openalex.org/C57733114","wikidata":"https://www.wikidata.org/wiki/Q1006032","display_name":"Discrete Fourier transform (general)","level":5,"score":0.419376939535141},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.37777066230773926},{"id":"https://openalex.org/C78944582","wikidata":"https://www.wikidata.org/wiki/Q5158264","display_name":"Concatenated error correction code","level":4,"score":0.3736010789871216},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.3364117443561554},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33003753423690796},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.29880839586257935},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2506028413772583},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.22853931784629822},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.15379923582077026},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.1263364553451538},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcomm.2014.2316174","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcomm.2014.2316174","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1453384114","display_name":null,"funder_award_id":"61231010","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2000742852","display_name":null,"funder_award_id":"61071070","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6322998825","display_name":null,"funder_award_id":"61201156","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7057091296","display_name":null,"funder_award_id":"61128002","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1593683169","https://openalex.org/W1770324186","https://openalex.org/W1969813053","https://openalex.org/W1997785613","https://openalex.org/W2008285919","https://openalex.org/W2017385815","https://openalex.org/W2024577968","https://openalex.org/W2039551368","https://openalex.org/W2062642782","https://openalex.org/W2069159122","https://openalex.org/W2081471788","https://openalex.org/W2099727759","https://openalex.org/W2109419341","https://openalex.org/W2113420173","https://openalex.org/W2123673731","https://openalex.org/W2128765501","https://openalex.org/W2129172904","https://openalex.org/W2138404167","https://openalex.org/W2147776616","https://openalex.org/W2150802958","https://openalex.org/W2155469840","https://openalex.org/W2157702143","https://openalex.org/W2159608595","https://openalex.org/W2164601298","https://openalex.org/W2168164928","https://openalex.org/W2895239415","https://openalex.org/W2951935814","https://openalex.org/W3101367291","https://openalex.org/W4239889878"],"related_works":["https://openalex.org/W1992338304","https://openalex.org/W2374517516","https://openalex.org/W1515861990","https://openalex.org/W2153873646","https://openalex.org/W2374649290","https://openalex.org/W2095636570","https://openalex.org/W2359558539","https://openalex.org/W2500293854","https://openalex.org/W2765334632","https://openalex.org/W2023715853"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"two":[3],"novel":[4],"low-complexity":[5],"encoding":[6,39,53,62,74],"algorithms":[7],"for":[8,73,117],"quasi-cyclic":[9],"(QC)":[10],"codes":[11,103,120],"based":[12],"on":[13],"Galois":[14,41,55,96],"Fourier":[15,42,56],"transform.":[16,57],"The":[17,35,58],"key":[18],"idea":[19],"behind":[20],"them":[21],"is":[22,44,104],"making":[23],"use":[24],"of":[25,30,50,83,95,114],"the":[26,31,47,51,64,80,84,111,115],"block":[27],"diagonal":[28],"structure":[29],"transformed":[32],"generator":[33],"matrix.":[34],"first":[36,81,85],"one,":[37,60],"named":[38,61],"by":[40,54,125],"transform,":[43],"equivalent":[45],"to":[46,90,101],"fast":[48],"implementations":[49],"traditional":[52],"second":[59],"in":[63,107],"transform":[65],"domain":[66],"(ETD),":[67],"requires":[68],"much":[69],"less":[70],"computational":[71],"complexity":[72],"binary":[75],"QC":[76],"codes.":[77],"It":[78],"skips":[79],"step":[82],"algorithm":[86],"and":[87],"applies":[88],"post-processing":[89],"save":[91],"a":[92],"large":[93],"number":[94],"field":[97],"multiplications.":[98],"Its":[99],"application":[100],"QC-LDPC":[102],"also":[105],"studied":[106],"this":[108],"paper.":[109],"Particularly,":[110],"hardware":[112],"cost":[113],"ETD":[116],"RS-based":[118],"LDPC":[119],"can":[121],"be":[122],"greatly":[123],"reduced":[124],"short":[126],"linear-feedback":[127],"shift":[128],"registers.":[129]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}