{"id":"https://openalex.org/W2017385815","doi":"https://doi.org/10.1109/isit.2012.6284127","title":"Low-density arrays of circulant matrices: Rank and row-redundancy, and QC-LDPC codes","display_name":"Low-density arrays of circulant matrices: Rank and row-redundancy, and QC-LDPC codes","publication_year":2012,"publication_date":"2012-07-01","ids":{"openalex":"https://openalex.org/W2017385815","doi":"https://doi.org/10.1109/isit.2012.6284127","mag":"2017385815"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2012.6284127","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2012.6284127","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE International Symposium on Information Theory Proceedings","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/A5013594198","display_name":"Qin Huang","orcid":"https://orcid.org/0000-0003-1621-6984"},"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":true,"raw_author_name":"Qin Huang","raw_affiliation_strings":["School of Electronic and Information Engineering, Beihang University, Beijing, China","School of Electronic and Information Engineering  Beihang University  Beijing 100191  China"],"affiliations":[{"raw_affiliation_string":"School of Electronic and Information Engineering, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]},{"raw_affiliation_string":"School of Electronic and Information Engineering  Beihang University  Beijing 100191  China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101690383","display_name":"Keke Liu","orcid":"https://orcid.org/0000-0003-3969-8808"},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Keke Liu","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of California, Davis, CA, USA","Department of Electrical and Computer Engineering, University of California, Davis; CA 95616 USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of California, Davis, CA, USA","institution_ids":["https://openalex.org/I84218800"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of California, Davis; CA 95616 USA","institution_ids":["https://openalex.org/I84218800"]}]},{"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","School of Electronic and Information Engineering  Beihang University  Beijing 100191  China"],"affiliations":[{"raw_affiliation_string":"School of Electronic and Information Engineering, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]},{"raw_affiliation_string":"School of Electronic and Information Engineering  Beihang University  Beijing 100191  China","institution_ids":["https://openalex.org/I82880672"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5013594198"],"corresponding_institution_ids":["https://openalex.org/I82880672"],"apc_list":null,"apc_paid":null,"fwci":1.4184,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.82121931,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"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":0.9997000098228455,"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":0.9997000098228455,"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/low-density-parity-check-code","display_name":"Low-density parity-check code","score":0.7693502902984619},{"id":"https://openalex.org/keywords/redundancy","display_name":"Redundancy (engineering)","score":0.6617668271064758},{"id":"https://openalex.org/keywords/circulant-matrix","display_name":"Circulant matrix","score":0.6477633714675903},{"id":"https://openalex.org/keywords/hadamard-transform","display_name":"Hadamard transform","score":0.5800396203994751},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4977474510669708},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.4916685223579407},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3890479505062103},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37836509943008423},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37414175271987915},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.29262471199035645}],"concepts":[{"id":"https://openalex.org/C67692717","wikidata":"https://www.wikidata.org/wiki/Q187444","display_name":"Low-density parity-check code","level":3,"score":0.7693502902984619},{"id":"https://openalex.org/C152124472","wikidata":"https://www.wikidata.org/wiki/Q1204361","display_name":"Redundancy (engineering)","level":2,"score":0.6617668271064758},{"id":"https://openalex.org/C115973184","wikidata":"https://www.wikidata.org/wiki/Q245457","display_name":"Circulant matrix","level":2,"score":0.6477633714675903},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.5800396203994751},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4977474510669708},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.4916685223579407},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3890479505062103},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37836509943008423},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37414175271987915},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.29262471199035645},{"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit.2012.6284127","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2012.6284127","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE International Symposium on Information Theory Proceedings","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"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":14,"referenced_works":["https://openalex.org/W1593683169","https://openalex.org/W1964402820","https://openalex.org/W1969813053","https://openalex.org/W1990436563","https://openalex.org/W2017385815","https://openalex.org/W2113420173","https://openalex.org/W2114869758","https://openalex.org/W2125117492","https://openalex.org/W2138404167","https://openalex.org/W2139645268","https://openalex.org/W2147776616","https://openalex.org/W2155469840","https://openalex.org/W4256264271","https://openalex.org/W6642974764"],"related_works":["https://openalex.org/W2139378013","https://openalex.org/W2560470131","https://openalex.org/W2049656902","https://openalex.org/W2394404719","https://openalex.org/W2903415888","https://openalex.org/W4287113494","https://openalex.org/W2348308003","https://openalex.org/W3148564979","https://openalex.org/W2063363084","https://openalex.org/W4313302755"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,83,87],"concerned":[3],"with":[4],"general":[5],"analysis":[6],"on":[7,25,42],"the":[8,26,30],"rank":[9,43],"and":[10,29,35,44,82,89],"row-redundancy":[11,45,54],"of":[12,15,32,38,57,68,74],"an":[13],"array":[14],"circulants":[16],"whose":[17],"null":[18],"space":[19],"defines":[20],"a":[21,65],"QC-LDPC":[22,58,69],"code.":[23],"Based":[24],"Fourier":[27],"transform":[28],"properties":[31],"conjugacy":[33],"classes":[34],"Hadamard":[36],"products":[37],"matrices,":[39],"tight":[40],"bounds":[41],"are":[46],"derived,":[47],"which":[48,77],"make":[49],"it":[50],"possible":[51],"to":[52,60],"consider":[53],"in":[55,85],"constructions":[56],"codes":[59,70],"achieve":[61],"better":[62],"performance.":[63],"Moreover,":[64],"new":[66],"construction":[67],"from":[71],"random":[72],"partitions":[73],"finite":[75],"fields,":[76],"has":[78],"flexible":[79],"code":[80],"dimensions":[81],"abundant":[84],"row-redundancy,":[86],"presented":[88],"analyzed.":[90]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}