{"id":"https://openalex.org/W4400680571","doi":"https://doi.org/10.1109/tit.2024.3429277","title":"Affine Automorphism Group of Polar Codes","display_name":"Affine Automorphism Group of Polar Codes","publication_year":2024,"publication_date":"2024-07-16","ids":{"openalex":"https://openalex.org/W4400680571","doi":"https://doi.org/10.1109/tit.2024.3429277"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2024.3429277","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1109/tit.2024.3429277","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Transactions on Information Theory","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/A5034323222","display_name":"Zicheng Ye","orcid":"https://orcid.org/0009-0005-8160-9698"},"institutions":[{"id":"https://openalex.org/I2250955327","display_name":"Huawei Technologies (China)","ror":"https://ror.org/00cmhce21","country_code":"CN","type":"company","lineage":["https://openalex.org/I2250955327"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zicheng Ye","raw_affiliation_strings":["Huawei Technologies Company Ltd., Hangzhou, China"],"raw_orcid":"https://orcid.org/0009-0005-8160-9698","affiliations":[{"raw_affiliation_string":"Huawei Technologies Company Ltd., Hangzhou, China","institution_ids":["https://openalex.org/I2250955327"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5104005007","display_name":"Yuan Li","orcid":"https://orcid.org/0009-0003-2672-0807"},"institutions":[{"id":"https://openalex.org/I2250955327","display_name":"Huawei Technologies (China)","ror":"https://ror.org/00cmhce21","country_code":"CN","type":"company","lineage":["https://openalex.org/I2250955327"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuan Li","raw_affiliation_strings":["Huawei Technologies Company Ltd., Hangzhou, China"],"raw_orcid":"https://orcid.org/0009-0003-2672-0807","affiliations":[{"raw_affiliation_string":"Huawei Technologies Company Ltd., Hangzhou, China","institution_ids":["https://openalex.org/I2250955327"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074783994","display_name":"Huazi Zhang","orcid":"https://orcid.org/0000-0001-5443-1314"},"institutions":[{"id":"https://openalex.org/I2250955327","display_name":"Huawei Technologies (China)","ror":"https://ror.org/00cmhce21","country_code":"CN","type":"company","lineage":["https://openalex.org/I2250955327"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huazi Zhang","raw_affiliation_strings":["Huawei Technologies Company Ltd., Hangzhou, China"],"raw_orcid":"https://orcid.org/0000-0001-5443-1314","affiliations":[{"raw_affiliation_string":"Huawei Technologies Company Ltd., Hangzhou, China","institution_ids":["https://openalex.org/I2250955327"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100691332","display_name":"Jun Wang","orcid":"https://orcid.org/0000-0002-7511-5553"},"institutions":[{"id":"https://openalex.org/I2250955327","display_name":"Huawei Technologies (China)","ror":"https://ror.org/00cmhce21","country_code":"CN","type":"company","lineage":["https://openalex.org/I2250955327"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun Wang","raw_affiliation_strings":["Huawei Technologies Company Ltd., Hangzhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Huawei Technologies Company Ltd., Hangzhou, China","institution_ids":["https://openalex.org/I2250955327"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108430975","display_name":"Guiying Yan","orcid":"https://orcid.org/0000-0002-4477-824X"},"institutions":[{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guiying Yan","raw_affiliation_strings":["School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5104108916","display_name":"Zhiming Ma","orcid":null},"institutions":[{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhiming Ma","raw_affiliation_strings":["School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0003-1169-7627","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4369,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.62849084,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"70","issue":"9","first_page":"6280","last_page":"6296"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":0.9998000264167786,"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":0.9998000264167786,"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/T11130","display_name":"Coding theory and cryptography","score":0.9987999796867371,"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/T12029","display_name":"DNA and Biological Computing","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5389074087142944},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.5346372127532959},{"id":"https://openalex.org/keywords/affine-group","display_name":"Affine group","score":0.497226744890213},{"id":"https://openalex.org/keywords/automorphism-group","display_name":"Automorphism group","score":0.4719986915588379},{"id":"https://openalex.org/keywords/polar","display_name":"Polar","score":0.4582504630088806},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4186505079269409},{"id":"https://openalex.org/keywords/automorphism","display_name":"Automorphism","score":0.3881208002567291},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.36711204051971436},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35197532176971436},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3278462886810303},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.17309197783470154},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15838298201560974}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5389074087142944},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5346372127532959},{"id":"https://openalex.org/C62623296","wikidata":"https://www.wikidata.org/wiki/Q686291","display_name":"Affine group","level":3,"score":0.497226744890213},{"id":"https://openalex.org/C2988750069","wikidata":"https://www.wikidata.org/wiki/Q60790315","display_name":"Automorphism group","level":3,"score":0.4719986915588379},{"id":"https://openalex.org/C29705727","wikidata":"https://www.wikidata.org/wiki/Q294562","display_name":"Polar","level":2,"score":0.4582504630088806},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4186505079269409},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.3881208002567291},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.36711204051971436},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35197532176971436},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3278462886810303},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.17309197783470154},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15838298201560974},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2024.3429277","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1109/tit.2024.3429277","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Transactions on Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5647958688","display_name":null,"funder_award_id":"2023YFA1009602","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"}],"funders":[{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1606480398","https://openalex.org/W1981735015","https://openalex.org/W2003204237","https://openalex.org/W2033234285","https://openalex.org/W2101067964","https://openalex.org/W2106045225","https://openalex.org/W2150498905","https://openalex.org/W2264554231","https://openalex.org/W2514963767","https://openalex.org/W2608866305","https://openalex.org/W2915736512","https://openalex.org/W2963684844","https://openalex.org/W2963710189","https://openalex.org/W3008435753","https://openalex.org/W3184425224","https://openalex.org/W3197313112","https://openalex.org/W3214771113","https://openalex.org/W4221143323","https://openalex.org/W4319993325","https://openalex.org/W4387485711","https://openalex.org/W4387489989","https://openalex.org/W6850423437"],"related_works":["https://openalex.org/W4289596368","https://openalex.org/W4302155387","https://openalex.org/W2545189445","https://openalex.org/W2115024785","https://openalex.org/W2085781584","https://openalex.org/W2901311998","https://openalex.org/W1965928613","https://openalex.org/W4392635288","https://openalex.org/W2962983948","https://openalex.org/W1678473343"],"abstract_inverted_index":{"The":[0],"automorphism":[1,52,87],"ensemble":[2],"(AE)":[3],"decoding":[4,40,74],"framework":[5,41],"for":[6,44],"polar":[7,121],"codes":[8,122],"attracts":[9],"much":[10],"attention":[11],"recently.":[12],"It":[13],"decodes":[14],"multiple":[15],"permuted":[16],"codewords":[17],"with":[18,115],"successive":[19,32],"cancellation":[20,33],"(SC)":[21],"decoders":[22],"in":[23,94,103],"parallel":[24],"and":[25,83,135],"hence":[26],"has":[27],"lower":[28],"latency":[29],"compared":[30],"to":[31,70,139,147],"list":[34],"(SCL)":[35],"decoding.":[36,60,105],"However,":[37,76],"the":[38,48,62,77,80,84,116,140],"AE":[39,73,104],"is":[42],"ineffective":[43],"permutations":[45],"falling":[46],"into":[47],"lower-triangular":[49,64,142],"affine":[50,65,86,128,161],"(LTA)":[51],"group,":[53],"as":[54,127],"they":[55],"are":[56,97,101],"invariant":[57],"under":[58,163],"SC":[59],"Therefore,":[61],"block":[63,141],"(BLTA)":[66],"group":[67,82,88,96,113],"was":[68,89],"discovered":[69],"achieve":[71],"better":[72],"performance.":[75],"equivalence":[78],"of":[79,119,144],"BLTA":[81,95,112],"complete":[85,117],"unresolved.":[90],"Additionally,":[91],"some":[92],"automorphisms":[93,118,162],"also":[98],"SC-invariant,":[99],"thus":[100],"redundant":[102],"In":[106],"this":[107],"paper,":[108],"we":[109,131],"prove":[110],"that":[111,123,156],"coincides":[114],"decreasing":[120],"can":[124],"be":[125],"formulated":[126],"transformations.":[129],"Also,":[130],"find":[132],"a":[133],"necessary":[134],"sufficient":[136],"condition":[137],"related":[138],"structure":[143],"transformation":[145],"matrices":[146],"identify":[148],"SC-invariant":[149,160],"automorphisms.":[150],"Furthermore,":[151],"We":[152],"present":[153],"an":[154],"algorithm":[155],"efficiently":[157],"identifies":[158],"all":[159],"specific":[164],"constructions.":[165]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}