{"id":"https://openalex.org/W2299251827","doi":"https://doi.org/10.1109/isit.2016.7541259","title":"Construction of Polar Codes for Arbitrary Discrete Memoryless Channels","display_name":"Construction of Polar Codes for Arbitrary Discrete Memoryless Channels","publication_year":2016,"publication_date":"2016-07-01","ids":{"openalex":"https://openalex.org/W2299251827","doi":"https://doi.org/10.1109/isit.2016.7541259","mag":"2299251827"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2016.7541259","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2016.7541259","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1603.05736","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032432450","display_name":"Talha Cihad G\u00fclc\u00fc","orcid":"https://orcid.org/0000-0002-8841-8617"},"institutions":[{"id":"https://openalex.org/I198068145","display_name":"Scientific and Technological Research Council of Turkey","ror":"https://ror.org/04w9kkr77","country_code":"TR","type":"government","lineage":["https://openalex.org/I198068145"]},{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["TR","US"],"is_corresponding":true,"raw_author_name":"Talha Cihad Gulcu","raw_affiliation_strings":["Institute for Systems Research, University of Maryland, College Park, MD, USA","TUBITAK Advanced Technologies Research Institute, Ankara, Turkey","Department of Electrical and Computer Engineering, University of Maryland College Park, MD USA"],"affiliations":[{"raw_affiliation_string":"Institute for Systems Research, University of Maryland, College Park, MD, USA","institution_ids":["https://openalex.org/I66946132"]},{"raw_affiliation_string":"TUBITAK Advanced Technologies Research Institute, Ankara, Turkey","institution_ids":["https://openalex.org/I198068145"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Maryland College Park, MD USA","institution_ids":["https://openalex.org/I66946132"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100725244","display_name":"Min Ye","orcid":"https://orcid.org/0000-0003-1351-8880"},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Min Ye","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Maryland, College Park, MD, USA","Department of Electrical and Computer Engineering, University of Maryland College Park, MD USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Maryland, College Park, MD, USA","institution_ids":["https://openalex.org/I66946132"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Maryland College Park, MD USA","institution_ids":["https://openalex.org/I66946132"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004622357","display_name":"Alexander Barg","orcid":"https://orcid.org/0000-0002-8972-4413"},"institutions":[{"id":"https://openalex.org/I4210107660","display_name":"Institute for Information Transmission Problems","ror":"https://ror.org/013w2d378","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210097085","https://openalex.org/I4210107660"]},{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["RU","US"],"is_corresponding":false,"raw_author_name":"Alexander Barg","raw_affiliation_strings":["Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia","Institute for Systems Research and the Department of Electrical and Computer Engineering, University of Maryland, College Park, MD, USA"],"affiliations":[{"raw_affiliation_string":"Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia","institution_ids":["https://openalex.org/I4210107660"]},{"raw_affiliation_string":"Institute for Systems Research and the Department of Electrical and Computer Engineering, University of Maryland, College Park, MD, USA","institution_ids":["https://openalex.org/I66946132"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5032432450"],"corresponding_institution_ids":["https://openalex.org/I198068145","https://openalex.org/I66946132"],"apc_list":null,"apc_paid":null,"fwci":0.2953,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.62030238,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"64","issue":"1","first_page":"309","last_page":"321"},"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":0.9947999715805054,"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/T12029","display_name":"DNA and Biological Computing","score":0.9940000176429749,"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/alphabet","display_name":"Alphabet","score":0.6725465655326843},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6168348789215088},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.5537324547767639},{"id":"https://openalex.org/keywords/merge","display_name":"Merge (version control)","score":0.5096337795257568},{"id":"https://openalex.org/keywords/polar","display_name":"Polar","score":0.5092567205429077},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.48969271779060364},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.4648159444332123},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4397546350955963},{"id":"https://openalex.org/keywords/quantization","display_name":"Quantization (signal processing)","score":0.4180070161819458},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.41532328724861145},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3955511450767517},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35178565979003906},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.202567458152771},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10638347268104553},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.09767764806747437}],"concepts":[{"id":"https://openalex.org/C112876837","wikidata":"https://www.wikidata.org/wiki/Q837518","display_name":"Alphabet","level":2,"score":0.6725465655326843},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6168348789215088},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.5537324547767639},{"id":"https://openalex.org/C197129107","wikidata":"https://www.wikidata.org/wiki/Q1921621","display_name":"Merge (version control)","level":2,"score":0.5096337795257568},{"id":"https://openalex.org/C29705727","wikidata":"https://www.wikidata.org/wiki/Q294562","display_name":"Polar","level":2,"score":0.5092567205429077},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.48969271779060364},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.4648159444332123},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4397546350955963},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.4180070161819458},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.41532328724861145},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3955511450767517},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35178565979003906},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.202567458152771},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10638347268104553},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.09767764806747437},{"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},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/isit.2016.7541259","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2016.7541259","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"},{"id":"doi:10.1109/tit.2017.2765663","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2017.2765663","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"},{"id":"pmh:oai:arXiv.org:1603.05736","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1603.05736","pdf_url":"https://arxiv.org/pdf/1603.05736","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2299251827","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1603.05736","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1603.05736","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1603.05736","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1603.05736","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1603.05736","pdf_url":"https://arxiv.org/pdf/1603.05736","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1502430853","display_name":null,"funder_award_id":"CCF1217245","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2317455502","display_name":null,"funder_award_id":"1422955","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2324036533","display_name":null,"funder_award_id":"CCF1217894","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5417119973","display_name":null,"funder_award_id":"CCF1422955","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6196167047","display_name":null,"funder_award_id":"CCF1618603","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7628774976","display_name":"CIF: Small: Ordered Metrics and Their Applications","funder_award_id":"1217245","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8091356298","display_name":null,"funder_award_id":"CF1217245","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2299251827.pdf","grobid_xml":"https://content.openalex.org/works/W2299251827.grobid-xml"},"referenced_works_count":50,"referenced_works":["https://openalex.org/W1569866271","https://openalex.org/W1587943761","https://openalex.org/W1634563480","https://openalex.org/W1830702501","https://openalex.org/W1893302682","https://openalex.org/W1904993380","https://openalex.org/W1915990350","https://openalex.org/W1971123554","https://openalex.org/W1975096885","https://openalex.org/W1975800702","https://openalex.org/W1981107808","https://openalex.org/W1981735015","https://openalex.org/W1983447663","https://openalex.org/W1998875316","https://openalex.org/W2009145605","https://openalex.org/W2031700647","https://openalex.org/W2039527871","https://openalex.org/W2055534149","https://openalex.org/W2076129236","https://openalex.org/W2096894382","https://openalex.org/W2099111195","https://openalex.org/W2107211662","https://openalex.org/W2121108749","https://openalex.org/W2126931301","https://openalex.org/W2145712176","https://openalex.org/W2150498905","https://openalex.org/W2150518053","https://openalex.org/W2158137498","https://openalex.org/W2159793310","https://openalex.org/W2161541170","https://openalex.org/W2164368671","https://openalex.org/W2169877013","https://openalex.org/W2170869643","https://openalex.org/W2172906094","https://openalex.org/W2175334662","https://openalex.org/W2211831180","https://openalex.org/W2569093245","https://openalex.org/W2588040356","https://openalex.org/W2949700586","https://openalex.org/W2950113883","https://openalex.org/W2962887023","https://openalex.org/W2963873929","https://openalex.org/W2964312190","https://openalex.org/W3037524284","https://openalex.org/W3099516920","https://openalex.org/W3100119739","https://openalex.org/W3123299285","https://openalex.org/W3124439737","https://openalex.org/W6674760679","https://openalex.org/W6685110532"],"related_works":["https://openalex.org/W2765658857","https://openalex.org/W2952954835","https://openalex.org/W2949700586","https://openalex.org/W2964170396","https://openalex.org/W2951494324","https://openalex.org/W3099794497","https://openalex.org/W2681925501","https://openalex.org/W2952436889","https://openalex.org/W1965882514","https://openalex.org/W2578448763","https://openalex.org/W1986921475","https://openalex.org/W2886159750","https://openalex.org/W2164083340","https://openalex.org/W3116151920","https://openalex.org/W2077100683","https://openalex.org/W2949401994","https://openalex.org/W3115431353","https://openalex.org/W2910453765","https://openalex.org/W2963279554","https://openalex.org/W2184280405"],"abstract_inverted_index":{"It":[0],"is":[1,44,81,88,122,141],"known":[2],"that":[3,43,131,183,199],"polar":[4,191,210],"codes":[5,174,192,211],"can":[6,187,204],"be":[7,188,205],"efficiently":[8],"constructed":[9],"for":[10,19,35,190,212,228],"binary-input":[11],"channels.":[12],"At":[13],"the":[14,32,36,50,55,66,82,89,93,97,103,108,123,126,133,168,172,200,225],"same":[15],"time,":[16],"existing":[17],"algorithms":[18,203],"general":[20,37],"input":[21,83],"alphabets":[22,213],"are":[23],"less":[24],"practical":[25],"because":[26],"of":[27,49,54,96,107,125,146,167,214,224,231],"high":[28],"complexity.":[29],"We":[30,128,180],"address":[31],"construction":[33,110,202],"problem":[34],"case,":[38],"and":[39,86,171,219],"analyze":[40],"an":[41],"algorithm":[42],"based":[45],"on":[46,137],"successive":[47],"reduction":[48],"output":[51,99,147],"alphabet":[52,84,100],"size":[53,85,95,215],"subchannels":[56],"in":[57,152,163],"each":[58,159],"recursion":[59],"step.":[60],"For":[61],"this":[62,156],"procedure,":[63],"we":[64],"estimate":[65],"approximation":[67,160],"error":[68],"as":[69,112],"O(\u03bc":[70],"<sup":[71,75,115],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[72,76,116],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">-1</sup>":[73,77],"/(q":[74],")),":[78],"where":[79,120],"q":[80,216],"\u03bc":[87,114],"\u201cquantization":[90],"parameter,\u201d":[91],"i.e.,":[92],"maximum":[94],"subchannel":[98,153],"allowed":[101],"by":[102],"algorithm.":[104],"The":[105],"complexity":[106],"code":[109,169,226],"scales":[111],"O(N":[113],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[117],"log":[118],"\u03bc),":[119],"N":[121],"length":[124],"code.":[127],"also":[129,181],"show":[130,182],"if":[132],"polarizing":[134,232],"operation":[135],"relies":[136],"modulo-q":[138],"addition,":[139],"it":[140],"possible":[142],"to":[143,178,207],"merge":[144],"subsets":[145],"symbols":[148],"without":[149],"any":[150],"loss":[151,223],"capacity.":[154,179],"Performing":[155],"procedure":[157],"before":[158],"step":[161],"results":[162],"a":[164,184,229],"further":[165],"speed-up":[166],"construction,":[170],"resulting":[173],"have":[175],"smaller":[176],"gap":[177],"similar":[185],"acceleration":[186],"attained":[189],"over":[193],"finite":[194],"field":[195],"alphabets.":[196],"Experimentation":[197],"shows":[198],"suggested":[201],"used":[206],"construct":[208],"long":[209],"=":[217],"16":[218],"more":[220],"with":[221],"acceptable":[222],"rate":[227],"variety":[230],"transforms.":[233]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}