{"id":"https://openalex.org/W2222463510","doi":"https://doi.org/10.1134/s0032946018040014","title":"Polar Codes with Higher-Order Memory","display_name":"Polar Codes with Higher-Order Memory","publication_year":2018,"publication_date":"2018-10-01","ids":{"openalex":"https://openalex.org/W2222463510","doi":"https://doi.org/10.1134/s0032946018040014","mag":"2222463510"},"language":"en","primary_location":{"id":"doi:10.1134/s0032946018040014","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s0032946018040014","pdf_url":null,"source":{"id":"https://openalex.org/S172430362","display_name":"Problems of Information Transmission","issn_l":"0032-9460","issn":["0032-9460","1608-3253"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Problems of Information Transmission","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1510.04489","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042618561","display_name":"H\u00fcseyin Af\u015fer","orcid":"https://orcid.org/0000-0002-6302-4558"},"institutions":[{"id":"https://openalex.org/I4405392","display_name":"Bo\u011fazi\u00e7i University","ror":"https://ror.org/03z9tma90","country_code":"TR","type":"education","lineage":["https://openalex.org/I4405392"]},{"id":"https://openalex.org/I50379099","display_name":"Adana Science and Technology University","ror":"https://ror.org/013z3yn41","country_code":"TR","type":"education","lineage":["https://openalex.org/I50379099"]}],"countries":["TR"],"is_corresponding":true,"raw_author_name":"H. Af\u015fer","raw_affiliation_strings":["Department of Electrical and Electronics Engineering, Adana Science and Technology University, Adana, Turkey","Wireless Communications Laboratory, Department of Electrical and Electronics Engineering, Bo\u011fazi\u00e7i University, Istanbul, Turkey","Bogazi\u00e7i University"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronics Engineering, Adana Science and Technology University, Adana, Turkey","institution_ids":["https://openalex.org/I50379099"]},{"raw_affiliation_string":"Wireless Communications Laboratory, Department of Electrical and Electronics Engineering, Bo\u011fazi\u00e7i University, Istanbul, Turkey","institution_ids":["https://openalex.org/I4405392"]},{"raw_affiliation_string":"Bogazi\u00e7i University","institution_ids":["https://openalex.org/I4405392"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108505608","display_name":"H. Deli\u00e7","orcid":null},"institutions":[{"id":"https://openalex.org/I4405392","display_name":"Bo\u011fazi\u00e7i University","ror":"https://ror.org/03z9tma90","country_code":"TR","type":"education","lineage":["https://openalex.org/I4405392"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"H. Deli\u00e7","raw_affiliation_strings":["Wireless Communications Laboratory, Department of Electrical and Electronics Engineering, Bo\u011fazi\u00e7i University, Istanbul, Turkey","Bogazi\u00e7i University"],"affiliations":[{"raw_affiliation_string":"Wireless Communications Laboratory, Department of Electrical and Electronics Engineering, Bo\u011fazi\u00e7i University, Istanbul, Turkey","institution_ids":["https://openalex.org/I4405392"]},{"raw_affiliation_string":"Bogazi\u00e7i University","institution_ids":["https://openalex.org/I4405392"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5042618561"],"corresponding_institution_ids":["https://openalex.org/I4405392","https://openalex.org/I50379099"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00551712,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"54","issue":"4","first_page":"301","last_page":"328"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","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"}},"topics":[{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","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"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9995999932289124,"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":0.9951000213623047,"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/combinatorics","display_name":"Combinatorics","score":0.673466682434082},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.6442270278930664},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6417217254638672},{"id":"https://openalex.org/keywords/polar-code","display_name":"Polar code","score":0.6107772588729858},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5124998092651367},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.49082526564598083},{"id":"https://openalex.org/keywords/polar","display_name":"Polar","score":0.4429019093513489},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.4420314431190491},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4162524342536926},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.41591113805770874},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4151134788990021},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35367998480796814},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.23503416776657104},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.21922796964645386},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08816564083099365},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08520805835723877}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.673466682434082},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.6442270278930664},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6417217254638672},{"id":"https://openalex.org/C2778396592","wikidata":"https://www.wikidata.org/wiki/Q7209069","display_name":"Polar code","level":3,"score":0.6107772588729858},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5124998092651367},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.49082526564598083},{"id":"https://openalex.org/C29705727","wikidata":"https://www.wikidata.org/wiki/Q294562","display_name":"Polar","level":2,"score":0.4429019093513489},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.4420314431190491},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4162524342536926},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.41591113805770874},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4151134788990021},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35367998480796814},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.23503416776657104},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.21922796964645386},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08816564083099365},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08520805835723877},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1134/s0032946018040014","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s0032946018040014","pdf_url":null,"source":{"id":"https://openalex.org/S172430362","display_name":"Problems of Information Transmission","issn_l":"0032-9460","issn":["0032-9460","1608-3253"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Problems of Information Transmission","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1510.04489","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1510.04489","pdf_url":"https://arxiv.org/pdf/1510.04489","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:2222463510","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1510.04489","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.1510.04489","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1510.04489","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:1510.04489","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1510.04489","pdf_url":"https://arxiv.org/pdf/1510.04489","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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2222463510.pdf","grobid_xml":"https://content.openalex.org/works/W2222463510.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W1490194873","https://openalex.org/W2055534149","https://openalex.org/W2100479399","https://openalex.org/W2145712176","https://openalex.org/W2150498905","https://openalex.org/W2164368671"],"related_works":["https://openalex.org/W2962893973","https://openalex.org/W2150498905","https://openalex.org/W2576249874","https://openalex.org/W2742871150","https://openalex.org/W1488043810","https://openalex.org/W3082278786","https://openalex.org/W2906226505","https://openalex.org/W2952479876","https://openalex.org/W3138004313","https://openalex.org/W2573719669","https://openalex.org/W2622606165","https://openalex.org/W2618548233","https://openalex.org/W2124591594","https://openalex.org/W2951718655","https://openalex.org/W2329655908","https://openalex.org/W2803874463","https://openalex.org/W1548479986","https://openalex.org/W1990567794","https://openalex.org/W2904911822","https://openalex.org/W2818756322"],"abstract_inverted_index":{"We":[0,73,94],"introduce":[1],"a":[2,5,28],"construction":[3],"of":[4,7,30,82,103,107,136,154,164],"set":[6],"code":[8,23],"sequences":[9],"{Cn(m)":[10],":":[11],"n":[12],"\u2265":[13,16],"1,":[14],"m":[15,21,70],"1}":[17],"with":[18,42,52,64,157],"memory":[19],"order":[20],"and":[22,57,61,109,151],"length":[24,43],"N(n).":[25],"{Cn(m)}":[26,62,76,108,155],"is":[27,45,118,131],"generalization":[29],"polar":[31,67,166],"codes":[32,68],"presented":[33],"by":[34],"Ar\u0131kan":[35],"in":[36],"[1],":[37],"where":[38,126],"the":[39,49,65,78,101,132,137,162],"encoder":[40,50],"mapping":[41],"N(n)":[44],"obtained":[46],"recursively":[47],"from":[48],"mappings":[51],"lengths":[53],"N(n":[54,58],"\u2212":[55,59,124,143,145,147],"1)":[56],"m),":[60],"coincides":[63],"original":[66],"when":[69],"=":[71,113,141],"1.":[72,148],"show":[74,110],"that":[75,111,169],"achieves":[77],"symmetric":[79],"capacity":[80],"I(W)":[81],"an":[83,97],"arbitrary":[84],"binary-input,":[85],"discrete-output":[86],"memoryless":[87],"channel":[88],"W":[89],"for":[90,120],"any":[91],"fixed":[92],"m.":[93],"also":[95],"obtain":[96],"upper":[98],"bound":[99],"on":[100],"probability":[102],"block-decoding":[104],"error":[105],"Pe":[106],"$${P_e}":[112],"O({2^{":[114],"-":[115],"{N^\\beta":[116],"}}})$$":[117],"achievable":[119],"\u03b2":[121],"<":[122],"1/[1+m(\u03d5":[123],"1)],":[125],"\u03d5":[127],"\u2208":[128],"(1,":[129],"2]":[130],"largest":[133],"real":[134],"root":[135],"polynomial":[138],"F(m,":[139],"\u03c1)":[140],"\u03c1m":[142,144],"1":[146],"The":[149],"encoding":[150],"decoding":[152],"complexities":[153],"decrease":[156],"increasing":[158],"m,":[159],"which":[160],"proves":[161],"existence":[163],"new":[165],"coding":[167],"schemes":[168],"have":[170],"lower":[171],"complexity":[172],"than":[173],"Ar\u0131kan\u2019s":[174],"construction.":[175]},"counts_by_year":[],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}