{"id":"https://openalex.org/W2930912956","doi":"https://doi.org/10.1109/globecom38437.2019.9013830","title":"The Penalty in Scaling Exponent for Polar Codes Is Analytically Approximated by the Golden Ratio","display_name":"The Penalty in Scaling Exponent for Polar Codes Is Analytically Approximated by the Golden Ratio","publication_year":2019,"publication_date":"2019-12-01","ids":{"openalex":"https://openalex.org/W2930912956","doi":"https://doi.org/10.1109/globecom38437.2019.9013830","mag":"2930912956"},"language":"en","primary_location":{"id":"doi:10.1109/globecom38437.2019.9013830","is_oa":false,"landing_page_url":"https://doi.org/10.1109/globecom38437.2019.9013830","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE Global Communications Conference (GLOBECOM)","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/1904.03768","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056556124","display_name":"Ori Shental","orcid":"https://orcid.org/0000-0001-6937-3743"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ori Shental","raw_affiliation_strings":["Communications Theory Department, Bell Labs, Holmdel, New Jersey, USA","Nokia Bell Labs"],"affiliations":[{"raw_affiliation_string":"Communications Theory Department, Bell Labs, Holmdel, New Jersey, USA","institution_ids":[]},{"raw_affiliation_string":"Nokia Bell Labs","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5056556124"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05392941,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"7"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":0.9976000189781189,"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/T12029","display_name":"DNA and Biological Computing","score":0.9962000250816345,"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/exponent","display_name":"Exponent","score":0.9138250350952148},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.7400683164596558},{"id":"https://openalex.org/keywords/critical-exponent","display_name":"Critical exponent","score":0.6009300351142883},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4750761389732361},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4551021158695221},{"id":"https://openalex.org/keywords/square-lattice","display_name":"Square lattice","score":0.4345606565475464},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4092678427696228},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.37961599230766296},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.33226704597473145},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.32925355434417725},{"id":"https://openalex.org/keywords/ising-model","display_name":"Ising model","score":0.1603713035583496},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12831291556358337}],"concepts":[{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.9138250350952148},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.7400683164596558},{"id":"https://openalex.org/C164154869","wikidata":"https://www.wikidata.org/wiki/Q901927","display_name":"Critical exponent","level":3,"score":0.6009300351142883},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4750761389732361},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4551021158695221},{"id":"https://openalex.org/C2777620828","wikidata":"https://www.wikidata.org/wiki/Q7582067","display_name":"Square lattice","level":3,"score":0.4345606565475464},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4092678427696228},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.37961599230766296},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33226704597473145},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.32925355434417725},{"id":"https://openalex.org/C51329190","wikidata":"https://www.wikidata.org/wiki/Q1076349","display_name":"Ising model","level":2,"score":0.1603713035583496},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12831291556358337},{"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":4,"locations":[{"id":"doi:10.1109/globecom38437.2019.9013830","is_oa":false,"landing_page_url":"https://doi.org/10.1109/globecom38437.2019.9013830","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE Global Communications Conference (GLOBECOM)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1904.03768","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1904.03768","pdf_url":"https://arxiv.org/pdf/1904.03768","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":null,"raw_type":"text"},{"id":"mag:2930912956","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1904.03768.pdf","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.1904.03768","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1904.03768","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:1904.03768","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1904.03768","pdf_url":"https://arxiv.org/pdf/1904.03768","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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2930912956.pdf","grobid_xml":"https://content.openalex.org/works/W2930912956.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1558937370","https://openalex.org/W1586772380","https://openalex.org/W1678925104","https://openalex.org/W1964541705","https://openalex.org/W1968317380","https://openalex.org/W2025786790","https://openalex.org/W2036424138","https://openalex.org/W2049951355","https://openalex.org/W2081158168","https://openalex.org/W2150498905","https://openalex.org/W2169017678","https://openalex.org/W2531627753","https://openalex.org/W2890292748","https://openalex.org/W2911546354","https://openalex.org/W3102122722","https://openalex.org/W3102477320"],"related_works":["https://openalex.org/W3009262221","https://openalex.org/W1996746155","https://openalex.org/W3186028989","https://openalex.org/W1970458258","https://openalex.org/W3196353518","https://openalex.org/W1678979181","https://openalex.org/W2133583151","https://openalex.org/W2065883678","https://openalex.org/W3107915677","https://openalex.org/W2795905385","https://openalex.org/W2062627882","https://openalex.org/W3046879492","https://openalex.org/W3105856416","https://openalex.org/W2055844269","https://openalex.org/W3102142279","https://openalex.org/W2979359141","https://openalex.org/W1746700466","https://openalex.org/W1663743429","https://openalex.org/W2159555068","https://openalex.org/W2762584821"],"abstract_inverted_index":{"The":[0],"polarization":[1],"process":[2],"of":[3,20,41,167],"conventional":[4],"polar":[5,161],"codes":[6,162],"in":[7,23,163,165],"binary":[8],"erasure":[9],"channel":[10],"(BEC)":[11],"is":[12,79,142,153],"recast":[13],"to":[14,119],"the":[15,29,39,42,49,55,62,85,107,120,124,143,148,158,168,177],"Domany-Kinzel":[16],"cellular":[17],"automaton":[18],"model":[19],"directed":[21],"percolation":[22,43,51],"a":[24],"tilted":[25],"square":[26],"lattice.":[27],"Consequently,":[28],"former's":[30],"scaling":[31,63,125,151,169],"exponent,":[32,45,109,170],"\u03bc,":[33],"can":[34,65,111,171],"be":[35,66,112,172],"analogously":[36],"expressed":[37],"as":[38,69],"inverse":[40],"critical":[44,108],"\u03b2.":[46],"Relying":[47],"on":[48,94],"vast":[50],"theory":[52,91],"literature":[53,92],"and":[54],"best":[56],"known":[57,86],"numerical":[58,95,104],"estimate":[59],"for":[60,106,123,160],"\u03b2,":[61,110],"exponent":[64,87,126,152],"easily":[67],"estimated":[68,175],"\u03bc":[70,97],"<sub":[71,98],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[72,75,99,138],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">num</sub>":[73,100],"<sup":[74,137],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">perc</sup>":[76],"\u22431/0.276486(8)\u22433.617,":[77],"which":[78],"only":[80,116],"about":[81],"0.25%":[82],"away":[83],"from":[84,89],"computation":[88],"coding":[90],"based":[93],"approximation,":[96],"\u22433.627.":[101],"Remarkably,":[102],"this":[103,155],"result":[105],"analytically":[113],"approximated":[114],"(within":[115],"0.028%)":[117],"leading":[118],"closed-form":[121],"expression":[122],"\u03bc\u22432":[127],"+":[128,132],"\u03c6":[129],"=":[130],"2":[131],"1.618":[133],"...\u22433.618,":[134],"where":[135],"\u03c6=":[136],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u0394</sup>":[139],"(1":[140],"+\u221a(5))/2":[141],"ubiquitous":[144],"golden":[145,178],"ratio.":[146],"As":[147],"ultimate":[149],"achievable":[150],"quadratic,":[154],"implies":[156],"that":[157],"penalty":[159],"BEC,":[164],"terms":[166],"very":[173],"well":[174],"by":[176],"ratio,":[179],"\u03c6,":[180],"itself.":[181]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}