{"id":"https://openalex.org/W2964010356","doi":"https://doi.org/10.1109/tit.2017.2717598","title":"A Note on Some Inequalities Used in Channel Polarization and Polar Coding","display_name":"A Note on Some Inequalities Used in Channel Polarization and Polar Coding","publication_year":2017,"publication_date":"2017-06-20","ids":{"openalex":"https://openalex.org/W2964010356","doi":"https://doi.org/10.1109/tit.2017.2717598","mag":"2964010356"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2017.2717598","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2017.2717598","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":true,"oa_status":"green","oa_url":"https://repository.bilkent.edu.tr/bitstreams/d4c025c3-039d-4778-a437-cbd768bd05c5/download","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023204485","display_name":"T. S. Jayram","orcid":"https://orcid.org/0000-0001-5235-4853"},"institutions":[{"id":"https://openalex.org/I4210085935","display_name":"IBM Research - Almaden","ror":"https://ror.org/005w8dd04","country_code":"US","type":"facility","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210085935","https://openalex.org/I4210114115"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"T. S. Jayram","raw_affiliation_strings":["IBM Almaden Research Center, San Jose, CA, USA"],"raw_orcid":"https://orcid.org/0000-0001-5235-4853","affiliations":[{"raw_affiliation_string":"IBM Almaden Research Center, San Jose, CA, USA","institution_ids":["https://openalex.org/I4210085935"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027597212","display_name":"Erdal Ar\u0131kan","orcid":"https://orcid.org/0000-0001-8810-4450"},"institutions":[{"id":"https://openalex.org/I168864056","display_name":"Bilkent University","ror":"https://ror.org/02vh8a032","country_code":"TR","type":"education","lineage":["https://openalex.org/I168864056"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Erdal Arikan","raw_affiliation_strings":["Department of Electrical-Electronics Engineering, Bilkent University, Ankara, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical-Electronics Engineering, Bilkent University, Ankara, Turkey","institution_ids":["https://openalex.org/I168864056"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4207,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.7000618,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"64","issue":"8","first_page":"5767","last_page":"5768"},"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/T10964","display_name":"Wireless Communication Security Techniques","score":0.9990000128746033,"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":0.9987999796867371,"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/mathematical-proof","display_name":"Mathematical proof","score":0.7405312657356262},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.6177695989608765},{"id":"https://openalex.org/keywords/polar","display_name":"Polar","score":0.5734974145889282},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.5674659609794617},{"id":"https://openalex.org/keywords/polarization","display_name":"Polarization (electrochemistry)","score":0.5570211410522461},{"id":"https://openalex.org/keywords/channel-code","display_name":"Channel code","score":0.48474690318107605},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.4758412837982178},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46467357873916626},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.451140433549881},{"id":"https://openalex.org/keywords/channel-capacity","display_name":"Channel capacity","score":0.4196874499320984},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.4165952205657959},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3653286397457123},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.34004953503608704},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3359830975532532},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.2642170786857605},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.18197107315063477},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.1466349959373474},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1335015892982483},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.0926147997379303},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07517483830451965}],"concepts":[{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.7405312657356262},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.6177695989608765},{"id":"https://openalex.org/C29705727","wikidata":"https://www.wikidata.org/wiki/Q294562","display_name":"Polar","level":2,"score":0.5734974145889282},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.5674659609794617},{"id":"https://openalex.org/C205049153","wikidata":"https://www.wikidata.org/wiki/Q2698605","display_name":"Polarization (electrochemistry)","level":2,"score":0.5570211410522461},{"id":"https://openalex.org/C166366890","wikidata":"https://www.wikidata.org/wiki/Q602136","display_name":"Channel code","level":3,"score":0.48474690318107605},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.4758412837982178},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46467357873916626},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.451140433549881},{"id":"https://openalex.org/C97744766","wikidata":"https://www.wikidata.org/wiki/Q870845","display_name":"Channel capacity","level":3,"score":0.4196874499320984},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.4165952205657959},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3653286397457123},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.34004953503608704},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3359830975532532},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.2642170786857605},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18197107315063477},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.1466349959373474},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1335015892982483},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0926147997379303},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07517483830451965},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C147789679","wikidata":"https://www.wikidata.org/wiki/Q11372","display_name":"Physical chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tit.2017.2717598","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2017.2717598","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:repository.bilkent.edu.tr:11693/50260","is_oa":true,"landing_page_url":"http://hdl.handle.net/11693/50260","pdf_url":"https://repository.bilkent.edu.tr/bitstreams/d4c025c3-039d-4778-a437-cbd768bd05c5/download","source":{"id":"https://openalex.org/S4306400079","display_name":"Bilkent University Institutional Repository (Bilkent University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I168864056","host_organization_name":"Bilkent University","host_organization_lineage":["https://openalex.org/I168864056"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"Article"},{"id":"pmh:oai:repository.bilkent.edu.tr:11693/36452","is_oa":false,"landing_page_url":"http://hdl.handle.net/11693/36452","pdf_url":null,"source":{"id":"https://openalex.org/S4306400079","display_name":"Bilkent University Institutional Repository (Bilkent University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I168864056","host_organization_name":"Bilkent University","host_organization_lineage":["https://openalex.org/I168864056"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:repository.bilkent.edu.tr:11693/50260","is_oa":true,"landing_page_url":"http://hdl.handle.net/11693/50260","pdf_url":"https://repository.bilkent.edu.tr/bitstreams/d4c025c3-039d-4778-a437-cbd768bd05c5/download","source":{"id":"https://openalex.org/S4306400079","display_name":"Bilkent University Institutional Repository (Bilkent University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I168864056","host_organization_name":"Bilkent University","host_organization_lineage":["https://openalex.org/I168864056"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"Article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.7099999785423279,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320334164","display_name":"Simons Institute for the Theory of Computing, University of California Berkeley","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W2964010356.pdf"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1536930200","https://openalex.org/W2037580822","https://openalex.org/W2098245138","https://openalex.org/W2146950091","https://openalex.org/W2150498905","https://openalex.org/W2513343158","https://openalex.org/W4205483176"],"related_works":["https://openalex.org/W2154612888","https://openalex.org/W1985968643","https://openalex.org/W2964140842","https://openalex.org/W2152012878","https://openalex.org/W2159839902","https://openalex.org/W2133231244","https://openalex.org/W2087060975","https://openalex.org/W2157619393","https://openalex.org/W2135879261","https://openalex.org/W1990402202"],"abstract_inverted_index":{"We":[0],"give":[1],"a":[2,19],"unified":[3],"treatment":[4],"of":[5,14],"some":[6],"inequalities":[7],"that":[8],"are":[9],"used":[10],"in":[11],"the":[12],"proofs":[13],"channel":[15],"polarization":[16],"theorems":[17],"involving":[18],"binary-input":[20],"discrete":[21],"memoryless":[22],"channel.":[23]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}