{"id":"https://openalex.org/W2029532841","doi":"https://doi.org/10.1109/allerton.2011.6120172","title":"Multilevel polarization for nonbinary codes and parallel channels","display_name":"Multilevel polarization for nonbinary codes and parallel channels","publication_year":2011,"publication_date":"2011-09-01","ids":{"openalex":"https://openalex.org/W2029532841","doi":"https://doi.org/10.1109/allerton.2011.6120172","mag":"2029532841"},"language":"en","primary_location":{"id":"doi:10.1109/allerton.2011.6120172","is_oa":false,"landing_page_url":"https://doi.org/10.1109/allerton.2011.6120172","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","raw_type":"proceedings-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/A5065451615","display_name":"Woomyoung Park","orcid":null},"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":true,"raw_author_name":"Woomyoung Park","raw_affiliation_strings":["Department of ECE and Institute System Research, University of Maryland, College Park, MD, USA","Department of ECE and Inst. Sys. Res., University of Maryland, College Park, Maryland, 20742"],"affiliations":[{"raw_affiliation_string":"Department of ECE and Institute System Research, University of Maryland, College Park, MD, USA","institution_ids":["https://openalex.org/I66946132"]},{"raw_affiliation_string":"Department of ECE and Inst. Sys. Res., University of Maryland, College Park, Maryland, 20742","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/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":"Alexander Barg","raw_affiliation_strings":["Department of ECE and Institute System Research, University of Maryland, College Park, MD, USA","Department of ECE and Inst. Sys. Res., University of Maryland, College Park, Maryland, 20742"],"affiliations":[{"raw_affiliation_string":"Department of ECE and Institute System Research, University of Maryland, College Park, MD, USA","institution_ids":["https://openalex.org/I66946132"]},{"raw_affiliation_string":"Department of ECE and Inst. Sys. Res., University of Maryland, College Park, Maryland, 20742","institution_ids":["https://openalex.org/I66946132"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5065451615"],"corresponding_institution_ids":["https://openalex.org/I66946132"],"apc_list":null,"apc_paid":null,"fwci":2.5655,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.90218151,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"228","last_page":"234"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998000264167786,"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/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.9997000098228455,"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/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"}}],"keywords":[{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.7587093114852905},{"id":"https://openalex.org/keywords/alphabet","display_name":"Alphabet","score":0.6580504179000854},{"id":"https://openalex.org/keywords/fading","display_name":"Fading","score":0.5894564986228943},{"id":"https://openalex.org/keywords/polarization","display_name":"Polarization (electrochemistry)","score":0.5779485702514648},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5246332287788391},{"id":"https://openalex.org/keywords/channel-capacity","display_name":"Channel capacity","score":0.4990537166595459},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.43283066153526306},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.4143886864185333},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4021293520927429},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3389672040939331},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3319389820098877},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.2638479173183441},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.21411892771720886}],"concepts":[{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.7587093114852905},{"id":"https://openalex.org/C112876837","wikidata":"https://www.wikidata.org/wiki/Q837518","display_name":"Alphabet","level":2,"score":0.6580504179000854},{"id":"https://openalex.org/C81978471","wikidata":"https://www.wikidata.org/wiki/Q1196572","display_name":"Fading","level":3,"score":0.5894564986228943},{"id":"https://openalex.org/C205049153","wikidata":"https://www.wikidata.org/wiki/Q2698605","display_name":"Polarization (electrochemistry)","level":2,"score":0.5779485702514648},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5246332287788391},{"id":"https://openalex.org/C97744766","wikidata":"https://www.wikidata.org/wiki/Q870845","display_name":"Channel capacity","level":3,"score":0.4990537166595459},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.43283066153526306},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.4143886864185333},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4021293520927429},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3389672040939331},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3319389820098877},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.2638479173183441},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.21411892771720886},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C147789679","wikidata":"https://www.wikidata.org/wiki/Q11372","display_name":"Physical chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/allerton.2011.6120172","is_oa":false,"landing_page_url":"https://doi.org/10.1109/allerton.2011.6120172","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","score":0.5099999904632568,"display_name":"Quality Education"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W638400246","https://openalex.org/W1905236300","https://openalex.org/W1984960835","https://openalex.org/W1986170574","https://openalex.org/W2001052745","https://openalex.org/W2096894382","https://openalex.org/W2101101242","https://openalex.org/W2127466643","https://openalex.org/W2144421688","https://openalex.org/W2150498905","https://openalex.org/W2552716967","https://openalex.org/W2786627918","https://openalex.org/W2906680874","https://openalex.org/W2950113883","https://openalex.org/W4298201074"],"related_works":["https://openalex.org/W2327053383","https://openalex.org/W2356834760","https://openalex.org/W1964600846","https://openalex.org/W2790025453","https://openalex.org/W2127563499","https://openalex.org/W2030191005","https://openalex.org/W2027568561","https://openalex.org/W1521521035","https://openalex.org/W1865172210","https://openalex.org/W2120897947"],"abstract_inverted_index":{"We":[0],"study":[1],"polarization":[2,41,67],"for":[3],"nonbiliary":[4],"channels":[5,34,45,86],"with":[6,46],"input":[7],"alphabet":[8],"of":[9,40,62,83,96],"size":[10],"q":[11],"=":[12,19],"2":[13],"<sup":[14],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[15],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">r</sup>":[16],",":[17],"r":[18,50],"2,":[20],"3,":[21],"...":[22],".":[23],"Using":[24],"Ankan's":[25],"successive":[26],"cancellation":[27],"decoding,":[28],"we":[29],"prove":[30],"that":[31,35,53,87],"the":[32,38,54,59,63,81,94],"virtual":[33],"arise":[36],"in":[37,69],"process":[39],"converge":[42],"to":[43,80,90,93],"q-ary":[44],"capacity":[47,61],"1,2,":[48],"...,":[49],"bits,":[51],"and":[52],"total":[55],"transmission":[56,71],"rate":[57],"approaches":[58],"symmetric":[60],"channel.":[64],"The":[65],"multilevel":[66],"arising":[68],"this":[70],"represents":[72],"a":[73],"new":[74],"phenomenon":[75],"which":[76],"is":[77],"well":[78],"suited":[79],"description":[82],"dependent":[84],"parallel":[85],"are":[88],"subject":[89],"fading":[91],"according":[92],"order":[95],"their":[97],"indices.":[98]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}