{"id":"https://openalex.org/W2041934224","doi":"https://doi.org/10.1109/tit.2010.2069211","title":"Error Correcting Coding for a Nonsymmetric Ternary Channel","display_name":"Error Correcting Coding for a Nonsymmetric Ternary Channel","publication_year":2010,"publication_date":"2010-10-20","ids":{"openalex":"https://openalex.org/W2041934224","doi":"https://doi.org/10.1109/tit.2010.2069211","mag":"2041934224"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2010.2069211","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2010.2069211","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066281088","display_name":"Nicolas Bitouz\u00e9","orcid":null},"institutions":[{"id":"https://openalex.org/I205703379","display_name":"Institut Mines-T\u00e9l\u00e9com","ror":"https://ror.org/025vp2923","country_code":"FR","type":"facility","lineage":["https://openalex.org/I205703379"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Nicolas Bitouze","raw_affiliation_strings":["Department of Electronics, Institut TELECOM\u2014TELECOM Bretagne, Brest Cedex, France","Dept. of Electron., Inst. TELECOM-TELECOM Bretagne, Brest, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronics, Institut TELECOM\u2014TELECOM Bretagne, Brest Cedex, France","institution_ids":["https://openalex.org/I205703379"]},{"raw_affiliation_string":"Dept. of Electron., Inst. TELECOM-TELECOM Bretagne, Brest, France","institution_ids":["https://openalex.org/I205703379"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014522913","display_name":"Alexandre Graell i Amat","orcid":"https://orcid.org/0000-0002-5725-869X"},"institutions":[{"id":"https://openalex.org/I205703379","display_name":"Institut Mines-T\u00e9l\u00e9com","ror":"https://ror.org/025vp2923","country_code":"FR","type":"facility","lineage":["https://openalex.org/I205703379"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Alexandre Graell i Amat","raw_affiliation_strings":["Department of Electronics, Institut TELECOM\u2014TELECOM Bretagne, Brest Cedex, France","Dept. of Electron., Inst. TELECOM-TELECOM Bretagne, Brest, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronics, Institut TELECOM\u2014TELECOM Bretagne, Brest Cedex, France","institution_ids":["https://openalex.org/I205703379"]},{"raw_affiliation_string":"Dept. of Electron., Inst. TELECOM-TELECOM Bretagne, Brest, France","institution_ids":["https://openalex.org/I205703379"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090738616","display_name":"Eirik Rosnes","orcid":"https://orcid.org/0000-0001-8236-6601"},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Eirik Rosnes","raw_affiliation_strings":["Selmer Center, University of Bergen, Bergen, Norway","[Dept. of Inf., Univ. of Bergen, Bergen, Norway]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Selmer Center, University of Bergen, Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]},{"raw_affiliation_string":"[Dept. of Inf., Univ. of Bergen, Bergen, Norway]","institution_ids":["https://openalex.org/I4432739"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1186,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.79215047,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"56","issue":"11","first_page":"5715","last_page":"5729"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9994999766349792,"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":0.9987000226974487,"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/decoding-methods","display_name":"Decoding methods","score":0.8082184791564941},{"id":"https://openalex.org/keywords/ternary-operation","display_name":"Ternary operation","score":0.6750968098640442},{"id":"https://openalex.org/keywords/binary-symmetric-channel","display_name":"Binary symmetric channel","score":0.5746966600418091},{"id":"https://openalex.org/keywords/list-decoding","display_name":"List decoding","score":0.5630147457122803},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.5576740503311157},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5118023753166199},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4780690670013428},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.47462475299835205},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.44347262382507324},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4140816330909729},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35787099599838257},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3550984561443329},{"id":"https://openalex.org/keywords/concatenated-error-correction-code","display_name":"Concatenated error correction code","score":0.2863849699497223},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.23991012573242188},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.21226295828819275},{"id":"https://openalex.org/keywords/low-density-parity-check-code","display_name":"Low-density parity-check code","score":0.17256897687911987},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.11176782846450806}],"concepts":[{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.8082184791564941},{"id":"https://openalex.org/C64452783","wikidata":"https://www.wikidata.org/wiki/Q1524945","display_name":"Ternary operation","level":2,"score":0.6750968098640442},{"id":"https://openalex.org/C173988684","wikidata":"https://www.wikidata.org/wiki/Q863510","display_name":"Binary symmetric channel","level":4,"score":0.5746966600418091},{"id":"https://openalex.org/C204397858","wikidata":"https://www.wikidata.org/wiki/Q4437907","display_name":"List decoding","level":5,"score":0.5630147457122803},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.5576740503311157},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5118023753166199},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4780690670013428},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.47462475299835205},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.44347262382507324},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4140816330909729},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35787099599838257},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3550984561443329},{"id":"https://openalex.org/C78944582","wikidata":"https://www.wikidata.org/wiki/Q5158264","display_name":"Concatenated error correction code","level":4,"score":0.2863849699497223},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.23991012573242188},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.21226295828819275},{"id":"https://openalex.org/C67692717","wikidata":"https://www.wikidata.org/wiki/Q187444","display_name":"Low-density parity-check code","level":3,"score":0.17256897687911987},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.11176782846450806},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tit.2010.2069211","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2010.2069211","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:CiteSeerX.psu:10.1.1.749.4912","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.749.4912","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0911.1072.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-01170753v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01170753","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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, 2010, 56 (11), pp.5715 - 5729","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W125120570","https://openalex.org/W1518796387","https://openalex.org/W1969261755","https://openalex.org/W1977781091","https://openalex.org/W2026320281","https://openalex.org/W2041588219","https://openalex.org/W2046112356","https://openalex.org/W2054252682","https://openalex.org/W2057383973","https://openalex.org/W2085021014","https://openalex.org/W2087021779","https://openalex.org/W2091364465","https://openalex.org/W2097632093","https://openalex.org/W2098922615","https://openalex.org/W2115108282","https://openalex.org/W2117942072","https://openalex.org/W2126542268","https://openalex.org/W2128765501","https://openalex.org/W2144030381","https://openalex.org/W2145570573","https://openalex.org/W2148575324","https://openalex.org/W2150585727","https://openalex.org/W2165062870","https://openalex.org/W2170507842","https://openalex.org/W4240374930","https://openalex.org/W4285719527","https://openalex.org/W4300188436"],"related_works":["https://openalex.org/W3017203753","https://openalex.org/W3083229674","https://openalex.org/W4205451769","https://openalex.org/W2385322349","https://openalex.org/W2369600518","https://openalex.org/W4390826522","https://openalex.org/W3096151594","https://openalex.org/W2226710168","https://openalex.org/W4298835066","https://openalex.org/W2145403642"],"abstract_inverted_index":{"Ternary":[0],"channels":[1],"can":[2],"be":[3],"used":[4],"to":[5,174],"model":[6],"the":[7,34,59,76,132,140,156,164,191,203],"behavior":[8],"of":[9,33,136,158,179],"some":[10,32,201],"memory":[11],"devices,":[12],"where":[13,31],"information":[14],"is":[15,40,45,96,100,119,188],"stored":[16],"in":[17,200],"three":[18],"different":[19],"levels.":[20],"In":[21],"this":[22,55,68],"paper,":[23],"error":[24,35,78,133],"correcting":[25,134],"coding":[26],"for":[27,54,64,171],"a":[28,151,184],"ternary":[29,65,137,142],"channel":[30,44,69,77],"transitions":[36],"are":[37,51,111,168,205],"not":[38,52],"allowed,":[39],"considered.":[41],"The":[42,160],"resulting":[43],"nonsymmetric,":[46],"therefore,":[47],"classical":[48],"linear":[49],"codes":[50,66,138,176,204],"optimal":[53,175],"channel.":[56,143],"We":[57,144],"define":[58],"maximum-likelihood":[60],"(ML)":[61],"decoding":[62,82,110],"rule":[63,83],"over":[67,139],"and":[70,108,150,198],"show":[71],"that":[72,102,190,199],"it":[73],"depends":[74,85],"on":[75,87,155],"probability.":[79],"An":[80],"alternative":[81],"which":[84],"only":[86],"code":[88,180],"properties,":[89],"called":[90],"d":[91,103,114,125],"<sub":[92,104,115,126],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[93,105,116,127],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">A</sub>":[94,106,117,128],"-decoding,":[95,129],"then":[97,169],"proposed.":[98],"It":[99,187],"shown":[101,189],"-decoding":[107,118],"ML":[109],"equivalent,":[112],"i.e.,":[113],"optimal,":[120],"under":[121],"certain":[122],"conditions.":[123],"Assuming":[124],"we":[130],"characterize":[131],"capabilities":[135],"nonsymmetric":[141],"also":[145],"derive":[146],"an":[147],"upper":[148],"bound":[149,154,167],"constructive":[152,165],"lower":[153,166],"size":[157],"codes.":[159],"results":[161],"arising":[162],"from":[163],"compared,":[170],"short":[172],"sizes,":[173],"(in":[177],"terms":[178],"size)":[181],"found":[182],"by":[183],"clique-based":[185],"search.":[186],"proposed":[192],"construction":[193],"method":[194],"gives":[195],"good":[196],"codes,":[197],"cases":[202],"optimal.":[206]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}