{"id":"https://openalex.org/W2046320168","doi":"https://doi.org/10.1109/tit.2014.2313696","title":"A Generalization of Omura's Decoding Algorithm and a Proof of Convergence","display_name":"A Generalization of Omura's Decoding Algorithm and a Proof of Convergence","publication_year":2014,"publication_date":"2014-03-25","ids":{"openalex":"https://openalex.org/W2046320168","doi":"https://doi.org/10.1109/tit.2014.2313696","mag":"2046320168"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2014.2313696","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2014.2313696","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/A5087713664","display_name":"Nathan Axvig","orcid":null},"institutions":[{"id":"https://openalex.org/I114526571","display_name":"Concordia College - Minnesota","ror":"https://ror.org/00ppb2x90","country_code":"US","type":"education","lineage":["https://openalex.org/I114526571"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Nathan Axvig","raw_affiliation_strings":["Department of Mathematics, Concordia College, Moorhead, MN, USA","Department of Mathematics, Concordia College, Moorhead, MN, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Concordia College, Moorhead, MN, USA","institution_ids":["https://openalex.org/I114526571"]},{"raw_affiliation_string":"Department of Mathematics, Concordia College, Moorhead, MN, USA#TAB#","institution_ids":["https://openalex.org/I114526571"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5087713664"],"corresponding_institution_ids":["https://openalex.org/I114526571"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.08587724,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"60","issue":"6","first_page":"3292","last_page":"3301"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"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":0.9998999834060669,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9994000196456909,"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":0.9987000226974487,"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":0.7921971082687378},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6671584844589233},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.6484721899032593},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.623712420463562},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5475417971611023},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.48529523611068726},{"id":"https://openalex.org/keywords/code-word","display_name":"Code word","score":0.44966191053390503},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.4314723610877991},{"id":"https://openalex.org/keywords/list-decoding","display_name":"List decoding","score":0.41205504536628723},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.375641405582428},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.12871429324150085},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.10214632749557495},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.0950833261013031},{"id":"https://openalex.org/keywords/concatenated-error-correction-code","display_name":"Concatenated error correction code","score":0.08041220903396606}],"concepts":[{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.7921971082687378},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6671584844589233},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.6484721899032593},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.623712420463562},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5475417971611023},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.48529523611068726},{"id":"https://openalex.org/C153207627","wikidata":"https://www.wikidata.org/wiki/Q863873","display_name":"Code word","level":3,"score":0.44966191053390503},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.4314723610877991},{"id":"https://openalex.org/C204397858","wikidata":"https://www.wikidata.org/wiki/Q4437907","display_name":"List decoding","level":5,"score":0.41205504536628723},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.375641405582428},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.12871429324150085},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.10214632749557495},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0950833261013031},{"id":"https://openalex.org/C78944582","wikidata":"https://www.wikidata.org/wiki/Q5158264","display_name":"Concatenated error correction code","level":4,"score":0.08041220903396606},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2014.2313696","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2014.2313696","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1586499344","https://openalex.org/W1614137482","https://openalex.org/W1762430620","https://openalex.org/W1969287452","https://openalex.org/W2033546746","https://openalex.org/W2052186517","https://openalex.org/W2090251262","https://openalex.org/W2099250555","https://openalex.org/W2170187382","https://openalex.org/W2986959318","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/W3096151594","https://openalex.org/W2964031101","https://openalex.org/W2983681086","https://openalex.org/W4200209838","https://openalex.org/W2165241191"],"abstract_inverted_index":{"An":[0],"approximation":[1],"of":[2,28,53,72],"maximum-likelihood":[3,65],"decoding":[4],"over":[5],"the":[6,29,51,54,70],"binary":[7],"symmetric":[8],"channel":[9],"was":[10],"introduced":[11],"by":[12],"Omura":[13,56],"in":[14],"1972.":[15],"This":[16],"decoder":[17,38,57],"employs":[18],"an":[19,42],"iterative,":[20],"randomized":[21],"algorithm":[22],"whose":[23],"behavior":[24],"closely":[25],"mimics":[26],"that":[27,50,79],"simplex":[30],"algorithm.":[31],"In":[32],"this":[33],"paper,":[34],"we":[35,48],"generalize":[36],"Omura's":[37,60],"to":[39,75],"operate":[40],"on":[41],"arbitrary":[43],"binary-input":[44],"memoryless":[45],"channel.":[46],"Further,":[47],"prove":[49],"probability":[52],"generalized":[55],"(and":[58],"hence":[59],"original":[61],"decoder)":[62],"returning":[63],"a":[64,77],"codeword":[66],"approaches":[67],"1":[68],"as":[69],"number":[71],"iterations":[73],"goes":[74],"infinity,":[76],"result":[78],"has":[80],"hereto":[81],"remained":[82],"unproven.":[83]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}