{"id":"https://openalex.org/W2075723463","doi":"https://doi.org/10.1137/120886674","title":"Local-Optimality Guarantees Based on Paths for Optimal Decoding","display_name":"Local-Optimality Guarantees Based on Paths for Optimal Decoding","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2075723463","doi":"https://doi.org/10.1137/120886674","mag":"2075723463"},"language":"en","primary_location":{"id":"doi:10.1137/120886674","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120886674","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","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/A5064059676","display_name":"Guy Even","orcid":"https://orcid.org/0000-0001-5407-330X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Guy Even","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5109588180","display_name":"Nissim Halabi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nissim Halabi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10413851,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"27","issue":"4","first_page":"2049","last_page":"2063"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9994000196456909,"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":0.9994000196456909,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9991000294685364,"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":0.9951000213623047,"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":0.8036744594573975},{"id":"https://openalex.org/keywords/code-word","display_name":"Code word","score":0.7863403558731079},{"id":"https://openalex.org/keywords/tanner-graph","display_name":"Tanner graph","score":0.7347777485847473},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6596099138259888},{"id":"https://openalex.org/keywords/list-decoding","display_name":"List decoding","score":0.5828288793563843},{"id":"https://openalex.org/keywords/parity-check-matrix","display_name":"Parity-check matrix","score":0.560736358165741},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5208749771118164},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.46264588832855225},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.43860602378845215},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41635140776634216},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37506717443466187},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36937040090560913},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.3044803738594055},{"id":"https://openalex.org/keywords/concatenated-error-correction-code","display_name":"Concatenated error correction code","score":0.2797504961490631},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2644481658935547},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.17052674293518066},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.08907890319824219}],"concepts":[{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.8036744594573975},{"id":"https://openalex.org/C153207627","wikidata":"https://www.wikidata.org/wiki/Q863873","display_name":"Code word","level":3,"score":0.7863403558731079},{"id":"https://openalex.org/C87117866","wikidata":"https://www.wikidata.org/wiki/Q7683664","display_name":"Tanner graph","level":5,"score":0.7347777485847473},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6596099138259888},{"id":"https://openalex.org/C204397858","wikidata":"https://www.wikidata.org/wiki/Q4437907","display_name":"List decoding","level":5,"score":0.5828288793563843},{"id":"https://openalex.org/C95925971","wikidata":"https://www.wikidata.org/wiki/Q3100414","display_name":"Parity-check matrix","level":4,"score":0.560736358165741},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5208749771118164},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.46264588832855225},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.43860602378845215},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41635140776634216},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37506717443466187},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36937040090560913},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.3044803738594055},{"id":"https://openalex.org/C78944582","wikidata":"https://www.wikidata.org/wiki/Q5158264","display_name":"Concatenated error correction code","level":4,"score":0.2797504961490631},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2644481658935547},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.17052674293518066},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.08907890319824219},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/120886674","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120886674","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","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":26,"referenced_works":["https://openalex.org/W7241855","https://openalex.org/W1537344883","https://openalex.org/W1588943481","https://openalex.org/W1969880716","https://openalex.org/W1970907073","https://openalex.org/W1993508000","https://openalex.org/W2033546746","https://openalex.org/W2035309551","https://openalex.org/W2035929826","https://openalex.org/W2052822863","https://openalex.org/W2064975723","https://openalex.org/W2067554595","https://openalex.org/W2087556581","https://openalex.org/W2114364830","https://openalex.org/W2118552378","https://openalex.org/W2128297707","https://openalex.org/W2128765501","https://openalex.org/W2141975070","https://openalex.org/W2169134868","https://openalex.org/W2175308498","https://openalex.org/W2176504112","https://openalex.org/W2340365916","https://openalex.org/W2751862591","https://openalex.org/W2949560198","https://openalex.org/W3099476509","https://openalex.org/W3106495992"],"related_works":["https://openalex.org/W2809536251","https://openalex.org/W4302175014","https://openalex.org/W2952823298","https://openalex.org/W2045996052","https://openalex.org/W2034577597","https://openalex.org/W2904381917","https://openalex.org/W2149558777","https://openalex.org/W3176812878","https://openalex.org/W4287640798","https://openalex.org/W2075723463"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"a":[3,80,169],"unified":[4],"analysis":[5],"framework":[6],"that":[7,85],"captures":[8],"recent":[9],"advances":[10],"in":[11,30,93,118,134],"the":[12,31,35,62,89,103,135,141,153],"study":[13],"of":[14,34,74,82,98,105,145],"local-optimality":[15,22],"characterizations":[16,23],"for":[17,148,166],"codes":[18,111,155],"on":[19,26,88,140],"graphs.":[20],"These":[21],"are":[24,138,156],"based":[25,87],"combinatorial":[27,91],"structures":[28,92],"embedded":[29],"Tanner":[32,94,110,150],"graph":[33],"code.":[36],"Local":[37],"optimality":[38,44,84,107],"implies":[39],"both":[40,125],"unique":[41,46,63],"maximum":[42],"likelihood":[43],"and":[45,117,127],"linear":[47],"programming":[48],"(LP)":[49],"decoding":[50,56,147,167,173],"optimality.":[51],"Also,":[52],"an":[53,72],"iterative":[54,171],"message-passing":[55,172],"algorithm":[57],"is":[58,86],"guaranteed":[59],"to":[60,108,158],"find":[61],"locally":[64],"optimal":[65],"codeword":[66],"if":[67],"one":[68],"exists.":[69],"We":[70,101],"demonstrate":[71],"instance":[73],"this":[75],"proof":[76],"technique":[77,104],"by":[78,168],"considering":[79],"definition":[81],"local":[83,106,154],"simplest":[90],"graphs,":[95],"namely,":[96],"paths":[97],"length":[99,137],"$h$.":[100],"apply":[102],"binary":[109,149],"(including":[112],"any":[113,120],"low-density":[114],"parity-check":[115,160],"code,":[116],"particular":[119],"irregular":[121],"repeat-accumulate":[122],"code":[123,136],"with":[124],"even":[126],"odd":[128],"repetition":[129],"factors).":[130],"Inverse":[131],"polynomial":[132],"bounds":[133,163],"proved":[139],"word":[142],"error":[143],"probability":[144],"LP":[146],"codes.":[151],"When":[152],"restricted":[157],"single":[159],"codes,":[161],"these":[162],"also":[164],"hold":[165],"certain":[170],"algorithm.":[174]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}