{"id":"https://openalex.org/W2099839668","doi":"https://doi.org/10.1109/tit.1972.1054750","title":"Variable-length codes and the Fano metric","display_name":"Variable-length codes and the Fano metric","publication_year":1972,"publication_date":"1972-01-01","ids":{"openalex":"https://openalex.org/W2099839668","doi":"https://doi.org/10.1109/tit.1972.1054750","mag":"2099839668"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1972.1054750","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1972.1054750","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/A5089069520","display_name":"J. Massey","orcid":"https://orcid.org/0000-0002-7793-7008"},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]},{"id":"https://openalex.org/I96673099","display_name":"Technical University of Denmark","ror":"https://ror.org/04qtj9h94","country_code":"DK","type":"education","lineage":["https://openalex.org/I96673099"]}],"countries":["DK","US"],"is_corresponding":true,"raw_author_name":"J. Massey","raw_affiliation_strings":["Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, USA","Laboratory for Communication Theory, Royal Technical University of Denmark, Lyngby, Denmark"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, USA","institution_ids":["https://openalex.org/I107639228"]},{"raw_affiliation_string":"Laboratory for Communication Theory, Royal Technical University of Denmark, Lyngby, Denmark","institution_ids":["https://openalex.org/I96673099"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5089069520"],"corresponding_institution_ids":["https://openalex.org/I107639228","https://openalex.org/I96673099"],"apc_list":null,"apc_paid":null,"fwci":7.9358,"has_fulltext":false,"cited_by_count":135,"citation_normalized_percentile":{"value":0.96803874,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"18","issue":"1","first_page":"196","last_page":"198"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9991000294685364,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9991000294685364,"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":0.9979000091552734,"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":0.9977999925613403,"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/fano-plane","display_name":"Fano plane","score":0.713398814201355},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.7054109573364258},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.6892045140266418},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5233275890350342},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5073885321617126},{"id":"https://openalex.org/keywords/statistic","display_name":"Statistic","score":0.4476347863674164},{"id":"https://openalex.org/keywords/sequential-decoding","display_name":"Sequential decoding","score":0.4433198571205139},{"id":"https://openalex.org/keywords/list-decoding","display_name":"List decoding","score":0.41224244236946106},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41170114278793335},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33985885977745056},{"id":"https://openalex.org/keywords/concatenated-error-correction-code","display_name":"Concatenated error correction code","score":0.2904062867164612},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.22963371872901917},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2186475396156311}],"concepts":[{"id":"https://openalex.org/C39757861","wikidata":"https://www.wikidata.org/wiki/Q1395814","display_name":"Fano plane","level":2,"score":0.713398814201355},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.7054109573364258},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.6892045140266418},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5233275890350342},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5073885321617126},{"id":"https://openalex.org/C89128539","wikidata":"https://www.wikidata.org/wiki/Q1949963","display_name":"Statistic","level":2,"score":0.4476347863674164},{"id":"https://openalex.org/C193969084","wikidata":"https://www.wikidata.org/wiki/Q7452500","display_name":"Sequential decoding","level":4,"score":0.4433198571205139},{"id":"https://openalex.org/C204397858","wikidata":"https://www.wikidata.org/wiki/Q4437907","display_name":"List decoding","level":5,"score":0.41224244236946106},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41170114278793335},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33985885977745056},{"id":"https://openalex.org/C78944582","wikidata":"https://www.wikidata.org/wiki/Q5158264","display_name":"Concatenated error correction code","level":4,"score":0.2904062867164612},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.22963371872901917},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2186475396156311},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","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},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1972.1054750","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1972.1054750","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":5,"referenced_works":["https://openalex.org/W1989008275","https://openalex.org/W2035227369","https://openalex.org/W2087362480","https://openalex.org/W2142901448","https://openalex.org/W2754491826"],"related_works":["https://openalex.org/W4205451769","https://openalex.org/W3017203753","https://openalex.org/W2385322349","https://openalex.org/W2029144766","https://openalex.org/W2348545647","https://openalex.org/W2983681086","https://openalex.org/W2369600518","https://openalex.org/W2089275957","https://openalex.org/W2165241191","https://openalex.org/W2964031101"],"abstract_inverted_index":{"It":[0],"is":[1,13,37,66,82],"shown":[2,67,83],"that":[3,28,84],"the":[4,15,29,35,38,46,53,77,85,88,91,95,106],"metric":[5,36,48],"proposed":[6],"originally":[7],"by":[8],"Fano":[9,47,78],"for":[10,18],"sequential":[11,58],"decoding":[12,20],"precisely":[14],"required":[16],"statistic":[17],"minimum-error-probability":[19],"of":[21,32,73,76,87,94,108],"variable-length":[22],"codes.":[23],"The":[24,60],"analysis":[25],"shows":[26],"further":[27],"\"natural\"":[30],"choice":[31,56],"bias":[33,89],"in":[34,57,90,102],"code":[39,96],"rate":[40],"and":[41],"gives":[42,98],"insight":[43],"into":[44],"why":[45],"has":[49],"proved":[50],"to":[51,68],"be":[52,69],"best":[54],"practical":[55],"decoding.":[59],"recently":[61],"devised":[62],"Jelinek-Zigangirov":[63],"\"stack":[64],"algorithm\"":[65],"a":[70,99],"natural":[71],"consequence":[72],"this":[74],"interpretation":[75],"metric.":[79],"Finally,":[80],"it":[81],"elimination":[86],"\"truncated\"":[92],"portion":[93],"tree":[97],"slight":[100],"reduction":[101],"average":[103],"computation":[104],"at":[105],"sacrifice":[107],"increased":[109],"error":[110],"probability.":[111]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
