{"id":"https://openalex.org/W1972376834","doi":"https://doi.org/10.1109/tit.1980.1056158","title":"On the redundancy of binary Huffman codes (Corresp.)","display_name":"On the redundancy of binary Huffman codes (Corresp.)","publication_year":1980,"publication_date":"1980-03-01","ids":{"openalex":"https://openalex.org/W1972376834","doi":"https://doi.org/10.1109/tit.1980.1056158","mag":"1972376834"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1980.1056158","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1980.1056158","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/A5031882680","display_name":"O. Johnsen","orcid":null},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"O. Johnsen","raw_affiliation_strings":["Bell Laboratories, Inc., Holmdel, NJ, USA","Signal Processing Laboratory, Swiss Federal Institute of Technology, Lausanne, Switzerland"],"affiliations":[{"raw_affiliation_string":"Bell Laboratories, Inc., Holmdel, NJ, USA","institution_ids":[]},{"raw_affiliation_string":"Signal Processing Laboratory, Swiss Federal Institute of Technology, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5031882680"],"corresponding_institution_ids":["https://openalex.org/I5124864"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":55,"citation_normalized_percentile":{"value":0.0653864,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"26","issue":"2","first_page":"220","last_page":"222"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":1.0,"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":1.0,"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/T12029","display_name":"DNA and Biological Computing","score":0.9926000237464905,"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"}},{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9596999883651733,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/huffman-coding","display_name":"Huffman coding","score":0.9666829109191895},{"id":"https://openalex.org/keywords/redundancy","display_name":"Redundancy (engineering)","score":0.6149464845657349},{"id":"https://openalex.org/keywords/canonical-huffman-code","display_name":"Canonical Huffman code","score":0.5058493614196777},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.49154195189476013},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.47950679063796997},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.4648036062717438},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4507066607475281},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4449276924133301},{"id":"https://openalex.org/keywords/source-code","display_name":"Source code","score":0.42641910910606384},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3991831839084625},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33247971534729004},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.2067197859287262},{"id":"https://openalex.org/keywords/data-compression","display_name":"Data compression","score":0.14138159155845642},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.13179901242256165},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.10621359944343567},{"id":"https://openalex.org/keywords/code-rate","display_name":"Code rate","score":0.10180318355560303}],"concepts":[{"id":"https://openalex.org/C46900642","wikidata":"https://www.wikidata.org/wiki/Q2647","display_name":"Huffman coding","level":3,"score":0.9666829109191895},{"id":"https://openalex.org/C152124472","wikidata":"https://www.wikidata.org/wiki/Q1204361","display_name":"Redundancy (engineering)","level":2,"score":0.6149464845657349},{"id":"https://openalex.org/C115223089","wikidata":"https://www.wikidata.org/wiki/Q4885542","display_name":"Canonical Huffman code","level":5,"score":0.5058493614196777},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49154195189476013},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.47950679063796997},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.4648036062717438},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4507066607475281},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4449276924133301},{"id":"https://openalex.org/C43126263","wikidata":"https://www.wikidata.org/wiki/Q128751","display_name":"Source code","level":2,"score":0.42641910910606384},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3991831839084625},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33247971534729004},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.2067197859287262},{"id":"https://openalex.org/C78548338","wikidata":"https://www.wikidata.org/wiki/Q2493","display_name":"Data compression","level":2,"score":0.14138159155845642},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.13179901242256165},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.10621359944343567},{"id":"https://openalex.org/C206468330","wikidata":"https://www.wikidata.org/wiki/Q834373","display_name":"Code rate","level":3,"score":0.10180318355560303},{"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/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0},{"id":"https://openalex.org/C70992990","wikidata":"https://www.wikidata.org/wiki/Q1681587","display_name":"Systematic code","level":4,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1980.1056158","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1980.1056158","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":4,"referenced_works":["https://openalex.org/W211350514","https://openalex.org/W1725430864","https://openalex.org/W2038649859","https://openalex.org/W2060108852"],"related_works":["https://openalex.org/W2104740387","https://openalex.org/W2142090582","https://openalex.org/W2161708016","https://openalex.org/W2003530001","https://openalex.org/W1532196460","https://openalex.org/W2080323488","https://openalex.org/W2166346116","https://openalex.org/W2147086091","https://openalex.org/W2070295459","https://openalex.org/W2026349924"],"abstract_inverted_index":{"Some":[0],"properties":[1],"of":[2,17,33,59],"Huffman":[3,35],"codes":[4],"are":[5,38,69],"presented.":[6],"It":[7,61],"is":[8,62,81,85],"shown":[9,64],"that":[10,65,83],"knowing":[11],"the":[12,18,31,34,55,66,70,86],"probability":[13],"<tex":[14,41,74],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[15,42,75],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">P_{1}</tex>":[16],"most":[19],"likely":[20],"source":[21],"letter,":[22],"there":[23],"exist":[24],"new":[25,67],"lower":[26],"and":[27],"upper":[28],"bounds":[29,68],"on":[30],"redundancy":[32],"code":[36],"which":[37],"tighter":[39],"for":[40,73],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">P_{1}":[43,76],"\\geq":[44,77],"0.4</tex>":[45,78],"than":[46],"those":[47],"given":[48],"by":[49,54],"Shannon's":[50],"first":[51],"theorem":[52],"or":[53],"more":[56],"recent":[57],"results":[58],"Gallager.":[60],"also":[63],"tightest":[71],"possible":[72],"when":[79],"it":[80],"supposed":[82],"PI":[84],"only":[87],"known":[88],"probability.":[89]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}