{"id":"https://openalex.org/W2126590220","doi":"https://doi.org/10.1109/tit.1961.1057615","title":"Minimum-redundancy coding for the discrete noiseless channel","display_name":"Minimum-redundancy coding for the discrete noiseless channel","publication_year":1961,"publication_date":"1961-01-01","ids":{"openalex":"https://openalex.org/W2126590220","doi":"https://doi.org/10.1109/tit.1961.1057615","mag":"2126590220"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1961.1057615","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1961.1057615","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/A5068875104","display_name":"Richard M. Karp","orcid":null},"institutions":[{"id":"https://openalex.org/I1341412227","display_name":"IBM (United States)","ror":"https://ror.org/05hh8d621","country_code":"US","type":"company","lineage":["https://openalex.org/I1341412227"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"R. Karp","raw_affiliation_strings":["Research Center, IBM, Corporation, Yorktown Heights, NY, USA","[Research Center, IBM, Corporation, Yorktown Heights, NY, USA]"],"affiliations":[{"raw_affiliation_string":"Research Center, IBM, Corporation, Yorktown Heights, NY, USA","institution_ids":["https://openalex.org/I1341412227"]},{"raw_affiliation_string":"[Research Center, IBM, Corporation, Yorktown Heights, NY, USA]","institution_ids":["https://openalex.org/I1341412227"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5068875104"],"corresponding_institution_ids":["https://openalex.org/I1341412227"],"apc_list":null,"apc_paid":null,"fwci":14.5158,"has_fulltext":false,"cited_by_count":135,"citation_normalized_percentile":{"value":0.9844358,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"7","issue":"1","first_page":"27","last_page":"38"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","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/T11269","display_name":"Algorithms and Data Compression","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/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"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"}}],"keywords":[{"id":"https://openalex.org/keywords/huffman-coding","display_name":"Huffman coding","score":0.8040063381195068},{"id":"https://openalex.org/keywords/prefix-code","display_name":"Prefix code","score":0.7532341480255127},{"id":"https://openalex.org/keywords/prefix","display_name":"Prefix","score":0.5386896133422852},{"id":"https://openalex.org/keywords/redundancy","display_name":"Redundancy (engineering)","score":0.5260669589042664},{"id":"https://openalex.org/keywords/channel-code","display_name":"Channel code","score":0.5134909749031067},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4965570569038391},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4871222972869873},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.4622291028499603},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.45873963832855225},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4561963677406311},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.44782555103302},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.42122673988342285},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.4142477512359619},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4113911986351013},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.26172471046447754},{"id":"https://openalex.org/keywords/data-compression","display_name":"Data compression","score":0.17878791689872742}],"concepts":[{"id":"https://openalex.org/C46900642","wikidata":"https://www.wikidata.org/wiki/Q2647","display_name":"Huffman coding","level":3,"score":0.8040063381195068},{"id":"https://openalex.org/C20079647","wikidata":"https://www.wikidata.org/wiki/Q1278039","display_name":"Prefix code","level":5,"score":0.7532341480255127},{"id":"https://openalex.org/C141603448","wikidata":"https://www.wikidata.org/wiki/Q134830","display_name":"Prefix","level":2,"score":0.5386896133422852},{"id":"https://openalex.org/C152124472","wikidata":"https://www.wikidata.org/wiki/Q1204361","display_name":"Redundancy (engineering)","level":2,"score":0.5260669589042664},{"id":"https://openalex.org/C166366890","wikidata":"https://www.wikidata.org/wiki/Q602136","display_name":"Channel code","level":3,"score":0.5134909749031067},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4965570569038391},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4871222972869873},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.4622291028499603},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.45873963832855225},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4561963677406311},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.44782555103302},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.42122673988342285},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.4142477512359619},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4113911986351013},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.26172471046447754},{"id":"https://openalex.org/C78548338","wikidata":"https://www.wikidata.org/wiki/Q2493","display_name":"Data compression","level":2,"score":0.17878791689872742},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1961.1057615","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1961.1057615","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W288256330","https://openalex.org/W1480469437","https://openalex.org/W1509016759","https://openalex.org/W1992649154","https://openalex.org/W1995875735","https://openalex.org/W2009683816","https://openalex.org/W2027875058","https://openalex.org/W2060108852","https://openalex.org/W2061796125","https://openalex.org/W2126711987","https://openalex.org/W2127470768","https://openalex.org/W2169476932","https://openalex.org/W2596773272","https://openalex.org/W3174910057","https://openalex.org/W4242994599","https://openalex.org/W6797722509"],"related_works":["https://openalex.org/W2056723920","https://openalex.org/W4237802754","https://openalex.org/W2011506041","https://openalex.org/W2166346116","https://openalex.org/W2016524125","https://openalex.org/W2142508314","https://openalex.org/W2094225155","https://openalex.org/W1650274465","https://openalex.org/W2018691674","https://openalex.org/W2952674952"],"abstract_inverted_index":{"This":[0],"paper":[1],"gives":[2],"a":[3,138],"method":[4],"for":[5,10,49,80],"constructing":[6],"minimum-redundancy":[7],"prefix":[8,84,102],"codes":[9,85,114],"the":[11,28,50,81,125,128],"general":[12],"discrete":[13],"noiseless":[14],"channel":[15],"without":[16],"constraints.":[17],"The":[18,62],"costs":[19],"of":[20,59,74,83,127,140],"code":[21,56],"letters":[22,57],"need":[23],"not":[24,32],"be":[25,35,87,98],"equal,":[26],"and":[27,77,137],"symbols":[29],"encoded":[30],"are":[31,58,70,94,135],"assumed":[33],"to":[34,100,111,116,123],"equally":[36],"probable.":[37],"A":[38],"solution":[39],"had":[40],"previously":[41],"been":[42],"given":[43],"by":[44],"Huffman":[45],"[10]":[46],"in":[47,53,72],"1952":[48],"special":[51],"case":[52],"which":[54,75,96],"all":[55],"equal":[60],"cost.":[61],"present":[63],"development":[64],"is":[65,108,121,142],"algebraic.":[66],"First,":[67],"structure":[68],"functions":[69],"defined,":[71],"terms":[73],"necessary":[76],"sufficient":[78],"conditions":[79],"existence":[82],"may":[86,97],"stated.":[88],"From":[89],"these":[90,117],"conditions,":[91],"linear":[92],"inequalities":[93],"derived":[95],"used":[99,110],"characterize":[101],"codes.":[103],"Gomory's":[104],"integer":[105],"programming":[106],"algorithm":[107],"then":[109],"construct":[112],"optimum":[113],"subject":[115],"inequalities;":[118],"computational":[119],"experience":[120],"presented":[122],"demonstrate":[124],"practicability":[126],"method.":[129],"Finally,":[130],"some":[131],"additional":[132],"coding":[133],"problems":[134],"discussed":[136],"problem":[139],"classification":[141],"treated.":[143]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":5},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-01T17:29:45.350535","created_date":"2025-10-10T00:00:00"}