{"id":"https://openalex.org/W2097071386","doi":"https://doi.org/10.1109/tit.1978.1055961","title":"Design of absolutely optimal quantizers for a wide class of distortion measures","display_name":"Design of absolutely optimal quantizers for a wide class of distortion measures","publication_year":1978,"publication_date":"1978-11-01","ids":{"openalex":"https://openalex.org/W2097071386","doi":"https://doi.org/10.1109/tit.1978.1055961","mag":"2097071386"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1978.1055961","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1978.1055961","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/A5111877393","display_name":"D. Sharma","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"D. Sharma","raw_affiliation_strings":["Bell Laboratories, Inc., Holmdel, NJ, USA","Bell Labs., Inc., Holmdel, NJ, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bell Laboratories, Inc., Holmdel, NJ, USA","institution_ids":[]},{"raw_affiliation_string":"Bell Labs., Inc., Holmdel, NJ, USA","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5111877393"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.3293,"has_fulltext":false,"cited_by_count":67,"citation_normalized_percentile":{"value":0.8828541,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"24","issue":"6","first_page":"693","last_page":"702"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10901","display_name":"Advanced Data Compression Techniques","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10901","display_name":"Advanced Data Compression Techniques","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.9629999995231628,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10754","display_name":"Neuroendocrine Tumor Research Advances","score":0.9520000219345093,"subfield":{"id":"https://openalex.org/subfields/2713","display_name":"Epidemiology"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/distortion","display_name":"Distortion (music)","score":0.49810075759887695},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.49117085337638855},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4380629360675812},{"id":"https://openalex.org/keywords/weighting","display_name":"Weighting","score":0.4363178014755249},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.43264690041542053},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4312821924686432},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4214402139186859},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.37152689695358276},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3411116600036621},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.22476106882095337},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07337081432342529},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06745103001594543}],"concepts":[{"id":"https://openalex.org/C126780896","wikidata":"https://www.wikidata.org/wiki/Q899871","display_name":"Distortion (music)","level":4,"score":0.49810075759887695},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.49117085337638855},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4380629360675812},{"id":"https://openalex.org/C183115368","wikidata":"https://www.wikidata.org/wiki/Q856577","display_name":"Weighting","level":2,"score":0.4363178014755249},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.43264690041542053},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4312821924686432},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4214402139186859},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37152689695358276},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3411116600036621},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.22476106882095337},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07337081432342529},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06745103001594543},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C194257627","wikidata":"https://www.wikidata.org/wiki/Q211554","display_name":"Amplifier","level":3,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1978.1055961","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1978.1055961","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":32,"referenced_works":["https://openalex.org/W999888728","https://openalex.org/W1976011531","https://openalex.org/W1985921956","https://openalex.org/W1994858116","https://openalex.org/W1995237734","https://openalex.org/W1995871078","https://openalex.org/W1997331932","https://openalex.org/W1999276251","https://openalex.org/W2001968606","https://openalex.org/W2004003571","https://openalex.org/W2006704346","https://openalex.org/W2023654794","https://openalex.org/W2024824071","https://openalex.org/W2048107208","https://openalex.org/W2048951246","https://openalex.org/W2062533874","https://openalex.org/W2065902423","https://openalex.org/W2068071220","https://openalex.org/W2070865817","https://openalex.org/W2099617207","https://openalex.org/W2109808436","https://openalex.org/W2129450987","https://openalex.org/W2134222103","https://openalex.org/W2135413013","https://openalex.org/W2136810817","https://openalex.org/W2137263269","https://openalex.org/W2146519989","https://openalex.org/W2156310455","https://openalex.org/W4234676312","https://openalex.org/W4235599520","https://openalex.org/W4285719527","https://openalex.org/W4298300677"],"related_works":["https://openalex.org/W2180954594","https://openalex.org/W2052835778","https://openalex.org/W2049003611","https://openalex.org/W2127804977","https://openalex.org/W2108418243","https://openalex.org/W164103134","https://openalex.org/W2787352659","https://openalex.org/W1970611213","https://openalex.org/W4206560911","https://openalex.org/W4372260270"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2,69],"designs":[3],"of":[4,7,27,34,53,106,130,133,141,151,192,201,238,246,285],"two":[5],"types":[6],"quantizers":[8,205],"are":[9,100,159,206,233,268],"presented.":[10,101],"The":[11,44,161,184,198,212,235],"first":[12,162],"type":[13,237],"is":[14,29,38,47,113,154,166,240,256,287],"designed":[15,241],"to":[16,89,242,259,265,290],"minimize":[17,90,243],"a":[18,41,83,92,104,144,170,193,261,273,277],"distortion":[19,45,93],"measure":[20,46,94],"under":[21,208],"the":[22,25,32,35,50,60,64,72,77,96,131,134,139,149,188,202,217,225,229,244,249,253,283,291],"constraint":[23,292],"that":[24,115,216,270],"number":[26,140,245],"levels":[28,247],"fixed":[30,120],"or":[31,248],"entropy":[33,210],"output":[36,250],"signal":[37],"bounded":[39],"below":[40,169],"given":[42],"value.":[43],"defined":[48],"asE[f(x,\\eta)],":[49],"expected":[51],"value":[52],"an":[54],"error":[55,230,255],"weighting":[56,231],"functionf(x,":[57],"\\eta),":[58],"wherexis":[59],"quantizer":[61,219,239],"input":[62,152,196],"and\\etais":[63],"corresponding":[65],"quantization":[66,191,254],"error.":[67],"This":[68,137],"departs":[70],"from":[71],"quautization":[73],"work":[74],"reported":[75],"in":[76,80,128,175,281],"literature":[78],"heretofore":[79],"allowingfto":[81],"be":[82,126,221],"function":[84,232],"ofxas":[85],"well":[86],"as\\eta.":[87],"Algorithms":[88],"such":[91],"ander":[95],"constraints":[97],"mentioned":[98,293],"above":[99],"They":[102],"use":[103],"combination":[105],"dynamic":[107,278],"programming":[108,279],"and":[109,228,276],"Fibonacci":[110,123],"search.":[111],"It":[112,173],"shown":[114],"iff(x,\\eta)is":[116],"semiconvex":[117],"in\\etafor":[118],"all":[119],"values":[121,153],"ofx,":[122],"search":[124,286],"can":[125,220],"used":[127],"one":[129],"steps":[132],"minimization":[135],"algorithm.":[136],"reduces":[138],"multiplications":[142],"by":[143,179],"factor":[145],"ofM/(5":[146],"\\log":[147],"M)when":[148],"range":[150],"divided":[155],"intoMparts.":[156],"Some":[157],"examples":[158],"considered.":[160],"deals":[163,186],"with":[164,187],"anf(x,\\eta)which":[165],"zero":[167],"if\\etais":[168],"certain":[171],"thresholdT(x)and\\eta_{2}-T_{2}(x)otherwise.":[172],"arises":[174],"coding":[176],"video":[177],"signals":[178],"differential":[180],"pulse-code":[181],"modulation":[182],"(PCM).":[183],"second":[185,236],"minimum":[189],"mean-square":[190],"truncated":[194],"Laplacian":[195],"density.":[197],"step":[199],"sizes":[200],"near-optimal":[203],"uniform":[204],"obtained":[207],"varions":[209],"constraints.":[211],"third":[213],"example":[214],"shows":[215],"optimal":[218],"asymmetric,":[222],"even":[223],"when":[224,252],"probability":[226],"density":[227],"symmetric.":[234],"entropy,":[251],"constrained":[257],"not":[258],"exceed":[260],"threshold":[262],"function.":[263],"Methods":[264],"design":[266],"them":[267],"presented":[269],"involve,":[271],"respectively,":[272],"geometric":[274],"construction":[275],"algorithm":[280],"which":[282],"domain":[284],"modified":[288],"according":[289],"above.":[294]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"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":3}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}