{"id":"https://openalex.org/W2142228262","doi":"https://doi.org/10.1109/tit.1979.1056067","title":"Asymptotically optimal block quantization","display_name":"Asymptotically optimal block quantization","publication_year":1979,"publication_date":"1979-07-01","ids":{"openalex":"https://openalex.org/W2142228262","doi":"https://doi.org/10.1109/tit.1979.1056067","mag":"2142228262"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1979.1056067","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1979.1056067","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/A5016272725","display_name":"A. Gersho","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"A. Gersho","raw_affiliation_strings":["Bell Laboratories, Inc., Murray Hill, NJ, USA","Bell Labs., Inc., Murray Hill, NJ, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bell Laboratories, Inc., Murray Hill, NJ, USA","institution_ids":[]},{"raw_affiliation_string":"Bell Labs., Inc., Murray Hill, NJ, USA","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5016272725"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":15.5213,"has_fulltext":false,"cited_by_count":874,"citation_normalized_percentile":{"value":0.99383381,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"25","issue":"4","first_page":"373","last_page":"380"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10964","display_name":"Wireless Communication Security Techniques","score":0.9980000257492065,"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"}},"topics":[{"id":"https://openalex.org/T10964","display_name":"Wireless Communication Security Techniques","score":0.9980000257492065,"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/T10901","display_name":"Advanced Data Compression Techniques","score":0.9979000091552734,"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/T12879","display_name":"Distributed Sensor Networks and Detection Algorithms","score":0.9965000152587891,"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/companding","display_name":"Companding","score":0.7303752899169922},{"id":"https://openalex.org/keywords/quantization","display_name":"Quantization (signal processing)","score":0.6123044490814209},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46461617946624756},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45395559072494507},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3739280700683594},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37120676040649414},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3620222210884094},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.26061415672302246}],"concepts":[{"id":"https://openalex.org/C104250799","wikidata":"https://www.wikidata.org/wiki/Q1780765","display_name":"Companding","level":4,"score":0.7303752899169922},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.6123044490814209},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46461617946624756},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45395559072494507},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3739280700683594},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37120676040649414},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3620222210884094},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.26061415672302246},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0},{"id":"https://openalex.org/C40409654","wikidata":"https://www.wikidata.org/wiki/Q375889","display_name":"Orthogonal frequency-division multiplexing","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1979.1056067","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1979.1056067","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":17,"referenced_works":["https://openalex.org/W1589055062","https://openalex.org/W1972736931","https://openalex.org/W1978382377","https://openalex.org/W2001968606","https://openalex.org/W2004003571","https://openalex.org/W2068071220","https://openalex.org/W2071740498","https://openalex.org/W2072649299","https://openalex.org/W2137263269","https://openalex.org/W2146519989","https://openalex.org/W2150593711","https://openalex.org/W2152316618","https://openalex.org/W2156908459","https://openalex.org/W4210849061","https://openalex.org/W4230860499","https://openalex.org/W4240853087","https://openalex.org/W6651367664"],"related_works":["https://openalex.org/W2141622453","https://openalex.org/W2116875580","https://openalex.org/W4364304235","https://openalex.org/W4312092255","https://openalex.org/W2014620860","https://openalex.org/W2135644862","https://openalex.org/W2057904974","https://openalex.org/W2013738012","https://openalex.org/W3182465333","https://openalex.org/W3136903108"],"abstract_inverted_index":{"In":[0,240],"1948":[1],"W.":[2],"R.":[3],"Bennett":[4],"used":[5],"a":[6,90,101,111,165,215,226,250,264,268],"companding":[7,298],"model":[8],"for":[9,31,93,154,160,185,192,219,229,237,242,277],"nonuniform":[10],"quantization":[11,109],"and":[12,56,84,180,188,191],"proposed":[13],"the":[14,32,41,50,54,63,66,75,78,124,132,142,155,186,193,234],"formula":[15,106],"<tex":[16,37,45,57,128,169,199,243],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[17,38,46,58,129,170,200,244],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">D":[18],"\\:":[19,21,23,25],"=":[20,246],"\\frac{1}{12N^{2}}":[22],"\\int":[24],"p(x)":[26],"[":[27],"\u00c9(x)":[28],"]^{-2}":[29],"\\dx</tex>":[30],"mean-square":[33],"quantizing":[34,157],"error":[35],"where":[36,110,127],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">N</tex>":[39,130],"is":[40,49,62,82,87,89,116,120,138,148,282,286],"number":[42,79,133],"of":[43,53,65,80,96,113,134,164,195,214,217,262],"levels,":[44],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">p</tex>":[47],"(x)":[48,61],"probability":[51],"density":[52],"input,":[55],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">E":[59],"\\prime</tex>":[60],"slope":[64],"compressor":[67],"curve.":[68],"The":[69,118,173,205,260],"formula,":[70,145],"an":[71,146,152,211,274,292],"approximation":[72],"based":[73,122],"on":[74,123,233],"assumption":[76],"that":[77,254],"levels":[81],"large":[83],"overload":[85],"distortion":[86,236],"negligible,":[88],"useful":[91],"tool":[92],"analytical":[94],"studies":[95],"quantization.":[97,221],"This":[98],"paper":[99],"gives":[100,210],"heuristic":[102,144,207],"argument":[103],"generalizing":[104],"Bennett's":[105],"to":[107,151,182,225,290],"block":[108,162,167,197,238,265,269,297],"vector":[112],"random":[114,280],"variables":[115],"quantized.":[117],"approach":[119,208,223],"again":[121],"asymptotic":[125],"situation":[126],",":[131],"quantized":[135],"output":[136],"vectors,":[137],"very":[139],"large.":[140],"Using":[141],"resulting":[143],"optimization":[147],"performed":[149],"leading":[150],"expression":[153],"minimum":[156,235],"noise":[158],"attainable":[159],"any":[161],"quantizer":[163,266,276,294],"given":[166],"size":[168],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">k</tex>":[171],".":[172,204],"results":[174,179,184],"are":[175],"consistent":[176],"with":[177,273,295],"Zador's":[178],"specialize":[181],"known":[183],"one-":[187],"two-dimensional":[189],"cases":[190],"case":[194],"infinite":[196],"length":[198],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">(k":[201],"\\rightarrow":[202],"\\infty)</tex>":[203],"same":[206],"also":[209,283],"alternate":[212],"derivation":[213],"bound":[216,253],"Elias":[218],"multidimensional":[220],"Our":[222],"leads":[224],"rigorous":[227],"method":[228],"obtaining":[230],"upper":[231,252],"bounds":[232],"quantizers.":[239],"particular,":[241],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">k":[245],"3</tex>":[247],"we":[248],"give":[249],"tight":[251],"may":[255],"in":[256],"fact":[257],"be":[258],"exact.":[259],"idea":[261],"representing":[263],"by":[267],"\"compressor\"":[270],"mapping":[271],"followed":[272],"optimal":[275,293],"uniformly":[278],"distributed":[279],"vectors":[281],"explored.":[284],"It":[285],"not":[287],"always":[288],"possible":[289],"represent":[291],"this":[296],"model.":[299]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":12},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":15},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":12},{"year":2015,"cited_by_count":20},{"year":2014,"cited_by_count":26},{"year":2013,"cited_by_count":22},{"year":2012,"cited_by_count":30}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}