{"id":"https://openalex.org/W2094672014","doi":"https://doi.org/10.1109/tit.1986.1057150","title":"A simple derivation of Lloyd's classical result for the optimum scalar quantizer (Corresp.)","display_name":"A simple derivation of Lloyd's classical result for the optimum scalar quantizer (Corresp.)","publication_year":1986,"publication_date":"1986-03-01","ids":{"openalex":"https://openalex.org/W2094672014","doi":"https://doi.org/10.1109/tit.1986.1057150","mag":"2094672014"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1986.1057150","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1986.1057150","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/A5074305040","display_name":"N. Judell","orcid":null},"institutions":[{"id":"https://openalex.org/I17626003","display_name":"University of Rhode Island","ror":"https://ror.org/013ckk937","country_code":"US","type":"education","lineage":["https://openalex.org/I17626003"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"N. Judell","raw_affiliation_strings":["Electrical Engineering Department, University of Rhode Island, Kingston, RI, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical Engineering Department, University of Rhode Island, Kingston, RI, USA","institution_ids":["https://openalex.org/I17626003"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080469112","display_name":"Louis L. Scharf","orcid":"https://orcid.org/0000-0003-1764-9335"},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"L. Scharf","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Engineering Center, University of Colorado, Boulder, CO, USA","[Department of Electrical and Computer Engineering, Engineering Center, University of Colorado, Boulder, CO, USA]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Engineering Center, University of Colorado, Boulder, CO, USA","institution_ids":["https://openalex.org/I188538660"]},{"raw_affiliation_string":"[Department of Electrical and Computer Engineering, Engineering Center, University of Colorado, Boulder, CO, USA]","institution_ids":["https://openalex.org/I188538660"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6209,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.75340183,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"32","issue":"2","first_page":"326","last_page":"328"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10901","display_name":"Advanced Data Compression Techniques","score":0.9739999771118164,"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":0.9739999771118164,"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/T10320","display_name":"Neural Networks and Applications","score":0.9075000286102295,"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/T12879","display_name":"Distributed Sensor Networks and Detection Algorithms","score":0.9004999995231628,"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/quantization","display_name":"Quantization (signal processing)","score":0.7529823780059814},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.6806951761245728},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.6013267636299133},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5524029731750488},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49369606375694275},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.48446083068847656},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.428849995136261},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38819801807403564},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10431021451950073},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.061930060386657715}],"concepts":[{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.7529823780059814},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.6806951761245728},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.6013267636299133},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5524029731750488},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49369606375694275},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.48446083068847656},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.428849995136261},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38819801807403564},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10431021451950073},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.061930060386657715},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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.1986.1057150","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1986.1057150","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/W2048916503","https://openalex.org/W2068071220","https://openalex.org/W2109808436","https://openalex.org/W2136810817","https://openalex.org/W2150593711"],"related_works":["https://openalex.org/W1585007175","https://openalex.org/W2382521049","https://openalex.org/W2144385241","https://openalex.org/W2165950148","https://openalex.org/W4253593777","https://openalex.org/W2951497643","https://openalex.org/W4300101996","https://openalex.org/W2142393343","https://openalex.org/W3101625811","https://openalex.org/W2338854850"],"abstract_inverted_index":{"The":[0,22],"classical":[1],"result":[2,40],"of":[3,14,36],"Lloyd":[4],"for":[5],"the":[6,11,39,45,61],"optimum":[7,46],"scalar":[8],"quantizer":[9,62],"in":[10],"asymptotic":[12],"case":[13],"fine":[15],"quantization":[16],"is":[17,24,41,63],"derived":[18],"from":[19],"first":[20],"principles.":[21],"derivation":[23],"offered":[25],"as":[26],"a":[27,52,65],"simple":[28],"alternative":[29],"to":[30,43,60],"Lloyd's":[31],"original":[32],"and":[33,38],"elegant":[34],"piece":[35],"analysis,":[37],"used":[42],"derive":[44],"compander.":[47],"We":[48],"then":[49],"show":[50],"why":[51],"compander":[53],"that":[54],"presents":[55],"uniformly":[56],"distributed":[57],"random":[58],"variables":[59],"not":[64],"good":[66],"idea.":[67]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}