{"id":"https://openalex.org/W1991569621","doi":"https://doi.org/10.1109/tit.1986.1057169","title":"A tree coding theorem for stationary Gaussian sources and the squared-error distortion measure","display_name":"A tree coding theorem for stationary Gaussian sources and the squared-error distortion measure","publication_year":1986,"publication_date":"1986-03-01","ids":{"openalex":"https://openalex.org/W1991569621","doi":"https://doi.org/10.1109/tit.1986.1057169","mag":"1991569621"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1986.1057169","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1986.1057169","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/A5088315894","display_name":"B. Mazor","orcid":null},"institutions":[{"id":"https://openalex.org/I165799507","display_name":"Rensselaer Polytechnic Institute","ror":"https://ror.org/01rtyzb94","country_code":"US","type":"education","lineage":["https://openalex.org/I165799507"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"B. Mazor","raw_affiliation_strings":["Electrical, Computer, and Systems Engineering Department, Rensselaer Polytechnic Institute, Troy, NY, USA","GTE Laboratories, Inc., Waltham, MA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical, Computer, and Systems Engineering Department, Rensselaer Polytechnic Institute, Troy, NY, USA","institution_ids":["https://openalex.org/I165799507"]},{"raw_affiliation_string":"GTE Laboratories, Inc., Waltham, MA, USA","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028597605","display_name":"William A. Pearlman","orcid":"https://orcid.org/0000-0002-4978-6812"},"institutions":[{"id":"https://openalex.org/I165799507","display_name":"Rensselaer Polytechnic Institute","ror":"https://ror.org/01rtyzb94","country_code":"US","type":"education","lineage":["https://openalex.org/I165799507"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"W. Pearlman","raw_affiliation_strings":["Electrical, Computer, and Systems Engineering Department, Rensselaer Polytechnic Institute, Troy, NY, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical, Computer, and Systems Engineering Department, Rensselaer Polytechnic Institute, Troy, NY, USA","institution_ids":["https://openalex.org/I165799507"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I165799507"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.10764322,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"32","issue":"2","first_page":"156","last_page":"165"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9937999844551086,"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":0.9937999844551086,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9936000108718872,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10964","display_name":"Wireless Communication Security Techniques","score":0.989799976348877,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.769699215888977},{"id":"https://openalex.org/keywords/shannon\u2013fano-coding","display_name":"Shannon\u2013Fano coding","score":0.5695087313652039},{"id":"https://openalex.org/keywords/variable-length-code","display_name":"Variable-length code","score":0.5603092908859253},{"id":"https://openalex.org/keywords/ergodic-theory","display_name":"Ergodic theory","score":0.5348492860794067},{"id":"https://openalex.org/keywords/gaussian-random-field","display_name":"Gaussian random field","score":0.49261409044265747},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.4775041937828064},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.47592881321907043},{"id":"https://openalex.org/keywords/shannons-source-coding-theorem","display_name":"Shannon's source coding theorem","score":0.44108515977859497},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.42952096462249756},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3394368588924408},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3016340136528015},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.2552265524864197},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.22715407609939575},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22341859340667725},{"id":"https://openalex.org/keywords/binary-entropy-function","display_name":"Binary entropy function","score":0.20075303316116333},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.1266283392906189},{"id":"https://openalex.org/keywords/maximum-entropy-thermodynamics","display_name":"Maximum entropy thermodynamics","score":0.10337689518928528}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.769699215888977},{"id":"https://openalex.org/C130811719","wikidata":"https://www.wikidata.org/wiki/Q2645","display_name":"Shannon\u2013Fano coding","level":4,"score":0.5695087313652039},{"id":"https://openalex.org/C60603091","wikidata":"https://www.wikidata.org/wiki/Q2981616","display_name":"Variable-length code","level":3,"score":0.5603092908859253},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.5348492860794067},{"id":"https://openalex.org/C51267290","wikidata":"https://www.wikidata.org/wiki/Q5527848","display_name":"Gaussian random field","level":4,"score":0.49261409044265747},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.4775041937828064},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47592881321907043},{"id":"https://openalex.org/C177409962","wikidata":"https://www.wikidata.org/wiki/Q2411312","display_name":"Shannon's source coding theorem","level":5,"score":0.44108515977859497},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.42952096462249756},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3394368588924408},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3016340136528015},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.2552265524864197},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.22715407609939575},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22341859340667725},{"id":"https://openalex.org/C44415725","wikidata":"https://www.wikidata.org/wiki/Q4913893","display_name":"Binary entropy function","level":3,"score":0.20075303316116333},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.1266283392906189},{"id":"https://openalex.org/C49775889","wikidata":"https://www.wikidata.org/wiki/Q6795896","display_name":"Maximum entropy thermodynamics","level":4,"score":0.10337689518928528},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1986.1057169","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1986.1057169","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":[{"display_name":"Life in Land","score":0.7200000286102295,"id":"https://metadata.un.org/sdg/15"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1502506486","https://openalex.org/W1975715138","https://openalex.org/W1978734565","https://openalex.org/W1989008275","https://openalex.org/W1989931183","https://openalex.org/W1994451489","https://openalex.org/W2005447187","https://openalex.org/W2007752401","https://openalex.org/W2021436622","https://openalex.org/W2071101972","https://openalex.org/W2081838720","https://openalex.org/W2085494434","https://openalex.org/W2104189974","https://openalex.org/W2145780659","https://openalex.org/W3015297855","https://openalex.org/W4210849731","https://openalex.org/W4239680662"],"related_works":["https://openalex.org/W2364472724","https://openalex.org/W1968693394","https://openalex.org/W2952888030","https://openalex.org/W2136452321","https://openalex.org/W2765672289","https://openalex.org/W1540819826","https://openalex.org/W2155973165","https://openalex.org/W4251361844","https://openalex.org/W2792852228","https://openalex.org/W4230922438"],"abstract_inverted_index":{"For":[0],"a":[1,73],"class":[2],"of":[3,29,50],"stationary":[4,54],"Gaussian":[5,70],"sources":[6,71],"and":[7,39,45],"the":[8,30,41,48,58,78,86],"squared-error":[9],"distortion":[10],"measure,":[11],"an":[12,36],"asymptotically":[13],"optimal":[14],"tree":[15,21],"coding":[16,43,60,87],"scheme":[17],"is":[18,33,62,66],"derived":[19,34],"using":[20,40],"codes":[22],"with":[23,53,72,82],"finite":[24],"branch":[25],"length.":[26],"The":[27,64],"distribution":[28],"reproduction":[31],"process":[32],"in":[35],"explicit":[37],"form,":[38],"random":[42],"argument":[44],"results":[46],"from":[47],"theory":[49],"branching":[51],"processes":[52],"ergodic":[55],"environmental":[56],"processes,":[57],"source":[59],"theorem":[61,65],"proved.":[63],"applicable":[67],"to":[68],"all":[69],"power":[74],"spectrum":[75],"that":[76],"satisfies":[77],"Lip":[79],"1":[80],"condition":[81],"no":[83],"restriction":[84],"on":[85],"rate.":[88]},"counts_by_year":[],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}
