{"id":"https://openalex.org/W2295426907","doi":"https://doi.org/10.1109/isit.2010.5513599","title":"MMSE dimension","display_name":"MMSE dimension","publication_year":2010,"publication_date":"2010-06-01","ids":{"openalex":"https://openalex.org/W2295426907","doi":"https://doi.org/10.1109/isit.2010.5513599","mag":"2295426907"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2010.5513599","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2010.5513599","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 IEEE International Symposium on Information Theory","raw_type":"proceedings-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/A5100645159","display_name":"Yihong Wu","orcid":"https://orcid.org/0000-0001-9239-7671"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Yihong Wu","raw_affiliation_strings":["Department of Electrical Engineering, Princeton University, Princeton, NJ, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Princeton University, Princeton, NJ, USA","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103184697","display_name":"Sergio Verd\u00fa","orcid":"https://orcid.org/0000-0003-1254-9116"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sergio Verdu","raw_affiliation_strings":["Department of Electrical Engineering, Princeton University, Princeton, NJ, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Princeton University, Princeton, NJ, USA","institution_ids":["https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100645159"],"corresponding_institution_ids":["https://openalex.org/I20089843"],"apc_list":null,"apc_paid":null,"fwci":1.3552,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.82536383,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":93},"biblio":{"volume":null,"issue":null,"first_page":"1463","last_page":"1467"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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":0.9980999827384949,"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"}},{"id":"https://openalex.org/T10964","display_name":"Wireless Communication Security Techniques","score":0.9962999820709229,"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/dimension","display_name":"Dimension (graph theory)","score":0.8475254774093628},{"id":"https://openalex.org/keywords/minimum-mean-square-error","display_name":"Minimum mean square error","score":0.7568196058273315},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6834867000579834},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.6441345810890198},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5102348327636719},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.503555953502655},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4190298020839691},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.4040292501449585},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37579575181007385},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34532129764556885},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3071209192276001},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.166128009557724},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08184373378753662}],"concepts":[{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.8475254774093628},{"id":"https://openalex.org/C90652560","wikidata":"https://www.wikidata.org/wiki/Q11091747","display_name":"Minimum mean square error","level":3,"score":0.7568196058273315},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6834867000579834},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.6441345810890198},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5102348327636719},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.503555953502655},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4190298020839691},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.4040292501449585},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37579575181007385},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34532129764556885},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3071209192276001},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.166128009557724},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08184373378753662},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit.2010.5513599","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2010.5513599","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 IEEE International Symposium on Information Theory","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W611756847","https://openalex.org/W1504907986","https://openalex.org/W1536252645","https://openalex.org/W1900311801","https://openalex.org/W1986051087","https://openalex.org/W2005914283","https://openalex.org/W2024211125","https://openalex.org/W2043371182","https://openalex.org/W2057146486","https://openalex.org/W2082029531","https://openalex.org/W2092151549","https://openalex.org/W2111616148","https://openalex.org/W2489822048","https://openalex.org/W2550925785","https://openalex.org/W6630354972","https://openalex.org/W6647049202","https://openalex.org/W6697190056","https://openalex.org/W6729847528"],"related_works":["https://openalex.org/W1583991000","https://openalex.org/W2353396818","https://openalex.org/W2370473919","https://openalex.org/W1987895267","https://openalex.org/W2350519135","https://openalex.org/W4287123541","https://openalex.org/W3166424422","https://openalex.org/W2163615703","https://openalex.org/W2295426907","https://openalex.org/W2949310342"],"abstract_inverted_index":{"If":[0],"N":[1,17,107],"is":[2],"standard":[3],"Gaussian,":[4],"the":[5,31,37,44,49,61,75],"minimum":[6],"mean-square":[7],"error":[8],"(MMSE)":[9],"of":[10,34,43,46,77],"estimating":[11],"X":[12,35,57],"based":[13],"on":[14],"\u221a(snr)X":[15],"+":[16],"vanishes":[18],"at":[19],"least":[20],"as":[21,23,25,36,39],"fast":[22],"1/snr":[24],"snr":[26,40,47,78,87],"\u2192":[27,41],"\u221e.":[28],"We":[29,89],"define":[30],"MMSE":[32,62,80,99],"dimension":[33,63,84],"limit":[38],"\u221e":[42],"product":[45,76],"and":[48,79],"MMSE.":[50],"For":[51],"discrete,":[52],"absolutely":[53],"continuous":[54],"or":[55],"mixed":[56],"we":[58,72],"show":[59,73,91],"that":[60,74,92],"equals":[64],"R\u00e9nyi's":[65],"information":[66,83,95],"dimension.":[67,100],"However,":[68],"for":[69],"singular":[70],"X,":[71],"oscillates":[81],"around":[82],"periodically":[85],"in":[86],"(dB).":[88],"also":[90],"discrete":[93],"side":[94],"does":[96],"not":[97],"reduce":[98],"These":[101],"results":[102],"extend":[103],"considerably":[104],"beyond":[105],"Gaussian":[106],"under":[108],"various":[109],"technical":[110],"conditions.":[111]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}