{"id":"https://openalex.org/W2976910008","doi":"https://doi.org/10.3390/e21100957","title":"Upper Bound on the Joint Entropy of Correlated Sources Encoded by Good Lattices","display_name":"Upper Bound on the Joint Entropy of Correlated Sources Encoded by Good Lattices","publication_year":2019,"publication_date":"2019-09-29","ids":{"openalex":"https://openalex.org/W2976910008","doi":"https://doi.org/10.3390/e21100957","mag":"2976910008"},"language":"en","primary_location":{"id":"doi:10.3390/e21100957","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21100957","pdf_url":"https://www.mdpi.com/1099-4300/21/10/957/pdf?version=1571902685","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/21/10/957/pdf?version=1571902685","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112292863","display_name":"Christian D. Chapman","orcid":null},"institutions":[{"id":"https://openalex.org/I55732556","display_name":"Arizona State University","ror":"https://ror.org/03efmqc40","country_code":"US","type":"education","lineage":["https://openalex.org/I55732556"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Christian Chapman","raw_affiliation_strings":["School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85281, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85281, USA","institution_ids":["https://openalex.org/I55732556"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025118532","display_name":"Daniel W. Bliss","orcid":"https://orcid.org/0000-0001-8962-2954"},"institutions":[{"id":"https://openalex.org/I55732556","display_name":"Arizona State University","ror":"https://ror.org/03efmqc40","country_code":"US","type":"education","lineage":["https://openalex.org/I55732556"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daniel W. Bliss","raw_affiliation_strings":["School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85281, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85281, USA","institution_ids":["https://openalex.org/I55732556"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5112292863"],"corresponding_institution_ids":["https://openalex.org/I55732556"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.09583275,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"21","issue":"10","first_page":"957","last_page":"957"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10964","display_name":"Wireless Communication Security Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9970999956130981,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9921000003814697,"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/encoder","display_name":"Encoder","score":0.6882016062736511},{"id":"https://openalex.org/keywords/dither","display_name":"Dither","score":0.676693320274353},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.603192925453186},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5600876808166504},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.5532075762748718},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5401808619499207},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5031113028526306},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4816788136959076},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.47713160514831543},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4669659435749054},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3817720115184784},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.36909255385398865},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35526949167251587},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.14619609713554382},{"id":"https://openalex.org/keywords/bandwidth","display_name":"Bandwidth (computing)","score":0.14310631155967712},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11624640226364136},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.09709218144416809},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07734480500221252}],"concepts":[{"id":"https://openalex.org/C118505674","wikidata":"https://www.wikidata.org/wiki/Q42586063","display_name":"Encoder","level":2,"score":0.6882016062736511},{"id":"https://openalex.org/C70451592","wikidata":"https://www.wikidata.org/wiki/Q376493","display_name":"Dither","level":3,"score":0.676693320274353},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.603192925453186},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5600876808166504},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.5532075762748718},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5401808619499207},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5031113028526306},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4816788136959076},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.47713160514831543},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4669659435749054},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3817720115184784},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.36909255385398865},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35526949167251587},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.14619609713554382},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.14310631155967712},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11624640226364136},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.09709218144416809},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07734480500221252},{"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e21100957","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21100957","pdf_url":"https://www.mdpi.com/1099-4300/21/10/957/pdf?version=1571902685","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:d2550385b8114ccb9f798bb6c21ca408","is_oa":true,"landing_page_url":"https://doaj.org/article/d2550385b8114ccb9f798bb6c21ca408","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 21, Iss 10, p 957 (2019)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/21/10/957/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e21100957","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:7514288","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7514288","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e21100957","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21100957","pdf_url":"https://www.mdpi.com/1099-4300/21/10/957/pdf?version=1571902685","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2976910008.pdf","grobid_xml":"https://content.openalex.org/works/W2976910008.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W591033613","https://openalex.org/W1494099594","https://openalex.org/W1512015702","https://openalex.org/W1531726993","https://openalex.org/W1612188034","https://openalex.org/W2005762169","https://openalex.org/W2012366779","https://openalex.org/W2027157239","https://openalex.org/W2101847097","https://openalex.org/W2122621581","https://openalex.org/W2124097148","https://openalex.org/W2124317079","https://openalex.org/W2126483728","https://openalex.org/W2127309169","https://openalex.org/W2166266048","https://openalex.org/W2564237603","https://openalex.org/W2564985867","https://openalex.org/W2603121810","https://openalex.org/W2798049157","https://openalex.org/W2951353692","https://openalex.org/W2952047331","https://openalex.org/W2971002949","https://openalex.org/W4237963784","https://openalex.org/W4300840296"],"related_works":["https://openalex.org/W2389128124","https://openalex.org/W2364812720","https://openalex.org/W2138725603","https://openalex.org/W2050335563","https://openalex.org/W3001913892","https://openalex.org/W2273639645","https://openalex.org/W2050646564","https://openalex.org/W1507581877","https://openalex.org/W2024780258","https://openalex.org/W2536702343"],"abstract_inverted_index":{"Lattices":[0],"provide":[1],"useful":[2],"structure":[3],"for":[4,101,142],"distributed":[5],"coding":[6],"of":[7,48,57,81,98,119,128,144],"correlated":[8,63,130],"sources.":[9],"A":[10,46],"common":[11],"lattice":[12,25,36],"encoder":[13,88,150],"construction":[14],"is":[15,51,138],"to":[16,22,33,116,140],"first":[17],"round":[18],"an":[19,73],"observed":[20],"sequence":[21],"a":[23,34,71,82,122,135],"\u2018fine\u2019":[24],"with":[26],"dither,":[27],"then":[28],"produce":[29],"the":[30,38,54,67,93,96,117,126,145],"result\u2019s":[31],"modulo":[32],"\u2018coarse\u2019":[35],"as":[37],"encoding.":[39],"However,":[40],"such":[41,58,134],"encodings":[42,59],"may":[43],"be":[44],"jointly-dependent.":[45],"class":[47],"upper":[49,77],"bounds":[50,78,91,113],"established":[52],"on":[53,107],"conditional":[55],"entropy-rates":[56],"when":[60,105],"sources":[61],"are":[62,70,114],"and":[64,66,133],"Gaussian":[65,131],"lattices":[68],"involved":[69],"from":[72],"asymptotically-well-behaved":[74],"sequence.":[75],"These":[76],"guarantee":[79],"existence":[80],"joint\u2013compression":[83,136],"stage":[84,137],"which":[85],"can":[86],"increase":[87],"efficiency.":[89],"The":[90,112],"exploit":[92],"property":[94],"that":[95],"amount":[97],"possible":[99],"values":[100],"one":[102],"encoding":[103],"collapses":[104],"conditioned":[106],"other":[108],"sufficiently":[109],"informative":[110],"encodings.":[111],"applied":[115],"scenario":[118],"communicating":[120],"through":[121],"many-help-one":[123],"network":[124],"in":[125,147],"presence":[127],"strong":[129],"interferers,":[132],"seen":[139],"compensate":[141],"some":[143],"inefficiency":[146],"certain":[148],"simple":[149],"designs.":[151]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}