{"id":"https://openalex.org/W4386221229","doi":"https://doi.org/10.3390/e25091267","title":"Closed-Form Expressions of Upper Bound for Polarization-MDCSK System","display_name":"Closed-Form Expressions of Upper Bound for Polarization-MDCSK System","publication_year":2023,"publication_date":"2023-08-27","ids":{"openalex":"https://openalex.org/W4386221229","doi":"https://doi.org/10.3390/e25091267","pmid":"https://pubmed.ncbi.nlm.nih.gov/37761566"},"language":"en","primary_location":{"id":"doi:10.3390/e25091267","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e25091267","pdf_url":"https://www.mdpi.com/1099-4300/25/9/1267/pdf?version=1693195773","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","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/25/9/1267/pdf?version=1693195773","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016540715","display_name":"Meiyuan Miao","orcid":"https://orcid.org/0000-0002-6252-9271"},"institutions":[{"id":"https://openalex.org/I41198531","display_name":"Nanjing University of Posts and Telecommunications","ror":"https://ror.org/043bpky34","country_code":"CN","type":"education","lineage":["https://openalex.org/I41198531"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Meiyuan Miao","raw_affiliation_strings":["School of Communication and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210023, China"],"raw_orcid":"https://orcid.org/0000-0002-6252-9271","affiliations":[{"raw_affiliation_string":"School of Communication and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210023, China","institution_ids":["https://openalex.org/I41198531"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100403185","display_name":"Lin Wang","orcid":"https://orcid.org/0009-0002-9835-2719"},"institutions":[{"id":"https://openalex.org/I191208505","display_name":"Xiamen University","ror":"https://ror.org/00mcjh785","country_code":"CN","type":"education","lineage":["https://openalex.org/I191208505"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lin Wang","raw_affiliation_strings":["Department of Information and Communication Engineering, Xiamen University, Xiamen 361005, China"],"raw_orcid":"https://orcid.org/0000-0002-6698-129X","affiliations":[{"raw_affiliation_string":"Department of Information and Communication Engineering, Xiamen University, Xiamen 361005, China","institution_ids":["https://openalex.org/I191208505"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021956496","display_name":"Weikai Xu","orcid":null},"institutions":[{"id":"https://openalex.org/I191208505","display_name":"Xiamen University","ror":"https://ror.org/00mcjh785","country_code":"CN","type":"education","lineage":["https://openalex.org/I191208505"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Weikai Xu","raw_affiliation_strings":["Department of Information and Communication Engineering, Xiamen University, Xiamen 361005, China"],"raw_orcid":"https://orcid.org/0000-0001-7172-1807","affiliations":[{"raw_affiliation_string":"Department of Information and Communication Engineering, Xiamen University, Xiamen 361005, China","institution_ids":["https://openalex.org/I191208505"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5016540715"],"corresponding_institution_ids":["https://openalex.org/I41198531"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.1599,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.45060041,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"25","issue":"9","first_page":"1267","last_page":"1267"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9933000206947327,"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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9933000206947327,"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/closed-form-expression","display_name":"Closed-form expression","score":0.7754616737365723},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.7385040521621704},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6696587204933167},{"id":"https://openalex.org/keywords/additive-white-gaussian-noise","display_name":"Additive white Gaussian noise","score":0.6066129207611084},{"id":"https://openalex.org/keywords/expression","display_name":"Expression (computer science)","score":0.5896759629249573},{"id":"https://openalex.org/keywords/rayleigh-fading","display_name":"Rayleigh fading","score":0.5129894614219666},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.42483535408973694},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4152318239212036},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3911921977996826},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34753280878067017},{"id":"https://openalex.org/keywords/white-noise","display_name":"White noise","score":0.3374032974243164},{"id":"https://openalex.org/keywords/fading","display_name":"Fading","score":0.27149611711502075},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2175077497959137},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16952627897262573},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.13900896906852722},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12847012281417847},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10400158166885376},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08440765738487244}],"concepts":[{"id":"https://openalex.org/C4530962","wikidata":"https://www.wikidata.org/wiki/Q777407","display_name":"Closed-form expression","level":2,"score":0.7754616737365723},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7385040521621704},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6696587204933167},{"id":"https://openalex.org/C169334058","wikidata":"https://www.wikidata.org/wiki/Q353292","display_name":"Additive white Gaussian noise","level":3,"score":0.6066129207611084},{"id":"https://openalex.org/C90559484","wikidata":"https://www.wikidata.org/wiki/Q778379","display_name":"Expression (computer science)","level":2,"score":0.5896759629249573},{"id":"https://openalex.org/C56985126","wikidata":"https://www.wikidata.org/wiki/Q854039","display_name":"Rayleigh fading","level":4,"score":0.5129894614219666},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.42483535408973694},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4152318239212036},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3911921977996826},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34753280878067017},{"id":"https://openalex.org/C112633086","wikidata":"https://www.wikidata.org/wiki/Q381287","display_name":"White noise","level":2,"score":0.3374032974243164},{"id":"https://openalex.org/C81978471","wikidata":"https://www.wikidata.org/wiki/Q1196572","display_name":"Fading","level":3,"score":0.27149611711502075},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2175077497959137},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16952627897262573},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.13900896906852722},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12847012281417847},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10400158166885376},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08440765738487244},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e25091267","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e25091267","pdf_url":"https://www.mdpi.com/1099-4300/25/9/1267/pdf?version=1693195773","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":"pmid:37761566","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/37761566","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:10528149","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/10528149","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC10528149/pdf/entropy-25-01267.pdf","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"},{"id":"pmh:oai:doaj.org/article:a9c26297f6b142208cba8b94819f9d34","is_oa":true,"landing_page_url":"https://doaj.org/article/a9c26297f6b142208cba8b94819f9d34","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 25, Iss 9, p 1267 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/25/9/1267/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e25091267","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; Volume 25; Issue 9; Pages: 1267","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e25091267","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e25091267","pdf_url":"https://www.mdpi.com/1099-4300/25/9/1267/pdf?version=1693195773","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":[{"id":"https://openalex.org/F4320320863","display_name":"University College Cork","ror":"https://ror.org/03265fv13"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4386221229.pdf"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W1504535869","https://openalex.org/W1962263196","https://openalex.org/W2133177257","https://openalex.org/W2142432203","https://openalex.org/W2508907196","https://openalex.org/W2524503450","https://openalex.org/W2539200098","https://openalex.org/W2613637551","https://openalex.org/W2749537481","https://openalex.org/W2810223892","https://openalex.org/W2985717788","https://openalex.org/W3011436510","https://openalex.org/W3017225612","https://openalex.org/W3040083384","https://openalex.org/W3045597887","https://openalex.org/W3100088463","https://openalex.org/W3130899136","https://openalex.org/W4210858837","https://openalex.org/W4226266619","https://openalex.org/W4313839108","https://openalex.org/W4381296758","https://openalex.org/W6728740949","https://openalex.org/W6770099587"],"related_works":["https://openalex.org/W2143696403","https://openalex.org/W1974392290","https://openalex.org/W2146473084","https://openalex.org/W1981270958","https://openalex.org/W2099812103","https://openalex.org/W2055927355","https://openalex.org/W2073378780","https://openalex.org/W2074565401","https://openalex.org/W2103813964","https://openalex.org/W1607924090"],"abstract_inverted_index":{"-ary":[0],"differential":[1],"chaos":[2],"shift":[3],"keying":[4],"(P-MDCSK)":[5],"has":[6,29],"been":[7,30],"expressed":[8],"using":[9],"a":[10,24,64,98,121],"tight":[11],"upper":[12,38,151],"bound":[13],"with":[14],"the":[15,19,37,44,53,68,102,105,115,129,132,140,150,163],"Q-function.":[16,69],"However,":[17],"evaluating":[18],"Q-function":[20],"directly":[21],"is":[22,60,112],"not":[23],"closed":[25,34],"expression":[26,35,59],"and":[27,85,104],"there":[28,95],"less":[31],"work":[32],"on":[33,52],"for":[36,158],"bound.":[39],"In":[40],"order":[41],"to":[42],"solve":[43],"problem,":[45],"this":[46],"paper":[47],"presents":[48],"approximate":[49,117,146],"closed-form":[50,71,107,118,147,166],"expressions":[51,72,119,148],"error":[54,134],"probability":[55],"of":[56,67,124,149],"P-MDCSK.":[57],"This":[58],"derived":[61,106],"by":[62],"employing":[63],"polynomial":[65],"approximation":[66],"These":[70],"are":[73],"verified":[74],"through":[75],"simulations":[76,103,130],"conducted":[77],"under":[78],"both":[79],"additive":[80],"white":[81],"Gaussian":[82],"noise":[83],"(AWGN)":[84],"multipath":[86],"Rayleigh":[87],"fading":[88],"channels.":[89],"The":[90],"simulation":[91],"results":[92],"reveal":[93],"that":[94,114],"exists":[96],"only":[97,144],"negligible":[99],"gap":[100],"between":[101],"expressions.":[108],"For":[109],"example,":[110],"it":[111,153],"observed":[113],"theoretical":[116],"exhibit":[120],"marginal":[122],"deviation":[123],"approximately":[125],"0.4":[126],"dB":[127],"from":[128],"when":[131],"bit":[133],"rate":[135],"(BER)":[136],"reaches":[137],"10-4.":[138],"Although":[139],"proposed":[141],"method":[142,157],"can":[143],"give":[145],"bound,":[152],"provides":[154],"an":[155],"effective":[156],"other":[159],"communication":[160],"schemes":[161],"where":[162],"exact":[164],"BER":[165],"formula":[167],"cannot":[168],"be":[169],"obtained.":[170]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}