{"id":"https://openalex.org/W2168896888","doi":"https://doi.org/10.1109/isit.2004.1365384","title":"On the discreteness of the capacity-achieving probability measure of conditional gaussian channels","display_name":"On the discreteness of the capacity-achieving probability measure of conditional gaussian channels","publication_year":2004,"publication_date":"2004-12-23","ids":{"openalex":"https://openalex.org/W2168896888","doi":"https://doi.org/10.1109/isit.2004.1365384","mag":"2168896888"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2004.1365384","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2004.1365384","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings.","raw_type":"proceedings-article"},"type":"conference-paper","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/A5010336848","display_name":"Terence Chan","orcid":"https://orcid.org/0000-0002-6550-7203"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"T.H. Chan","raw_affiliation_strings":["Department of Electrical & Computer Engineering, University of Toronto, Toronto, ONT, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical & Computer Engineering, University of Toronto, Toronto, ONT, Canada","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077846751","display_name":"Frank R. Kschischang","orcid":"https://orcid.org/0000-0002-4274-1785"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"F.R. Kschischang","raw_affiliation_strings":["Department of Electrical & Computer Engineering, University of Toronto, Toronto, ONT, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical & Computer Engineering, University of Toronto, Toronto, ONT, Canada","institution_ids":["https://openalex.org/I185261750"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I185261750"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"347","last_page":"347"},"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/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.9995999932289124,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9993000030517578,"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/measure","display_name":"Measure (data warehouse)","score":0.6741983890533447},{"id":"https://openalex.org/keywords/probability-mass-function","display_name":"Probability mass function","score":0.6306194067001343},{"id":"https://openalex.org/keywords/probability-measure","display_name":"Probability measure","score":0.6157336235046387},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.5853905081748962},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5805923938751221},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5526394248008728},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.5353596210479736},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.5254610776901245},{"id":"https://openalex.org/keywords/conditional-probability-distribution","display_name":"Conditional probability distribution","score":0.5243018865585327},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.49606379866600037},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4851720929145813},{"id":"https://openalex.org/keywords/conditional-probability","display_name":"Conditional probability","score":0.46728619933128357},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.45207950472831726},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4022065997123718},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2786329388618469},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.26891180872917175},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2657718062400818},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1754665970802307},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.17209655046463013},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.14385941624641418},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1003074049949646},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.0978570282459259}],"concepts":[{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.6741983890533447},{"id":"https://openalex.org/C197096303","wikidata":"https://www.wikidata.org/wiki/Q869887","display_name":"Probability mass function","level":3,"score":0.6306194067001343},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.6157336235046387},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.5853905081748962},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5805923938751221},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5526394248008728},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.5353596210479736},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.5254610776901245},{"id":"https://openalex.org/C43555835","wikidata":"https://www.wikidata.org/wiki/Q2300258","display_name":"Conditional probability distribution","level":2,"score":0.5243018865585327},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.49606379866600037},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4851720929145813},{"id":"https://openalex.org/C44492722","wikidata":"https://www.wikidata.org/wiki/Q327069","display_name":"Conditional probability","level":2,"score":0.46728619933128357},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.45207950472831726},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4022065997123718},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2786329388618469},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.26891180872917175},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2657718062400818},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1754665970802307},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.17209655046463013},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.14385941624641418},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1003074049949646},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0978570282459259},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"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/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit.2004.1365384","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2004.1365384","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings.","raw_type":"proceedings-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/W2031724611","https://openalex.org/W2101506680","https://openalex.org/W2111930879","https://openalex.org/W2154750699","https://openalex.org/W6675259992"],"related_works":["https://openalex.org/W4383821505","https://openalex.org/W2017723308","https://openalex.org/W4248569664","https://openalex.org/W1523756637","https://openalex.org/W283024757","https://openalex.org/W23363913","https://openalex.org/W2156656573","https://openalex.org/W2062631641","https://openalex.org/W2198158822","https://openalex.org/W2317246346"],"abstract_inverted_index":{"A":[0],"conditional":[1],"Gaussian":[2,24],"(CG)":[3],"channel":[4,9,14,20,45,59,71],"is":[5,23,47,52,74,80,99,112],"a":[6,19,31,102],"discrete-time":[7],"memoryless":[8],"such":[10],"that":[11,22],"an":[12,27,64],"admissible":[13],"input":[15,60,65,72,77],"gives":[16],"rise":[17],"to":[18,82],"output":[21,62],"distributed":[25,114],"with":[26,63,101],"expectation":[28],"vector":[29],"and":[30,38,43,61,87,109],"covariance":[32],"matrix.":[33],"In":[34],"this":[35],"paper,":[36],"closed":[37],"bounded":[39],"subset":[40],"of":[41,96,105],"receiver,":[42],"the":[44,49,58,70,93,97,110],"constraint":[46,51],"called":[48],"bounded-input":[50],"presented.":[53],"The":[54],"mutual":[55],"information":[56],"between":[57],"probability":[66,78,94,106],"measure":[67,79],"which":[68],"satisfies":[69],"constraints":[73],"maximized.":[75],"An":[76],"said":[81],"be":[83],"discrete":[84,100],"in":[85,89],"amplitude":[86,98],"uniform":[88],"phase":[90,111],"(DAUP)":[91],"if":[92],"distribution":[95],"finite":[103],"number":[104],"mass":[107],"points,":[108],"uniformly":[113]},"counts_by_year":[],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
