{"id":"https://openalex.org/W2339081671","doi":"https://doi.org/10.1109/tit.2017.2690994","title":"Achievable Rates for Gaussian Degraded Relay Channels With Non-Vanishing Error Probabilities","display_name":"Achievable Rates for Gaussian Degraded Relay Channels With Non-Vanishing Error Probabilities","publication_year":2017,"publication_date":"2017-04-04","ids":{"openalex":"https://openalex.org/W2339081671","doi":"https://doi.org/10.1109/tit.2017.2690994","mag":"2339081671"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2017.2690994","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2017.2690994","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1604.01566","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081121300","display_name":"Silas L. Fong","orcid":"https://orcid.org/0000-0002-8762-5294"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Silas L. Fong","raw_affiliation_strings":["Department of Electrical and Computer Engineering, National University of Singapore, Singapore","[Dept of Electrical and Computer Engineering, National University of Singapore, Singapore]"],"raw_orcid":"https://orcid.org/0000-0002-8762-5294","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, National University of Singapore, Singapore","institution_ids":["https://openalex.org/I165932596"]},{"raw_affiliation_string":"[Dept of Electrical and Computer Engineering, National University of Singapore, Singapore]","institution_ids":["https://openalex.org/I165932596"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058345431","display_name":"Vincent Y. F. Tan","orcid":"https://orcid.org/0000-0002-5008-4527"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Vincent Y. F. Tan","raw_affiliation_strings":["Department of Mathematics, National University of Singapore, Singapore","[Dept of Electrical and Computer Engineering, National University of Singapore, Singapore]"],"raw_orcid":"https://orcid.org/0000-0002-5008-4527","affiliations":[{"raw_affiliation_string":"Department of Mathematics, National University of Singapore, Singapore","institution_ids":["https://openalex.org/I165932596"]},{"raw_affiliation_string":"[Dept of Electrical and Computer Engineering, National University of Singapore, Singapore]","institution_ids":["https://openalex.org/I165932596"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00524753,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"63","issue":"7","first_page":"4183","last_page":"4201"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":1.0,"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":1.0,"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/T10148","display_name":"Advanced MIMO Systems Optimization","score":0.9965000152587891,"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/converse","display_name":"Converse","score":0.8411411643028259},{"id":"https://openalex.org/keywords/relay","display_name":"Relay","score":0.7718973755836487},{"id":"https://openalex.org/keywords/relay-channel","display_name":"Relay channel","score":0.6580328345298767},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.563271701335907},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5574138164520264},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5513614416122437},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.518022358417511},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.4833190441131592},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.4356902539730072},{"id":"https://openalex.org/keywords/fading","display_name":"Fading","score":0.4335308074951172},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.4270574152469635},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.42176929116249084},{"id":"https://openalex.org/keywords/binary-symmetric-channel","display_name":"Binary symmetric channel","score":0.41372767090797424},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3890606462955475},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3674688935279846},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3666705787181854},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.33677375316619873},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.296609491109848},{"id":"https://openalex.org/keywords/channel-code","display_name":"Channel code","score":0.2740175724029541},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2496899962425232},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2369639277458191},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.22156229615211487},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.09505429863929749}],"concepts":[{"id":"https://openalex.org/C2776809875","wikidata":"https://www.wikidata.org/wiki/Q1375963","display_name":"Converse","level":2,"score":0.8411411643028259},{"id":"https://openalex.org/C2778156585","wikidata":"https://www.wikidata.org/wiki/Q174053","display_name":"Relay","level":3,"score":0.7718973755836487},{"id":"https://openalex.org/C46257984","wikidata":"https://www.wikidata.org/wiki/Q7310895","display_name":"Relay channel","level":4,"score":0.6580328345298767},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.563271701335907},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5574138164520264},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5513614416122437},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.518022358417511},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4833190441131592},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.4356902539730072},{"id":"https://openalex.org/C81978471","wikidata":"https://www.wikidata.org/wiki/Q1196572","display_name":"Fading","level":3,"score":0.4335308074951172},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.4270574152469635},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.42176929116249084},{"id":"https://openalex.org/C173988684","wikidata":"https://www.wikidata.org/wiki/Q863510","display_name":"Binary symmetric channel","level":4,"score":0.41372767090797424},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3890606462955475},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3674688935279846},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3666705787181854},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.33677375316619873},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.296609491109848},{"id":"https://openalex.org/C166366890","wikidata":"https://www.wikidata.org/wiki/Q602136","display_name":"Channel code","level":3,"score":0.2740175724029541},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2496899962425232},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2369639277458191},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.22156229615211487},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.09505429863929749},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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},{"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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tit.2017.2690994","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2017.2690994","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"},{"id":"pmh:oai:arXiv.org:1604.01566","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1604.01566","pdf_url":"https://arxiv.org/pdf/1604.01566","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2339081671","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1604.01566.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1604.01566","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1604.01566","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1604.01566","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1604.01566","pdf_url":"https://arxiv.org/pdf/1604.01566","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7368699825","display_name":null,"funder_award_id":"R-263-000-B37-133","funder_id":"https://openalex.org/F4320320698","funder_display_name":"National University of Singapore"},{"id":"https://openalex.org/G7529095484","display_name":null,"funder_award_id":"R-263-000-B61-113","funder_id":"https://openalex.org/F4320320751","funder_display_name":"Ministry of Education - Singapore"}],"funders":[{"id":"https://openalex.org/F4320320698","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49"},{"id":"https://openalex.org/F4320320751","display_name":"Ministry of Education - Singapore","ror":"https://ror.org/01kcva023"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2339081671.pdf","grobid_xml":"https://content.openalex.org/works/W2339081671.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W79265410","https://openalex.org/W1494099594","https://openalex.org/W1588709600","https://openalex.org/W1775810734","https://openalex.org/W1991759432","https://openalex.org/W2000311239","https://openalex.org/W2001921622","https://openalex.org/W2008825922","https://openalex.org/W2022136008","https://openalex.org/W2050437625","https://openalex.org/W2051707898","https://openalex.org/W2054922961","https://openalex.org/W2098567664","https://openalex.org/W2103326592","https://openalex.org/W2106864314","https://openalex.org/W2144476727","https://openalex.org/W2167447263","https://openalex.org/W2212422103","https://openalex.org/W2276299490","https://openalex.org/W2963434345","https://openalex.org/W3103381487","https://openalex.org/W4251984466","https://openalex.org/W6675088578"],"related_works":["https://openalex.org/W2962872424","https://openalex.org/W2963368320","https://openalex.org/W2742949471","https://openalex.org/W3177379484","https://openalex.org/W2515326210","https://openalex.org/W2951789634","https://openalex.org/W1810714366","https://openalex.org/W2766775506","https://openalex.org/W2604822672","https://openalex.org/W1553451787","https://openalex.org/W2577226118","https://openalex.org/W1746209723","https://openalex.org/W2807144684","https://openalex.org/W2951345697","https://openalex.org/W2887270792","https://openalex.org/W2787585953","https://openalex.org/W2949733436","https://openalex.org/W2720283205","https://openalex.org/W1816874293","https://openalex.org/W3103875393"],"abstract_inverted_index":{"This":[0],"paper":[1],"revisits":[2],"the":[3,9,15,18,26,32,35,40,51,61,71,76,83,99,117,121,140,147,168,175,179,182,189,193],"Gaussian":[4,106],"degraded":[5,23],"relay":[6,41],"channel,":[7],"where":[8],"link":[10,27],"that":[11,28,70],"carries":[12,29],"information":[13,30],"from":[14,31,146],"source":[16,33,38,180],"to":[17,34,44,167],"destination":[19],"is":[20,53,57,86,96,130,159],"a":[21,113],"physically":[22],"version":[24],"of":[25,50,82,124,150,170,174,192],"relay.":[36,183],"The":[37,48,80,127],"and":[39,55,112,120,181,185],"are":[42,144,197],"subject":[43],"expected":[45,109],"power":[46,103,110,169],"constraints.":[47],"\u03b5-capacity":[49],"channel":[52,72],"characterized":[54],"it":[56],"strictly":[58],"larger":[59],"than":[60],"capacity":[62],"for":[63,105],"any":[64],"\u03b5":[65],">":[66],"0,":[67],"which":[68,95,143],"implies":[69],"does":[73],"not":[74],"possess":[75],"strong":[77],"converse":[78,128],"property.":[79],"proof":[81],"achievability":[84],"part":[85,129],"based":[87],"on":[88,139,163,188],"several":[89],"key":[90],"ideas:":[91],"block":[92,118,125],"Markov":[93],"coding,":[94],"used":[97],"in":[98],"classical":[100],"decode-forward":[101],"strategy,":[102],"control":[104],"channels":[107],"under":[108],"constraints,":[111],"careful":[114],"scaling":[115],"between":[116],"size":[119],"total":[122],"number":[123],"uses.":[126],"proved":[131],"by":[132,161,178],"first":[133],"establishing":[134],"two":[135],"non-asymptotic":[136],"lower":[137,157],"bounds":[138,187],"error":[141],"probability,":[142],"derived":[145],"type-II":[148],"errors":[149],"some":[151,171],"binary":[152],"hypothesis":[153],"tests.":[154],"Subsequently,":[155],"each":[156],"bound":[158],"simplified":[160],"conditioning":[162],"an":[164],"event":[165],"related":[166],"linear":[172],"combination":[173],"codewords":[176],"transmitted":[177],"Lower":[184],"upper":[186],"second-order":[190],"term":[191],"optimal":[194],"coding":[195],"rate":[196],"also":[198],"obtained.":[199]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
