{"id":"https://openalex.org/W2783136786","doi":"https://doi.org/10.1109/allerton.2017.8262827","title":"A solution to cover's problem for the binary symmetric relay channel: Geometry of sets on the hamming sphere","display_name":"A solution to cover's problem for the binary symmetric relay channel: Geometry of sets on the hamming sphere","publication_year":2017,"publication_date":"2017-10-01","ids":{"openalex":"https://openalex.org/W2783136786","doi":"https://doi.org/10.1109/allerton.2017.8262827","mag":"2783136786"},"language":"en","primary_location":{"id":"doi:10.1109/allerton.2017.8262827","is_oa":false,"landing_page_url":"https://doi.org/10.1109/allerton.2017.8262827","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2017 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","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/A5029028070","display_name":"Leighton Pate Barnes","orcid":"https://orcid.org/0000-0002-9472-2770"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Leighton Pate Barnes","raw_affiliation_strings":["Stanford University, CA"],"affiliations":[{"raw_affiliation_string":"Stanford University, CA","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041915281","display_name":"Xiugang Wu","orcid":"https://orcid.org/0000-0002-8130-975X"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xiugang Wu","raw_affiliation_strings":["Stanford University, CA"],"affiliations":[{"raw_affiliation_string":"Stanford University, CA","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003322209","display_name":"Ayfer \u00d6zg\u00fcr","orcid":"https://orcid.org/0000-0002-4455-4692"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ayfer Ozgur","raw_affiliation_strings":["Stanford University, CA"],"affiliations":[{"raw_affiliation_string":"Stanford University, CA","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5029028070"],"corresponding_institution_ids":["https://openalex.org/I97018004"],"apc_list":null,"apc_paid":null,"fwci":1.6576,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.86891006,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"844","last_page":"851"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9991000294685364,"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":0.9991000294685364,"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":0.9944000244140625,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9271000027656555,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6012060642242432},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5749539732933044},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5531246066093445},{"id":"https://openalex.org/keywords/hamming-code","display_name":"Hamming code","score":0.531805157661438},{"id":"https://openalex.org/keywords/cover","display_name":"Cover (algebra)","score":0.5021989345550537},{"id":"https://openalex.org/keywords/relay","display_name":"Relay","score":0.49087244272232056},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.47068387269973755},{"id":"https://openalex.org/keywords/binary-symmetric-channel","display_name":"Binary symmetric channel","score":0.4571407437324524},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.39948809146881104},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.3984590172767639},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37655285000801086},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.35008302330970764},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3235047161579132},{"id":"https://openalex.org/keywords/channel-capacity","display_name":"Channel capacity","score":0.2912599444389343},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2546497881412506},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.24040743708610535},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18618246912956238},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.18462178111076355},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.1457584798336029},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11984705924987793},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.11567315459251404}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6012060642242432},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5749539732933044},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5531246066093445},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.531805157661438},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.5021989345550537},{"id":"https://openalex.org/C2778156585","wikidata":"https://www.wikidata.org/wiki/Q174053","display_name":"Relay","level":3,"score":0.49087244272232056},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.47068387269973755},{"id":"https://openalex.org/C173988684","wikidata":"https://www.wikidata.org/wiki/Q863510","display_name":"Binary symmetric channel","level":4,"score":0.4571407437324524},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.39948809146881104},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.3984590172767639},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37655285000801086},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.35008302330970764},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3235047161579132},{"id":"https://openalex.org/C97744766","wikidata":"https://www.wikidata.org/wiki/Q870845","display_name":"Channel capacity","level":3,"score":0.2912599444389343},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2546497881412506},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.24040743708610535},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18618246912956238},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.18462178111076355},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.1457584798336029},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11984705924987793},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.11567315459251404},{"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/allerton.2017.8262827","is_oa":false,"landing_page_url":"https://doi.org/10.1109/allerton.2017.8262827","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2017 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","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":12,"referenced_works":["https://openalex.org/W138183650","https://openalex.org/W157108002","https://openalex.org/W950997499","https://openalex.org/W1494099594","https://openalex.org/W1971536606","https://openalex.org/W2088641045","https://openalex.org/W2090226360","https://openalex.org/W2157142525","https://openalex.org/W2167447263","https://openalex.org/W2575063269","https://openalex.org/W2963368320","https://openalex.org/W4300840296"],"related_works":["https://openalex.org/W2953173877","https://openalex.org/W4298083944","https://openalex.org/W2398586267","https://openalex.org/W4307367836","https://openalex.org/W2963737449","https://openalex.org/W2139209768","https://openalex.org/W2892673973","https://openalex.org/W3104878415","https://openalex.org/W2964304063","https://openalex.org/W2028698464"],"abstract_inverted_index":{"We":[0],"solve":[1,57],"a":[2,114,128],"long-standing":[3],"open":[4],"problem":[5,51,59],"posed":[6],"by":[7,60],"Cover":[8],"and":[9,21,37],"named":[10],"\u201cThe":[11],"Capacity":[12],"of":[13,49,83,91,102,135],"the":[14,26,29,32,35,38,53,71,77,84,92,97,100,108,120,133,136,149,155,160],"Relay":[15],"Channel,\u201d":[16],"Open":[17],"Problems":[18],"in":[19,25,52,70,159],"Communication":[20],"Computation,":[22],"Springer-Verlag,":[23],"1987,":[24],"case":[27,73,86,151],"when":[28],"channels":[30],"from":[31,76],"source":[33],"to":[34,45,63,126,167],"relay":[36,139],"destination":[39],"are":[40],"binary":[41,72,137,150],"symmetric":[42,138],"channels.":[43],"Similar":[44],"our":[46,67,81,145],"recent":[47],"solution":[48],"this":[50,58],"Gaussian":[54,78,85,161],"case,":[55,79,162],"we":[56,112,157],"connecting":[61],"it":[62],"high-dimensional":[64],"geometry.":[65],"However,":[66],"geometric":[68],"approach":[69],"significantly":[74],"deviates":[75],"since":[80],"treatment":[82],"relied":[87],"on":[88,96,107,119,132],"an":[89],"extension":[90],"classical":[93],"isoperimetric":[94],"inequality":[95,118],"Euclidean":[98],"sphere,":[99,122],"counterpart":[101],"which":[103,123],"does":[104],"not":[105],"exist":[106],"Hamming":[109,121],"sphere.":[110],"Instead,":[111],"prove":[113],"Riesz":[115],"rearrangement":[116],"type":[117],"allows":[124],"us":[125],"develop":[127],"new":[129],"upper":[130,146],"bound":[131],"capacity":[134],"channel.":[140],"Our":[141],"argument":[142],"(and":[143],"consequently":[144],"bound)":[147],"for":[148],"is":[152],"weaker":[153],"than":[154],"one":[156],"obtained":[158],"but":[163],"nevertheless":[164],"strong":[165],"enough":[166],"resolve":[168],"Cover's":[169],"problem.":[170]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}