{"id":"https://openalex.org/W2095743061","doi":"https://doi.org/10.1109/isit.2009.5205529","title":"Spherical codes on torus layers","display_name":"Spherical codes on torus layers","publication_year":2009,"publication_date":"2009-06-01","ids":{"openalex":"https://openalex.org/W2095743061","doi":"https://doi.org/10.1109/isit.2009.5205529","mag":"2095743061"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2009.5205529","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2009.5205529","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE International Symposium on Information Theory","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/A5071997819","display_name":"Cristiano Torezzan","orcid":"https://orcid.org/0000-0001-9538-9538"},"institutions":[{"id":"https://openalex.org/I181391015","display_name":"Universidade Estadual de Campinas (UNICAMP)","ror":"https://ror.org/04wffgt70","country_code":"BR","type":"education","lineage":["https://openalex.org/I181391015"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Cristiano Torezzan","raw_affiliation_strings":["State University of Campinas-UNICAMP, Sao Paulo, Brazil","University of Campinas, SP 13083-970, Brazil"],"affiliations":[{"raw_affiliation_string":"State University of Campinas-UNICAMP, Sao Paulo, Brazil","institution_ids":["https://openalex.org/I181391015"]},{"raw_affiliation_string":"University of Campinas, SP 13083-970, Brazil","institution_ids":["https://openalex.org/I181391015"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077453229","display_name":"Sueli I. R. Costa","orcid":"https://orcid.org/0000-0002-8837-9291"},"institutions":[{"id":"https://openalex.org/I181391015","display_name":"Universidade Estadual de Campinas (UNICAMP)","ror":"https://ror.org/04wffgt70","country_code":"BR","type":"education","lineage":["https://openalex.org/I181391015"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Sueli I. R. Costa","raw_affiliation_strings":["State University of Campinas-UNICAMP, Sao Paulo, Brazil","University of Campinas, SP 13083-970, Brazil"],"affiliations":[{"raw_affiliation_string":"State University of Campinas-UNICAMP, Sao Paulo, Brazil","institution_ids":["https://openalex.org/I181391015"]},{"raw_affiliation_string":"University of Campinas, SP 13083-970, Brazil","institution_ids":["https://openalex.org/I181391015"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032236593","display_name":"Vinay A. Vaishampayan","orcid":"https://orcid.org/0000-0001-7781-0990"},"institutions":[{"id":"https://openalex.org/I1283103587","display_name":"AT&T (United States)","ror":"https://ror.org/02bbd5539","country_code":"US","type":"company","lineage":["https://openalex.org/I1283103587"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Vinay A. Vaishampayan","raw_affiliation_strings":["AT and T Shannon Laboratories, Florham Park, NJ, USA","AT&T Shannon Laboratory, Florham Park, NJ 07932, USA"],"affiliations":[{"raw_affiliation_string":"AT and T Shannon Laboratories, Florham Park, NJ, USA","institution_ids":["https://openalex.org/I1283103587"]},{"raw_affiliation_string":"AT&T Shannon Laboratory, Florham Park, NJ 07932, USA","institution_ids":["https://openalex.org/I1283103587"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5071997819"],"corresponding_institution_ids":["https://openalex.org/I181391015"],"apc_list":null,"apc_paid":null,"fwci":1.8065,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.87654947,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"2033","last_page":"2037"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11130","display_name":"Coding theory and cryptography","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9857000112533569,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9853000044822693,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/codebook","display_name":"Codebook","score":0.9142227172851562},{"id":"https://openalex.org/keywords/torus","display_name":"Torus","score":0.7803937196731567},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5309165120124817},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.46433910727500916},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.4254443645477295},{"id":"https://openalex.org/keywords/homogeneity","display_name":"Homogeneity (statistics)","score":0.42105937004089355},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4115930497646332},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39972904324531555},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.39724355936050415},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3016820251941681},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19323599338531494},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1603117287158966}],"concepts":[{"id":"https://openalex.org/C127759330","wikidata":"https://www.wikidata.org/wiki/Q637416","display_name":"Codebook","level":2,"score":0.9142227172851562},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.7803937196731567},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5309165120124817},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.46433910727500916},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.4254443645477295},{"id":"https://openalex.org/C142259097","wikidata":"https://www.wikidata.org/wiki/Q5891314","display_name":"Homogeneity (statistics)","level":2,"score":0.42105937004089355},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4115930497646332},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39972904324531555},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39724355936050415},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3016820251941681},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19323599338531494},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1603117287158966},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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":1,"locations":[{"id":"doi:10.1109/isit.2009.5205529","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2009.5205529","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE International Symposium on Information Theory","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":14,"referenced_works":["https://openalex.org/W1502435410","https://openalex.org/W1634005169","https://openalex.org/W1979598217","https://openalex.org/W1991932593","https://openalex.org/W1995990042","https://openalex.org/W2000123186","https://openalex.org/W2027891831","https://openalex.org/W2046273783","https://openalex.org/W2098936473","https://openalex.org/W2127413069","https://openalex.org/W2137836566","https://openalex.org/W2165750745","https://openalex.org/W2253314417","https://openalex.org/W4292408570"],"related_works":["https://openalex.org/W2293149949","https://openalex.org/W2026099691","https://openalex.org/W4284672201","https://openalex.org/W2377486419","https://openalex.org/W2943202426","https://openalex.org/W2950156284","https://openalex.org/W2736714427","https://openalex.org/W2163679795","https://openalex.org/W2137816434","https://openalex.org/W2017956276"],"abstract_inverted_index":{"A":[0],"new":[1],"class":[2],"of":[3,13,50],"spherical":[4,101],"codes":[5,102],"is":[6,47,92],"constructed":[7],"by":[8],"selecting":[9],"a":[10,32,51,55,88],"finite":[11,40],"subset":[12],"flat":[14],"tori":[15],"that":[16],"foliate":[17],"the":[18,39,48,75,111],"unit":[19],"sphere":[20],"S":[21],"<sup":[22,27,60],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[23,28,61],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2L-1</sup>":[24],"sub":[25],"R":[26,59],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2L</sup>":[29],"and":[30,66,80,87,116],"constructing":[31,95],"structured":[33],"codebook":[34,43],"on":[35,44,83],"each":[36,45],"torus":[37,46,99],"in":[38,58],"subset.":[41],"The":[42,98],"image":[49],"lattice":[52,77],"restricted":[53],"to":[54,110],"specific":[56],"hyperbox":[57],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">L</sup>":[62],".":[63],"Group":[64],"structure":[65],"homogeneity,":[67],"useful":[68],"for":[69,94],"efficient":[70],"decoding,":[71],"are":[72,85],"inherited":[73],"from":[74],"underlying":[76],"codebook.":[78],"Upper":[79],"lower":[81],"bounds":[82],"performance":[84,107],"derived":[86],"systematic":[89],"search":[90],"algorithm":[91],"presented":[93,103],"optimal":[96],"codebooks.":[97],"layer":[100],"here":[104],"exhibit":[105],"good":[106],"when":[108],"compared":[109],"well":[112],"known":[113],"apple-peeling,":[114],"wrapped":[115],"laminated":[117],"codes.":[118]},"counts_by_year":[{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}