{"id":"https://openalex.org/W2093654311","doi":"https://doi.org/10.1002/ett.4460040208","title":"On Lattice Coding for the Gaussian Channel","display_name":"On Lattice Coding for the Gaussian Channel","publication_year":1993,"publication_date":"1993-03-01","ids":{"openalex":"https://openalex.org/W2093654311","doi":"https://doi.org/10.1002/ett.4460040208","mag":"2093654311"},"language":"en","primary_location":{"id":"doi:10.1002/ett.4460040208","is_oa":false,"landing_page_url":"https://doi.org/10.1002/ett.4460040208","pdf_url":null,"source":{"id":"https://openalex.org/S4393917101","display_name":"European Transactions on Telecommunications","issn_l":"1124-318X","issn":["1124-318X","1541-8251"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"European Transactions on Telecommunications","raw_type":"journal-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/A5101671840","display_name":"H. M. de Oliveira","orcid":"https://orcid.org/0000-0002-6843-0635"},"institutions":[{"id":"https://openalex.org/I25112270","display_name":"Universidade Federal de Pernambuco","ror":"https://ror.org/047908t24","country_code":"BR","type":"education","lineage":["https://openalex.org/I25112270"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"H\u00e9lio Magalh\u00e4es De Oliveira","raw_affiliation_strings":["Department of Electronics and Systems - Communication Research Group CODEC, Universidade Federal de Pernambuco, Cid. Universita\u0301ria, 50.741 Recife-Brazil","Department of Electronics and Systems \u2010 Communication Research Group CODEC, Universidade Federal de Pernambuco, Cid. Universit\u00e1ria, 50.741 Recife\u2010Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronics and Systems - Communication Research Group CODEC, Universidade Federal de Pernambuco, Cid. Universita\u0301ria, 50.741 Recife-Brazil","institution_ids":["https://openalex.org/I25112270"]},{"raw_affiliation_string":"Department of Electronics and Systems \u2010 Communication Research Group CODEC, Universidade Federal de Pernambuco, Cid. Universit\u00e1ria, 50.741 Recife\u2010Brazil","institution_ids":["https://openalex.org/I25112270"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062370690","display_name":"G\u00e9rard Battail","orcid":null},"institutions":[{"id":"https://openalex.org/I12356871","display_name":"T\u00e9l\u00e9com Paris","ror":"https://ror.org/01naq7912","country_code":"FR","type":"education","lineage":["https://openalex.org/I12356871","https://openalex.org/I205703379","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I29607241","display_name":"\u00c9cole Normale Sup\u00e9rieure - PSL","ror":"https://ror.org/05a0dhs15","country_code":"FR","type":"other","lineage":["https://openalex.org/I2746051580","https://openalex.org/I29607241"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"G\u00e9rard Battail","raw_affiliation_strings":["Ecole Nationale Supre\u0301rieure des Te\u0301le\u0301communications, De\u0301partement Communications (also URA 820 of C.N.R.S.), 46, rue Barrault, F - 75634 Paris Cedex 13 - France","Ecole Nationale Supr\u00e9rieure des T\u00e9l\u00e9communications, D\u00e9partement Communications (also URA 820 of C.N.R.S.), 46, rue Barrault, F \u2010 75634 Paris Cedex 13 \u2010 France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ecole Nationale Supre\u0301rieure des Te\u0301le\u0301communications, De\u0301partement Communications (also URA 820 of C.N.R.S.), 46, rue Barrault, F - 75634 Paris Cedex 13 - France","institution_ids":["https://openalex.org/I12356871"]},{"raw_affiliation_string":"Ecole Nationale Supr\u00e9rieure des T\u00e9l\u00e9communications, D\u00e9partement Communications (also URA 820 of C.N.R.S.), 46, rue Barrault, F \u2010 75634 Paris Cedex 13 \u2010 France","institution_ids":["https://openalex.org/I29607241"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.11634218,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"4","issue":"2","first_page":"133","last_page":"140"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9988999962806702,"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":0.9983000159263611,"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/lattice","display_name":"Lattice (music)","score":0.7113598585128784},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.6329386234283447},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.5154553055763245},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4744350016117096},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.45852580666542053},{"id":"https://openalex.org/keywords/channel-code","display_name":"Channel code","score":0.4561014771461487},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.443460613489151},{"id":"https://openalex.org/keywords/channel-capacity","display_name":"Channel capacity","score":0.44080987572669983},{"id":"https://openalex.org/keywords/probability-of-error","display_name":"Probability of error","score":0.42513948678970337},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4227999448776245},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38468503952026367},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3646308481693268},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.29833561182022095},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.27758675813674927},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.25581687688827515},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.15048909187316895},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14865130186080933},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.058502525091171265}],"concepts":[{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.7113598585128784},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.6329386234283447},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.5154553055763245},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4744350016117096},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.45852580666542053},{"id":"https://openalex.org/C166366890","wikidata":"https://www.wikidata.org/wiki/Q602136","display_name":"Channel code","level":3,"score":0.4561014771461487},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.443460613489151},{"id":"https://openalex.org/C97744766","wikidata":"https://www.wikidata.org/wiki/Q870845","display_name":"Channel capacity","level":3,"score":0.44080987572669983},{"id":"https://openalex.org/C92224547","wikidata":"https://www.wikidata.org/wiki/Q1673216","display_name":"Probability of error","level":2,"score":0.42513948678970337},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4227999448776245},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38468503952026367},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3646308481693268},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.29833561182022095},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.27758675813674927},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.25581687688827515},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.15048909187316895},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14865130186080933},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.058502525091171265},{"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:10.1002/ett.4460040208","is_oa":false,"landing_page_url":"https://doi.org/10.1002/ett.4460040208","pdf_url":null,"source":{"id":"https://openalex.org/S4393917101","display_name":"European Transactions on Telecommunications","issn_l":"1124-318X","issn":["1124-318X","1541-8251"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"European Transactions on Telecommunications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1577906631","https://openalex.org/W2029495080","https://openalex.org/W2086736427","https://openalex.org/W2098234850","https://openalex.org/W2135479785","https://openalex.org/W2142399380","https://openalex.org/W2144552676","https://openalex.org/W2156360762","https://openalex.org/W2162819547","https://openalex.org/W2165406488","https://openalex.org/W2912432925","https://openalex.org/W2986057930","https://openalex.org/W3040853709","https://openalex.org/W3155676947","https://openalex.org/W4252713891","https://openalex.org/W4293259454"],"related_works":["https://openalex.org/W2964140842","https://openalex.org/W2545303390","https://openalex.org/W2159839902","https://openalex.org/W2804347328","https://openalex.org/W2112407231","https://openalex.org/W1968724537","https://openalex.org/W2087060975","https://openalex.org/W2801607032","https://openalex.org/W2161770327","https://openalex.org/W1833671883"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"definition":[2],"and":[3,23,44,58],"basic":[4],"properties":[5],"of":[6,19,53],"lattice":[7,54],"codes":[8,32,55],"for":[9],"the":[10,20,26,39,50],"Gaussian":[11],"channel":[12,40],"are":[13,29,33,47,60],"first":[14],"recalled.":[15],"Then,":[16],"an":[17],"estimation":[18],"code":[21],"rate":[22],"bounds":[24],"on":[25],"error":[27],"probability":[28],"presented.":[30],"Lattice":[31],"shown":[34],"to":[35,62],"exit":[36],"which":[37],"reach":[38],"capacity.":[41],"Separate":[42],"coding":[43],"shape":[45],"gains":[46],"introduced.":[48],"Finally,":[49],"asymptotic":[51],"behaviour":[52],"is":[56,67],"examined":[57],"we":[59],"led":[61],"conjecture":[63],"that":[64],"achieving":[65],"capacity":[66],"a":[68],"covering":[69],"\u2010":[70,74],"rather":[71],"than":[72],"packing":[73],"problem.":[75]},"counts_by_year":[],"updated_date":"2026-06-23T06:36:01.041984","created_date":"2025-10-10T00:00:00"}
