{"id":"https://openalex.org/W2745310171","doi":"https://doi.org/10.1109/isit.2017.8006998","title":"On shaping complex lattice constellations from multi-level constructions","display_name":"On shaping complex lattice constellations from multi-level constructions","publication_year":2017,"publication_date":"2017-06-01","ids":{"openalex":"https://openalex.org/W2745310171","doi":"https://doi.org/10.1109/isit.2017.8006998","mag":"2745310171"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2017.8006998","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2017.8006998","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2017 IEEE International Symposium on Information Theory (ISIT)","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/A5037681236","display_name":"Perathorn Pooksombat","orcid":"https://orcid.org/0000-0003-2442-9517"},"institutions":[{"id":"https://openalex.org/I25399158","display_name":"Mahidol University","ror":"https://ror.org/01znkr924","country_code":"TH","type":"education","lineage":["https://openalex.org/I25399158"]}],"countries":["TH"],"is_corresponding":true,"raw_author_name":"Perathorn Pooksombat","raw_affiliation_strings":["Department of Mathematics Faculty of Science, Mahidol University, Bangkok, Thailand"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics Faculty of Science, Mahidol University, Bangkok, Thailand","institution_ids":["https://openalex.org/I25399158"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089433499","display_name":"J. Harshan","orcid":"https://orcid.org/0000-0001-7333-4958"},"institutions":[{"id":"https://openalex.org/I4210108443","display_name":"Advanced Digital Sciences Center","ror":"https://ror.org/01xaqx887","country_code":"SG","type":"facility","lineage":["https://openalex.org/I4210108443"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"J. Harshan","raw_affiliation_strings":["Advanced Digital Sciences Center, Singapore"],"affiliations":[{"raw_affiliation_string":"Advanced Digital Sciences Center, Singapore","institution_ids":["https://openalex.org/I4210108443"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001009310","display_name":"Wittawat Kositwattanarerk","orcid":null},"institutions":[{"id":"https://openalex.org/I4210117768","display_name":"Centre of Excellence in Mathematics","ror":"https://ror.org/02df7gw66","country_code":"TH","type":"education","lineage":["https://openalex.org/I4210117768"]},{"id":"https://openalex.org/I25399158","display_name":"Mahidol University","ror":"https://ror.org/01znkr924","country_code":"TH","type":"education","lineage":["https://openalex.org/I25399158"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"Wittawat Kositwattanarerk","raw_affiliation_strings":["Department of Mathematics Centre of Excellence in Mathematics Faculty of Science, Mahidol University, Bangkok, Thailand"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics Centre of Excellence in Mathematics Faculty of Science, Mahidol University, Bangkok, Thailand","institution_ids":["https://openalex.org/I4210117768","https://openalex.org/I25399158"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5037681236"],"corresponding_institution_ids":["https://openalex.org/I25399158"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.10342612,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"2593","last_page":"2597"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"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":0.9998999834060669,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9984999895095825,"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":0.9976000189781189,"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":0.7137156128883362},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.6144726276397705},{"id":"https://openalex.org/keywords/parallelepiped","display_name":"Parallelepiped","score":0.4787570536136627},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4743179976940155},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4561244249343872},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4427722692489624},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4358150064945221},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3864997625350952},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.28675949573516846},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11060848832130432},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10943740606307983}],"concepts":[{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.7137156128883362},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.6144726276397705},{"id":"https://openalex.org/C2779788511","wikidata":"https://www.wikidata.org/wiki/Q181658","display_name":"Parallelepiped","level":2,"score":0.4787570536136627},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4743179976940155},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4561244249343872},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4427722692489624},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4358150064945221},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3864997625350952},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28675949573516846},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11060848832130432},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10943740606307983},{"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.2017.8006998","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2017.8006998","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2017 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5699999928474426,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W2023530046","https://openalex.org/W2077388449","https://openalex.org/W2124524819","https://openalex.org/W2152402018","https://openalex.org/W2160130902","https://openalex.org/W2165406488","https://openalex.org/W4234345623","https://openalex.org/W4292408570"],"related_works":["https://openalex.org/W4383816821","https://openalex.org/W4283382972","https://openalex.org/W4367557258","https://openalex.org/W118848820","https://openalex.org/W2059014664","https://openalex.org/W2065245699","https://openalex.org/W3148891486","https://openalex.org/W4282968753","https://openalex.org/W2021770428","https://openalex.org/W4296526515"],"abstract_inverted_index":{"Constructions":[0],"of":[1,13,29,42,48,60,71,91,100,111,117,120,168,177,205,209,224],"lattices":[2,32,178],"are":[3],"known":[4],"to":[5,10,55,78,86,113],"have":[6],"a":[7,108,121,129,136,156,186,193,203],"strong":[8],"connection":[9],"the":[11,49,56,74,88,92,98,118,166,174,206],"study":[12],"classical":[14],"linear":[15,140,232],"codes":[16,45,141,226],"over":[17,33,46,124,139,142,230],"F":[18,143],"<sub":[19,144],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[20,145],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sub>":[21],";":[22],"one":[23],"such":[24,192],"celebrated":[25],"construction":[26,59,138],"is":[27,128,133],"that":[28,132,173,198],"Barnes-Wall":[30],"(BW)":[31],"\u2124[i],":[34],"with":[35],"i":[36,53],"=":[37],"\u221a-1,":[38],"wherein":[39],"weighted":[40],"sum":[41],"nested":[43],"Reed-Muller":[44],"powers":[47],"base":[50],"1":[51],"+":[52],"leads":[54],"famous":[57],"multi-level":[58,137,180,228],"BW":[61,101],"lattices.":[62],"Although":[63],"these":[64],"constructions":[65,181,229],"facilitate":[66],"simple":[67],"encoding":[68,221],"and":[69,171,222],"decoding":[70,223],"information":[72],"bits,":[73],"resulting":[75],"codewords":[76,119],"need":[77],"be":[79,183],"mapped":[80],"onto":[81],"their":[82],"representatives":[83,116],"in":[84,103,202,217,220],"order":[85],"reduce":[87],"average":[89,207],"energy":[90,208],"lattice":[93,122,169,210,225],"code.":[94],"Drawing":[95],"inspirations":[96],"from":[97,179,227],"case":[99],"lattices,":[102],"this":[104],"work,":[105],"we":[106,154],"address":[107],"general":[109],"question":[110],"how":[112],"arrive":[114],"at":[115],"code":[123],"\u2124[\u03b8],":[125],"where":[126],"\u03b8":[127],"quadratic":[130],"integer,":[131],"generated":[134],"via":[135],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">q</sub>":[146],",":[147],"for":[148],"q":[149],">":[150],"2.":[151],"In":[152],"particular,":[153],"introduce":[155],"novel":[157],"shaping":[158],"function":[159],"\u03c4":[160],":":[161],"\u2124[\u03b8]":[162,164],"\u2192":[163],"on":[165],"components":[167],"codewords,":[170],"prove":[172],"natural":[175],"constellation":[176],"can":[182],"rearranged":[184],"into":[185],"multi-dimensional":[187],"cube":[188],"or":[189],"parallelepiped":[190],"under":[191],"map.":[194],"We":[195],"demonstrate":[196],"numerically":[197],"our":[199],"mapping":[200,214],"results":[201],"reduction":[204],"constellations.":[211],"Our":[212],"proposed":[213],"has":[215],"applications":[216],"communications,":[218],"particularly":[219],"q-ary":[231],"codes.":[233]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
