{"id":"https://openalex.org/W4401692579","doi":"https://doi.org/10.1109/isit57864.2024.10619275","title":"On the Equivalence Between Probabilistic Shaping and Geometric Shaping: A Polar Lattice Perspective","display_name":"On the Equivalence Between Probabilistic Shaping and Geometric Shaping: A Polar Lattice Perspective","publication_year":2024,"publication_date":"2024-07-07","ids":{"openalex":"https://openalex.org/W4401692579","doi":"https://doi.org/10.1109/isit57864.2024.10619275"},"language":"en","primary_location":{"id":"doi:10.1109/isit57864.2024.10619275","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit57864.2024.10619275","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2024 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5101448188","display_name":"Ling Liu","orcid":"https://orcid.org/0000-0001-5926-7058"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ling Liu","raw_affiliation_strings":["Guangzhou Institute of Technology, Xidian University,Guangzhou,China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Guangzhou Institute of Technology, Xidian University,Guangzhou,China","institution_ids":["https://openalex.org/I149594827"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021761593","display_name":"Shanxiang Lyu","orcid":"https://orcid.org/0000-0002-5005-5056"},"institutions":[{"id":"https://openalex.org/I159948400","display_name":"Jinan University","ror":"https://ror.org/02xe5ns62","country_code":"CN","type":"education","lineage":["https://openalex.org/I159948400"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shanxiang Lyu","raw_affiliation_strings":["College of Cyber Security, Jinan University,Guangzhou,China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Cyber Security, Jinan University,Guangzhou,China","institution_ids":["https://openalex.org/I159948400"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065795716","display_name":"Cong Ling","orcid":"https://orcid.org/0000-0001-7873-4862"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Cong Ling","raw_affiliation_strings":["Imperial College London,Department of Electrical and Electronic Engineering,London,UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Imperial College London,Department of Electrical and Electronic Engineering,London,UK","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063124926","display_name":"Baoming Bai","orcid":"https://orcid.org/0000-0002-6161-5493"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Baoming Bai","raw_affiliation_strings":["Guangzhou Institute of Technology, Xidian University,Guangzhou,China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Guangzhou Institute of Technology, Xidian University,Guangzhou,China","institution_ids":["https://openalex.org/I149594827"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.6913,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.90394089,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"2174","last_page":"2179"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9487000107765198,"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"}},"topics":[{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9487000107765198,"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/probabilistic-logic","display_name":"Probabilistic logic","score":0.6482436656951904},{"id":"https://openalex.org/keywords/perspective","display_name":"Perspective (graphical)","score":0.5854840278625488},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5467844605445862},{"id":"https://openalex.org/keywords/polar","display_name":"Polar","score":0.5357649922370911},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5182023644447327},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43649983406066895},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.403985857963562},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3780257999897003},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.36173945665359497},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3116692900657654},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.24284791946411133},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2263331115245819},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.133281409740448}],"concepts":[{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.6482436656951904},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.5854840278625488},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5467844605445862},{"id":"https://openalex.org/C29705727","wikidata":"https://www.wikidata.org/wiki/Q294562","display_name":"Polar","level":2,"score":0.5357649922370911},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5182023644447327},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43649983406066895},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.403985857963562},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3780257999897003},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.36173945665359497},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3116692900657654},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24284791946411133},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2263331115245819},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.133281409740448},{"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/isit57864.2024.10619275","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit57864.2024.10619275","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2024 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Climate action","score":0.4099999964237213,"id":"https://metadata.un.org/sdg/13"}],"awards":[{"id":"https://openalex.org/G2569668766","display_name":null,"funder_award_id":"2021.YFA1000500","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G3347531412","display_name":null,"funder_award_id":"20201200300072","funder_id":"https://openalex.org/F4320329334","funder_display_name":"Dongguan Science and Technology Bureau"},{"id":"https://openalex.org/G400639621","display_name":null,"funder_award_id":"62171356,61902149,62001300,62311530098","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320329334","display_name":"Dongguan Science and Technology Bureau","ror":null},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1512015702","https://openalex.org/W1966447089","https://openalex.org/W2018877773","https://openalex.org/W2023530046","https://openalex.org/W2055534149","https://openalex.org/W2064158368","https://openalex.org/W2106045225","https://openalex.org/W2107211662","https://openalex.org/W2107288243","https://openalex.org/W2111992817","https://openalex.org/W2115001548","https://openalex.org/W2116631972","https://openalex.org/W2117009122","https://openalex.org/W2122621581","https://openalex.org/W2138293524","https://openalex.org/W2144099979","https://openalex.org/W2144552676","https://openalex.org/W2150498905","https://openalex.org/W2164368671","https://openalex.org/W2164654926","https://openalex.org/W2165406488","https://openalex.org/W2168226105","https://openalex.org/W2171760107","https://openalex.org/W2175334662","https://openalex.org/W2295374613","https://openalex.org/W2963680123","https://openalex.org/W2964284420","https://openalex.org/W3037524284","https://openalex.org/W3190285128","https://openalex.org/W4237963784","https://openalex.org/W4292414116","https://openalex.org/W4353030701"],"related_works":["https://openalex.org/W2885615566","https://openalex.org/W1973916483","https://openalex.org/W1996076013","https://openalex.org/W2065102984","https://openalex.org/W2025479331","https://openalex.org/W2149101979","https://openalex.org/W1971383138","https://openalex.org/W1497573972","https://openalex.org/W2071659383","https://openalex.org/W1846253165"],"abstract_inverted_index":{"This":[0,162],"paper":[1],"aims":[2],"to":[3,62,93,128,182],"build":[4],"a":[5,36,68,130,157,165],"bridge":[6],"between":[7],"the":[8,12,19,29,44,57,63,74,80,85,99,105,109,113,119,122,136,145,151,184],"probabilistic":[9,160],"shaping":[10,14,32,37,58],"and":[11,56,112,133,172,191],"geometric":[13,148],"for":[15,43,118],"lattice":[16,30,38,101,115,123,132,137],"codes":[17],"from":[18],"perspective":[20,167],"of":[21,84,104,121,147,159,168,187],"polar":[22,34],"lattices.":[23],"We":[24],"prove":[25],"that":[26],"when":[27],"performing":[28],"Gaussian":[31,49,87,106,138,188],"on":[33,176],"lattices,":[35],"As":[39,65],"which":[40],"is":[41,53,60,92,116,127,154],"good":[42],"so-called":[45],"discrete":[46],"additive":[47],"white":[48],"noise":[50,107],"(AWGN)":[51],"channel":[52,77,189],"constructed":[54],"indeed,":[55],"process":[59],"equivalent":[61],"modulo":[64],"operation":[66],"within":[67],"multi-level":[69],"decoding":[70],"manner.":[71],"To":[72],"achieve":[73,183],"power-constraint":[75],"AWGN":[76],"capacity":[78],"or":[79,108],"rate":[81],"distortion":[82],"bound":[83],"i.i.d.":[86],"source,":[88],"one":[89,153],"classical":[90],"approach":[91,126,142],"construct":[94,129],"two":[95,170],"nested":[96],"lattices":[97],"where":[98],"fine":[100],"takes":[102],"care":[103],"target":[110],"distortion,":[111],"coarse":[114],"responsible":[117],"boundary":[120],"codewords.":[124],"Another":[125],"single":[131],"then":[134],"perform":[135],"shaping.":[139,161],"The":[140],"former":[141],"falls":[143],"into":[144],"category":[146],"shaping,":[149],"while":[150],"latter":[152],"regarded":[155],"as":[156],"type":[158],"work":[163],"proposes":[164],"unified":[166],"these":[169],"approaches,":[171],"provides":[173],"new":[174],"evidence":[175],"why":[177],"they":[178],"are":[179],"both":[180],"able":[181],"optimal":[185],"performance":[186],"coding":[190,193],"source":[192],"problems.":[194]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2}],"updated_date":"2026-08-08T01:25:22.217667","created_date":"2025-10-10T00:00:00"}
