{"id":"https://openalex.org/W2910657214","doi":"https://doi.org/10.1109/itw.2018.8613506","title":"Geometric shaping: low-density coding of Gaussian-like constellations","display_name":"Geometric shaping: low-density coding of Gaussian-like constellations","publication_year":2018,"publication_date":"2018-11-01","ids":{"openalex":"https://openalex.org/W2910657214","doi":"https://doi.org/10.1109/itw.2018.8613506","mag":"2910657214"},"language":"en","primary_location":{"id":"doi:10.1109/itw.2018.8613506","is_oa":false,"landing_page_url":"https://doi.org/10.1109/itw.2018.8613506","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 IEEE Information Theory Workshop (ITW)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://biblio.ugent.be/publication/8589494/file/8599455.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077116161","display_name":"Joseph J. Boutros","orcid":"https://orcid.org/0000-0002-6014-8328"},"institutions":[{"id":"https://openalex.org/I58152225","display_name":"Texas A&M University at Qatar","ror":"https://ror.org/03vb4dm14","country_code":"QA","type":"education","lineage":["https://openalex.org/I58152225","https://openalex.org/I91045830"]}],"countries":["QA"],"is_corresponding":true,"raw_author_name":"Joseph J. Boutros","raw_affiliation_strings":["Texas A& M University, Qatar"],"affiliations":[{"raw_affiliation_string":"Texas A& M University, Qatar","institution_ids":["https://openalex.org/I58152225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029983697","display_name":"Uri Erez","orcid":"https://orcid.org/0000-0001-7720-1116"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Uri Erez","raw_affiliation_strings":["Tel Aviv University, Israel"],"affiliations":[{"raw_affiliation_string":"Tel Aviv University, Israel","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052028156","display_name":"Johannes Van Wonterghem","orcid":"https://orcid.org/0000-0002-7567-2851"},"institutions":[{"id":"https://openalex.org/I2801227569","display_name":"Ghent University Hospital","ror":"https://ror.org/00xmkp704","country_code":"BE","type":"healthcare","lineage":["https://openalex.org/I2801227569"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Johannes Van Wonterghem","raw_affiliation_strings":["Ghent University, Belgium"],"affiliations":[{"raw_affiliation_string":"Ghent University, Belgium","institution_ids":["https://openalex.org/I2801227569"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072780983","display_name":"Gil I. Shamir","orcid":"https://orcid.org/0000-0002-4307-9180"},"institutions":[{"id":"https://openalex.org/I1291425158","display_name":"Google (United States)","ror":"https://ror.org/00njsd438","country_code":"US","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210128969"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Gil I. Shamir","raw_affiliation_strings":["Google Pittsburgh, USA"],"affiliations":[{"raw_affiliation_string":"Google Pittsburgh, USA","institution_ids":["https://openalex.org/I1291425158"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064676731","display_name":"Gilles Z\u00e9mor","orcid":"https://orcid.org/0000-0002-6041-9554"},"institutions":[{"id":"https://openalex.org/I15057530","display_name":"Universit\u00e9 de Bordeaux","ror":"https://ror.org/057qpr032","country_code":"FR","type":"education","lineage":["https://openalex.org/I15057530"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Gilles Zemor","raw_affiliation_strings":["Bordeaux University, France"],"affiliations":[{"raw_affiliation_string":"Bordeaux University, France","institution_ids":["https://openalex.org/I15057530"]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5077116161"],"corresponding_institution_ids":["https://openalex.org/I58152225"],"apc_list":null,"apc_paid":null,"fwci":0.5848,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.73520778,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"5"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":0.9997000098228455,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9997000098228455,"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":0.9997000098228455,"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"}},{"id":"https://openalex.org/T10125","display_name":"Advanced Wireless Communication Techniques","score":0.9987999796867371,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/codebook","display_name":"Codebook","score":0.925245463848114},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.6502818465232849},{"id":"https://openalex.org/keywords/channel-capacity","display_name":"Channel capacity","score":0.6080805063247681},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5805132389068604},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5714632272720337},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.5304348468780518},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.48977160453796387},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48974061012268066},{"id":"https://openalex.org/keywords/encoder","display_name":"Encoder","score":0.4820619523525238},{"id":"https://openalex.org/keywords/constellation","display_name":"Constellation","score":0.4681307077407837},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4390750229358673},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.42924246191978455},{"id":"https://openalex.org/keywords/voronoi-diagram","display_name":"Voronoi diagram","score":0.42017948627471924},{"id":"https://openalex.org/keywords/constellation-diagram","display_name":"Constellation diagram","score":0.41484397649765015},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.40277355909347534},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.32759228348731995},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.31349408626556396},{"id":"https://openalex.org/keywords/bit-error-rate","display_name":"Bit error rate","score":0.20082536339759827},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.14901459217071533},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12244293093681335},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11901929974555969},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.11401206254959106},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10159403085708618},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08759322762489319}],"concepts":[{"id":"https://openalex.org/C127759330","wikidata":"https://www.wikidata.org/wiki/Q637416","display_name":"Codebook","level":2,"score":0.925245463848114},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.6502818465232849},{"id":"https://openalex.org/C97744766","wikidata":"https://www.wikidata.org/wiki/Q870845","display_name":"Channel capacity","level":3,"score":0.6080805063247681},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5805132389068604},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5714632272720337},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.5304348468780518},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.48977160453796387},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48974061012268066},{"id":"https://openalex.org/C118505674","wikidata":"https://www.wikidata.org/wiki/Q42586063","display_name":"Encoder","level":2,"score":0.4820619523525238},{"id":"https://openalex.org/C70352696","wikidata":"https://www.wikidata.org/wiki/Q8928","display_name":"Constellation","level":2,"score":0.4681307077407837},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4390750229358673},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.42924246191978455},{"id":"https://openalex.org/C24881265","wikidata":"https://www.wikidata.org/wiki/Q757267","display_name":"Voronoi diagram","level":2,"score":0.42017948627471924},{"id":"https://openalex.org/C185837786","wikidata":"https://www.wikidata.org/wiki/Q1782940","display_name":"Constellation diagram","level":4,"score":0.41484397649765015},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.40277355909347534},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.32759228348731995},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.31349408626556396},{"id":"https://openalex.org/C56296756","wikidata":"https://www.wikidata.org/wiki/Q840922","display_name":"Bit error rate","level":3,"score":0.20082536339759827},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.14901459217071533},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12244293093681335},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11901929974555969},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.11401206254959106},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10159403085708618},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08759322762489319},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/itw.2018.8613506","is_oa":false,"landing_page_url":"https://doi.org/10.1109/itw.2018.8613506","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 IEEE Information Theory Workshop (ITW)","raw_type":"proceedings-article"},{"id":"pmh:oai:archive.ugent.be:8589494","is_oa":true,"landing_page_url":"http://hdl.handle.net/1854/LU-8589494","pdf_url":"https://biblio.ugent.be/publication/8589494/file/8599455.pdf","source":{"id":"https://openalex.org/S4306400478","display_name":"Ghent University Academic Bibliography (Ghent University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I32597200","host_organization_name":"Ghent University","host_organization_lineage":["https://openalex.org/I32597200"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2018 IEEE INFORMATION THEORY WORKSHOP (ITW)","raw_type":"conference"}],"best_oa_location":{"id":"pmh:oai:archive.ugent.be:8589494","is_oa":true,"landing_page_url":"http://hdl.handle.net/1854/LU-8589494","pdf_url":"https://biblio.ugent.be/publication/8589494/file/8599455.pdf","source":{"id":"https://openalex.org/S4306400478","display_name":"Ghent University Academic Bibliography (Ghent University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I32597200","host_organization_name":"Ghent University","host_organization_lineage":["https://openalex.org/I32597200"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2018 IEEE INFORMATION THEORY WORKSHOP (ITW)","raw_type":"conference"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2910657214.pdf","grobid_xml":"https://content.openalex.org/works/W2910657214.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W627952176","https://openalex.org/W1506964462","https://openalex.org/W1635319022","https://openalex.org/W1749807555","https://openalex.org/W1989008275","https://openalex.org/W2039465699","https://openalex.org/W2115001548","https://openalex.org/W2115198523","https://openalex.org/W2125566184","https://openalex.org/W2130718424","https://openalex.org/W2142901448","https://openalex.org/W2146774798","https://openalex.org/W2155206380","https://openalex.org/W2295374613","https://openalex.org/W2395094252","https://openalex.org/W2583246406","https://openalex.org/W2798333393","https://openalex.org/W2964133401","https://openalex.org/W2964294725","https://openalex.org/W6733047850"],"related_works":["https://openalex.org/W2082947723","https://openalex.org/W2097133655","https://openalex.org/W2162782586","https://openalex.org/W2541426150","https://openalex.org/W1600065361","https://openalex.org/W4289337235","https://openalex.org/W2314551182","https://openalex.org/W4384919582","https://openalex.org/W2951788044","https://openalex.org/W4229045008"],"abstract_inverted_index":{"Constellation":[0],"shaping":[1,15,35,48],"is":[2,27,49,60,117],"necessary":[3],"to":[4,20,29,43,82,90,104,107,130],"approach":[5],"channel":[6,74],"capacity":[7,75,131],"for":[8],"information":[9],"rates":[10],"above":[11],"1":[12],"bit/dim.":[13],"Probabilistic":[14],"shows":[16],"a":[17,23,61,87,136],"small":[18,52],"gap":[19,42,129],"capacity,":[21,44],"however":[22],"complex":[24],"distribution":[25],"matcher":[26],"required":[28],"modify":[30],"the":[31,41,77,97,100,108,112,140],"source":[32],"distribution.":[33],"Spherical":[34],"of":[36,79,111],"lattice":[37],"constellations":[38],"also":[39],"reduces":[40],"but":[45],"practical":[46,122],"Voronoi":[47],"feasible":[50],"in":[51],"dimensions":[53],"only.":[54],"In":[55],"this":[56,70],"paper,":[57],"our":[58],"codebook":[59,72,113],"real":[62],"geometrically":[63],"non-uniform":[64],"Gaussian-like":[65],"constellation.":[66],"We":[67],"prove":[68],"that":[69],"discrete":[71],"achieves":[73],"when":[76],"number":[78],"points":[80],"goes":[81],"infinity.":[83],"Then":[84],"we":[85],"build":[86],"special":[88],"mapping":[89],"interface":[91],"between":[92],"non-binary":[93],"low-density":[94],"codes":[95],"and":[96,121],"codebook,":[98],"allowing":[99],"code":[101,137],"alphabet":[102],"size":[103],"be":[105],"equal":[106],"square":[109],"root":[110],"size.":[114],"Excellent":[115],"performance":[116],"shown":[118],"with":[119,135],"fast-encoding":[120],"iterative":[123],"probabilistic":[124],"decoding,":[125],"e.g.":[126],"0.7":[127],"dB":[128],"at":[132],"6":[133],"bits/s/Hz":[134],"defined":[138],"over":[139],"ring":[141],"Z/8Z.":[142]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}
