{"id":"https://openalex.org/W2562001552","doi":"https://doi.org/10.1109/tit.2017.2778726","title":"An Algebraic Framework for End-to-End Physical-Layer Network Coding","display_name":"An Algebraic Framework for End-to-End Physical-Layer Network Coding","publication_year":2017,"publication_date":"2017-12-04","ids":{"openalex":"https://openalex.org/W2562001552","doi":"https://doi.org/10.1109/tit.2017.2778726","mag":"2562001552"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2017.2778726","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2017.2778726","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","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/A5073554693","display_name":"Elisa Gorla","orcid":"https://orcid.org/0000-0002-6418-4887"},"institutions":[{"id":"https://openalex.org/I57825437","display_name":"University of Neuch\u00e2tel","ror":"https://ror.org/00vasag41","country_code":"CH","type":"education","lineage":["https://openalex.org/I57825437"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Elisa Gorla","raw_affiliation_strings":["University of Neuch\u00e2tel, Neuch\u00e2tel, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Neuch\u00e2tel, Neuch\u00e2tel, Switzerland","institution_ids":["https://openalex.org/I57825437"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025356502","display_name":"Alberto Ravagnani","orcid":"https://orcid.org/0000-0001-5901-9484"},"institutions":[{"id":"https://openalex.org/I57825437","display_name":"University of Neuch\u00e2tel","ror":"https://ror.org/00vasag41","country_code":"CH","type":"education","lineage":["https://openalex.org/I57825437"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Alberto Ravagnani","raw_affiliation_strings":["University of Neuch\u00e2tel, Neuch\u00e2tel, Switzerland"],"raw_orcid":"https://orcid.org/0000-0001-5901-9484","affiliations":[{"raw_affiliation_string":"University of Neuch\u00e2tel, Neuch\u00e2tel, Switzerland","institution_ids":["https://openalex.org/I57825437"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I57825437"],"apc_list":null,"apc_paid":null,"fwci":1.2621,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.81753708,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"64","issue":"6","first_page":"4480","last_page":"4495"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":1.0,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":1.0,"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/T11458","display_name":"Advanced Wireless Communication Technologies","score":0.9607999920845032,"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"}},{"id":"https://openalex.org/T12791","display_name":"Full-Duplex Wireless Communications","score":0.955299973487854,"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/cardinality","display_name":"Cardinality (data modeling)","score":0.6087157726287842},{"id":"https://openalex.org/keywords/linear-network-coding","display_name":"Linear network coding","score":0.5376167893409729},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5127238035202026},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4902084469795227},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.46510300040245056},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4645898640155792},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.4240560531616211},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.40714073181152344},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4031590223312378},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3644291162490845},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34504663944244385},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.20039567351341248},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.17424994707107544},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.09375128149986267}],"concepts":[{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.6087157726287842},{"id":"https://openalex.org/C138293262","wikidata":"https://www.wikidata.org/wiki/Q1089578","display_name":"Linear network coding","level":3,"score":0.5376167893409729},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5127238035202026},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4902084469795227},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.46510300040245056},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4645898640155792},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.4240560531616211},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.40714073181152344},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4031590223312378},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3644291162490845},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34504663944244385},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.20039567351341248},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.17424994707107544},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.09375128149986267},{"id":"https://openalex.org/C158379750","wikidata":"https://www.wikidata.org/wiki/Q214111","display_name":"Network packet","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2017.2778726","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2017.2778726","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3442523362","display_name":null,"funder_award_id":"200021_150207","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1490215229","https://openalex.org/W1563677781","https://openalex.org/W1975099099","https://openalex.org/W2005196269","https://openalex.org/W2046471908","https://openalex.org/W2053399991","https://openalex.org/W2067089839","https://openalex.org/W2067232511","https://openalex.org/W2095547380","https://openalex.org/W2100770837","https://openalex.org/W2139416652","https://openalex.org/W2153739324","https://openalex.org/W2569741146","https://openalex.org/W2962878445","https://openalex.org/W3103017684","https://openalex.org/W3125267404","https://openalex.org/W4298054792","https://openalex.org/W6633614042"],"related_works":["https://openalex.org/W2002177687","https://openalex.org/W2058438338","https://openalex.org/W2019471580","https://openalex.org/W2212571888","https://openalex.org/W2941284322","https://openalex.org/W2168299207","https://openalex.org/W4224920876","https://openalex.org/W2139379087","https://openalex.org/W2585354854","https://openalex.org/W2026059297"],"abstract_inverted_index":{"We":[0,63,80,101],"propose":[1,103],"an":[2],"algebraic":[3],"framework":[4],"for":[5,51,115,136],"end-to-end":[6,26],"physical-layer":[7],"network":[8,20],"coding":[9,21],"based":[10],"on":[11],"submodules":[12],"transmission.":[13],"Our":[14],"approach":[15],"is":[16,45],"motivated":[17],"by":[18],"nested-lattice-based":[19],"schemes,":[22],"that":[23,83,130],"naturally":[24],"induce":[25],"channels":[27],"where":[28],"the":[29,33,85,92,98,116,140],"ambient":[30],"space":[31],"has":[32],"structure":[34],"of":[35,94,106,118,126,139],"a":[36,39,65,104],"module":[37],"over":[38],"principal":[40,60],"ideal":[41,61],"ring.":[42,100],"The":[43],"setup":[44],"compatible":[46],"with":[47],"previously":[48],"proposed":[49],"approaches":[50],"finite":[52],"chain":[53],"rings,":[54],"and":[55,70,78,110],"extends":[56],"them":[57],"to":[58,75,90],"arbitrary":[59],"rings.":[62],"introduce":[64],"distance":[66,86],"function":[67],"between":[68,87],"modules,":[69],"describe":[71],"how":[72],"it":[73],"relates":[74],"information":[76],"loss":[77],"errors.":[79],"also":[81],"show":[82],"computing":[84,91],"modules":[88],"reduces":[89],"length":[93],"certain":[95,137],"ideals":[96],"in":[97],"base":[99],"then":[102],"definition":[105],"submodule":[107,127],"error-correcting":[108],"code,":[109],"establish":[111],"two":[112],"upper":[113],"bounds":[114],"cardinality":[117,135],"these":[119],"codes.":[120],"Finally,":[121],"we":[122],"present":[123],"some":[124],"constructions":[125],"codes,":[128],"showing":[129],"they":[131],"have":[132],"asymptotically":[133],"optimal":[134],"choices":[138],"parameters.":[141]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}