{"id":"https://openalex.org/W2569741146","doi":"https://doi.org/10.1109/tit.2013.2274264","title":"An Algebraic Approach to Physical-Layer Network Coding","display_name":"An Algebraic Approach to Physical-Layer Network Coding","publication_year":2013,"publication_date":"2013-08-16","ids":{"openalex":"https://openalex.org/W2569741146","doi":"https://doi.org/10.1109/tit.2013.2274264","mag":"2569741146"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2013.2274264","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2013.2274264","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1005.2646","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100699149","display_name":"Chen Feng","orcid":"https://orcid.org/0000-0002-6726-0259"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Chen Feng","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Toronto, Toronto, ONT, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Toronto, Toronto, ONT, Canada","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101822966","display_name":"Danilo Silva","orcid":"https://orcid.org/0000-0001-6290-7968"},"institutions":[{"id":"https://openalex.org/I4104125","display_name":"Universidade Federal de Santa Catarina","ror":"https://ror.org/041akq887","country_code":"BR","type":"education","lineage":["https://openalex.org/I4104125"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Danilo Silva","raw_affiliation_strings":["Department of Electrical Engineering, Federal University of Santa Catarina, Santa Catarina, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Federal University of Santa Catarina, Santa Catarina, Brazil","institution_ids":["https://openalex.org/I4104125"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077846751","display_name":"Frank R. Kschischang","orcid":"https://orcid.org/0000-0002-4274-1785"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Frank R. Kschischang","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Toronto, Toronto, ONT, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Toronto, Toronto, ONT, Canada","institution_ids":["https://openalex.org/I185261750"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":44.2874,"has_fulltext":false,"cited_by_count":234,"citation_normalized_percentile":{"value":0.99885754,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"59","issue":"11","first_page":"7576","last_page":"7596"},"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/T10964","display_name":"Wireless Communication Security Techniques","score":0.9983000159263611,"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/T11458","display_name":"Advanced Wireless Communication Technologies","score":0.996999979019165,"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/linear-network-coding","display_name":"Linear network coding","score":0.6770431399345398},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.6345311403274536},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.604830265045166},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.556167483329773},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.5532827973365784},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.4867715835571289},{"id":"https://openalex.org/keywords/relay","display_name":"Relay","score":0.45773887634277344},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4568524956703186},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.45684540271759033},{"id":"https://openalex.org/keywords/encoding","display_name":"Encoding (memory)","score":0.4198739528656006},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3828886151313782},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36614298820495605},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3419055938720703},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.11466717720031738},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08147168159484863}],"concepts":[{"id":"https://openalex.org/C138293262","wikidata":"https://www.wikidata.org/wiki/Q1089578","display_name":"Linear network coding","level":3,"score":0.6770431399345398},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.6345311403274536},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.604830265045166},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.556167483329773},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5532827973365784},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.4867715835571289},{"id":"https://openalex.org/C2778156585","wikidata":"https://www.wikidata.org/wiki/Q174053","display_name":"Relay","level":3,"score":0.45773887634277344},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4568524956703186},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.45684540271759033},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.4198739528656006},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3828886151313782},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36614298820495605},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3419055938720703},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.11466717720031738},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08147168159484863},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2013.2274264","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2013.2274264","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"},{"id":"pmh:oai:arXiv.org:1005.2646","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1005.2646","pdf_url":"https://arxiv.org/pdf/1005.2646","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1005.2646","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1005.2646","pdf_url":"https://arxiv.org/pdf/1005.2646","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/9","score":0.4699999988079071,"display_name":"Industry, innovation and infrastructure"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":75,"referenced_works":["https://openalex.org/W3320337","https://openalex.org/W169134948","https://openalex.org/W569064703","https://openalex.org/W1512888666","https://openalex.org/W1538714775","https://openalex.org/W1542869039","https://openalex.org/W1552540770","https://openalex.org/W1557027117","https://openalex.org/W1949836348","https://openalex.org/W1974398767","https://openalex.org/W1975099099","https://openalex.org/W1975868872","https://openalex.org/W2005196269","https://openalex.org/W2017970496","https://openalex.org/W2028445731","https://openalex.org/W2034379372","https://openalex.org/W2036845965","https://openalex.org/W2048540241","https://openalex.org/W2050374329","https://openalex.org/W2071788187","https://openalex.org/W2081934635","https://openalex.org/W2084641497","https://openalex.org/W2086969113","https://openalex.org/W2088719955","https://openalex.org/W2092901733","https://openalex.org/W2093032017","https://openalex.org/W2098192607","https://openalex.org/W2100770837","https://openalex.org/W2101111985","https://openalex.org/W2102613170","https://openalex.org/W2103320637","https://openalex.org/W2104507248","https://openalex.org/W2106403318","https://openalex.org/W2107242185","https://openalex.org/W2109962983","https://openalex.org/W2122621581","https://openalex.org/W2123973657","https://openalex.org/W2127068662","https://openalex.org/W2127117141","https://openalex.org/W2129344187","https://openalex.org/W2129498976","https://openalex.org/W2132100261","https://openalex.org/W2135073150","https://openalex.org/W2138577627","https://openalex.org/W2138928022","https://openalex.org/W2139416652","https://openalex.org/W2141040012","https://openalex.org/W2142465343","https://openalex.org/W2147017752","https://openalex.org/W2147355810","https://openalex.org/W2149615851","https://openalex.org/W2151450116","https://openalex.org/W2151805451","https://openalex.org/W2152496949","https://openalex.org/W2153739324","https://openalex.org/W2153810958","https://openalex.org/W2154089176","https://openalex.org/W2160130902","https://openalex.org/W2164654926","https://openalex.org/W2165325690","https://openalex.org/W2167709639","https://openalex.org/W2168945554","https://openalex.org/W2171404116","https://openalex.org/W2570053574","https://openalex.org/W2949712139","https://openalex.org/W2963217749","https://openalex.org/W3099152093","https://openalex.org/W3103017684","https://openalex.org/W3158755844","https://openalex.org/W4237963784","https://openalex.org/W4292408570","https://openalex.org/W6632495270","https://openalex.org/W6673621702","https://openalex.org/W6785394758","https://openalex.org/W6785672084"],"related_works":["https://openalex.org/W2258031046","https://openalex.org/W2368824897","https://openalex.org/W2151578621","https://openalex.org/W2030775967","https://openalex.org/W1508050556","https://openalex.org/W1910862367","https://openalex.org/W2379365082","https://openalex.org/W2370747590","https://openalex.org/W2030109976","https://openalex.org/W2369260257"],"abstract_inverted_index":{"The":[0,105,144],"problem":[1],"of":[2,21,100,131,147,150,161,185,200,217],"designing":[3],"physical-layer":[4],"network":[5,57,114,123],"coding":[6,58,115,124,183],"(PNC)":[7],"schemes":[8,60,102,133,152,171],"via":[9],"nested":[10,87,164],"lattices":[11],"is":[12,36,49,78,91,153,205,220],"considered.":[13],"Building":[14],"on":[15,84,120,140,175],"the":[16,85,157,162,198,210],"compute-and-forward":[17],"(C&F)":[18],"relaying":[19],"strategy":[20],"Nazer":[22],"and":[23,69,96,178,207],"Gastpar,":[24],"who":[25],"demonstrated":[26],"its":[27,40],"asymptotic":[28],"gain":[29],"using":[30],"information-theoretic":[31],"tools,":[32],"an":[33],"algebraic":[34],"approach":[35],"taken":[37],"to":[38,111,187,209],"show":[39],"potential":[41],"in":[42,93],"practical,":[43],"nonasymptotic,":[44],"settings.":[45],"A":[46,177,215],"general":[47],"framework":[48],"developed":[50,221],"for":[51,61],"studying":[52],"nested-lattice-based":[53],"PNC":[54],"schemes-called":[55],"lattice":[56,88,165],"(LNC)":[59],"short-by":[62],"making":[63],"a":[64,74,112,137,224],"direct":[65],"connection":[66],"between":[67],"C&F":[68,90],"module":[70],"theory.":[71],"In":[72],"particular,":[73],"generic":[75,106],"LNC":[76,101,107,132,142,151,170],"scheme":[77,108],"presented":[79],"that":[80,181],"makes":[81],"no":[82],"assumptions":[83],"underlying":[86,163],"code.":[89,166],"reinterpreted":[92],"this":[94,148],"framework,":[95],"several":[97],"generalized":[98],"constructions":[99],"are":[103,134,172],"given.":[104],"naturally":[109],"leads":[110],"linear":[113,203],"channel":[116],"over":[117],"modules,":[118],"based":[119,174],"which":[121],"noncoherent":[122],"can":[125,190],"be":[126,191],"achieved.":[127],"Next,":[128],"performance/complexity":[129],"tradeoffs":[130],"studied,":[135],"with":[136,193,223],"particular":[138],"focus":[139],"hypercube-shaped":[141,169],"schemes.":[143],"error":[145],"probability":[146],"class":[149],"largely":[154],"determined":[155],"by":[156],"minimum":[158],"intercoset":[159],"distances":[160],"Several":[167],"illustrative":[168],"designed":[173],"Constructions":[176],"D,":[179],"showing":[180],"nominal":[182],"gains":[184],"3":[186],"7.5":[188],"dB":[189],"obtained":[192],"reasonable":[194],"decoding":[195,201],"complexity.":[196],"Finally,":[197],"possibility":[199],"multiple":[202],"combinations":[204],"considered":[206],"related":[208],"shortest":[211],"independent":[212],"vectors":[213],"problem.":[214],"notion":[216],"dominant":[218],"solutions":[219],"together":[222],"suitable":[225],"lattice-reduction-based":[226],"algorithm.":[227]},"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":23},{"year":2017,"cited_by_count":23},{"year":2016,"cited_by_count":29},{"year":2015,"cited_by_count":36},{"year":2014,"cited_by_count":31},{"year":2013,"cited_by_count":25},{"year":2012,"cited_by_count":12}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
