Well-Rounded Lattices and Applications to Physical Layer Security

dc.contributorAalto-yliopistofi
dc.contributorAalto Universityen
dc.contributor.advisorHollanti Camilla, Prof., Aalto University, Department of Mathematics and Systems Analysis, Finland
dc.contributor.authorDamir, Mohamed Taoufiq
dc.contributor.departmentMatematiikan ja systeemianalyysin laitosfi
dc.contributor.departmentDepartment of Mathematics and Systems Analysisen
dc.contributor.labANTAen
dc.contributor.schoolPerustieteiden korkeakoulufi
dc.contributor.schoolSchool of Scienceen
dc.contributor.supervisorHollanti Camilla, Prof., Aalto University, Department of Mathematics and Systems Analysis, Finland
dc.date.accessioned2020-10-26T13:57:52Z
dc.date.available2020-10-26T13:57:52Z
dc.date.defence2020-11-06
dc.date.issued2020
dc.description.abstract This thesis is devoted to the analysis and construction of well-rounded lattices. The main motivation for studying these objects comes from problems in wireless communications.  In particular, we study lattice codes for wiretap channels in the context of physical layer security. The set of well-rounded lattices has been investigated from topological, geometric and arithmetic point of views.  We contribute to this study by first answering various questions about well-rounded lattices arising from real quadratic fields. Then, motivated by number theoretic constructions, we derive a more general generic construction of lattices generated by their minimal vectors in every dimension.  The last part of the thesis is dedicated to analysing the performance of lattice codes carved from well-rounded lattices. We then motivate the use of such codes over fading channels to achieve both reliable and secure communication. We show that these codes provide nearly optimal solutions in terms of reliability for both additive white Gaussian noisy channels and Rayleigh fading channels. For the security part, we led an experimental and analytical study of well-rounded lattice codes on the wiretap channel.  We conclude that, similarly as well-rounded lattices provide maximisers of lattice sphere packings, they also provide excellent candidates for minimising the eavesdroppers' chances of intercepting a transmitted message.en
dc.format.extent86 + app. 130
dc.format.mimetypeapplication/pdfen
dc.identifier.isbn978-952-64-0042-6 (electronic)
dc.identifier.isbn978-952-60-8830-3 (printed)
dc.identifier.issn1799-4942 (electronic)
dc.identifier.issn1799-4934 (printed)
dc.identifier.issn1799-4934 (ISSN-L)
dc.identifier.urihttps://aaltodoc.aalto.fi/handle/123456789/47215
dc.identifier.urnURN:ISBN:978-952-64-0042-6
dc.language.isoenen
dc.opnBüyükboduk Kazim, Prof., University College Dublin, Ireland
dc.publisherAalto Universityen
dc.publisherAalto-yliopistofi
dc.relation.haspart[Publication 1]: Mohamed Taoufiq Damir, David Karpuk. Well-Rounded Twists of Ideal Lattices from Real Quadratic Fields. Journal of Number Theory, 196, pp. 168–196, 2019. DOI: 10.1016/j.jnt.2018.09.017
dc.relation.haspart[Publication 2]: Mohamed Taoufiq Damir, Lenny Fukshansky. Canonical Basis Twists of Ideal Lattices from Real Quadratic Number Fields. Houston Journal of Mathematics, 45, pp. 103–107, 2019
dc.relation.haspart[Publication 3]: Mohamed Taoufiq Damir, Laia Amorós, Oliver Gnilke, Camilla Hollanti. Analysis of Some Well-Rounded Lattices in Wiretap Channels. 2018 IEEE 19th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), June, 2018. Full text in Acris/Aaltodoc: http://urn.fi/URN:NBN:fi:aalto-201812106348. DOI: 10.1109/SPAWC.2018.8445937
dc.relation.haspart[Publication 4]: Mohamed Taoufiq Damir, Alex Karrila, Laia Amorós, Oliver Gnilke, David Karpuk, Camilla Hollanti. Well-Rounded Lattices: Towards Optimal Coset Codes for Gaussian and Fading Wiretap Channels. Submitted, 29 pages, December 2019
dc.relation.haspart[Publication 5]: Mohamed Taoufiq Damir, Guillermo Mantilla-Soler. Bases of Minimal Vectors in Lagrangian Lattices. Submitted, 24 pages, June 2020
dc.relation.ispartofseriesAalto University publication series DOCTORAL DISSERTATIONSen
dc.relation.ispartofseries160/2020
dc.revVelani, Sanju, Prof., University of York UK
dc.revCosta Sueli, I.R., Prof., University of Campinas, Brazil
dc.subject.keywordwell-rounded latticesen
dc.subject.keywordnumber theoryen
dc.subject.keywordcommunicationen
dc.subject.keywordsecurityen
dc.subject.otherMathematicsen
dc.titleWell-Rounded Lattices and Applications to Physical Layer Securityen
dc.typeG5 Artikkeliväitöskirjafi
dc.type.dcmitypetexten
dc.type.ontasotDoctoral dissertation (article-based)en
dc.type.ontasotVäitöskirja (artikkeli)fi
local.aalto.acrisexportstatuschecked 2020-11-17_2051
local.aalto.archiveyes
local.aalto.formfolder2020_10_26_klo_15_47

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