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dc.contributor.authorMartínez Peñas, Umberto 
dc.date.accessioned2024-12-20T10:33:30Z
dc.date.available2024-12-20T10:33:30Z
dc.date.issued2024
dc.identifier.citationFinite Fields and Their Applications, 2024, vol. 96, 102421es
dc.identifier.issn1071-5797es
dc.identifier.urihttps://uvadoc.uva.es/handle/10324/72945
dc.descriptionProducción Científicaes
dc.description.abstractWe consider information-theoretical private information retrieval (PIR) from a coded database with colluding servers. We target, for the first time, locally repairable storage codes (LRCs). We consider any number of local groups g, locality r, local distance δ and dimension k. Our main contribution is a PIR scheme for maximally recoverable (MR) LRCs based on linearized Reed–Solomon codes, which achieve the smallest field sizes among MR-LRCs for many parameter regimes. In our scheme, nodes are identified with codeword symbols and servers are identified with local groups of nodes. Only locally non-redundant information is downloaded from each server, that is, only r nodes (out of r + δ − 1) are downloaded per server. The PIR scheme achieves the (download) rate R = (N −k−rt+1)/N, where N = gr is the length of the MDS code obtained after removing the local parities, and for any t colluding servers such that k+rt ≤ N. For an unbounded number of stored files, the obtained rate is strictly larger than those of known PIR schemes that work for any MDS code. Finally, the obtained PIR scheme can also be adapted when communication between the user and each server is performed via linear network coding, achieving the same rate as previous PIR schemes for this scenario but with polynomial finite field sizes, instead of exponential. Our rates are equal to those of PIR schemes for Reed–Solomon codes, but Reed–Solomon codes are incompatible with the MR-LRC property or linear network coding, thus our PIR scheme is less restrictive in its applications.es
dc.format.mimetypeapplication/pdfes
dc.language.isoenges
dc.publisherElsevieres
dc.rights.accessRightsinfo:eu-repo/semantics/openAccesses
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/*
dc.subject.classificationDistributed storagees
dc.subject.classificationLinearized Reed-Solomon codeses
dc.subject.classificationLocally repairable codeses
dc.subject.classificationNetwork codinges
dc.subject.classificationPrivate information retrievales
dc.titlePrivate information retrieval from locally repairable databases with colluding serverses
dc.typeinfo:eu-repo/semantics/articlees
dc.rights.holder© 2024 The Authores
dc.identifier.doi10.1016/j.ffa.2024.102421es
dc.relation.publisherversionhttps://www.sciencedirect.com/science/article/pii/S1071579724000601es
dc.identifier.publicationfirstpage102421es
dc.identifier.publicationtitleFinite Fields and Their Applicationses
dc.identifier.publicationvolume96es
dc.peerreviewedSIes
dc.description.projectThe Independent Research Fund Denmark (Grant No. DFF-7027-00053B)es
dc.rightsAtribución 4.0 Internacional*
dc.type.hasVersioninfo:eu-repo/semantics/publishedVersiones


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