Repairing Cartesian Codes with Linear Exact Repair Schemes

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dc.contributor.authorValvo, Daniel Williamen
dc.contributor.committeechairMatthews, Gretchen L.en
dc.contributor.committeememberMihalcea, Constantin Leonardoen
dc.contributor.committeememberOrr, Daniel D.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2020-06-11T08:00:24Zen
dc.date.available2020-06-11T08:00:24Zen
dc.date.issued2020-06-10en
dc.description.abstractIn this paper, we develop a scheme to recover a single erasure when using a Cartesian code,in the context of a distributed storage system. Particularly, we develop a scheme withconsiderations to minimize the associated bandwidth and maximize the associateddimension. The problem of recovering a missing node's data exactly in a distributedstorage system is known as theexact repair problem. Previous research has studied theexact repair problem for Reed-Solomon codes. We focus on Cartesian codes, and show wecan enact the recovery using a linear exact repair scheme framework, similar to the oneoutlined by Guruswami and Wooters in 2017.en
dc.description.abstractgeneralDistributed storage systems are systems which store a single data file over multiple storage nodes. Each storage node has a certain storage efficiency, the "space" required to store the information on that node. The value of these systems, is their ability to safely store data for extended periods of time. We want to design distributed storage systems such that if one storage node fails, we can recover it from the data in the remaining nodes. Recovering a node from the data stored in the other nodes requires the nodes to communicate data with each other. Ideally, these systems are designed to minimize the bandwidth, the inter-nodal communication required to recover a lost node, as well as maximize the storage efficiency of each node. A great mathematical framework to build these distributed storage systems on is erasure codes. In this paper, we will specifically develop distributed storage systems that use Cartesian codes. We will show that in the right setting, these systems can have a very similar bandwidth to systems build from Reed-Solomon codes, without much loss in storage efficiency.en
dc.description.degreeMaster of Scienceen
dc.format.mediumETDen
dc.identifier.othervt_gsexam:26553en
dc.identifier.urihttp://hdl.handle.net/10919/98818en
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectCartesian codeen
dc.subjectReed-Solomon codeen
dc.subjectexact repair schemesen
dc.subjectfinite fieldsen
dc.subjectdistributed storage networksen
dc.subjectmultivariate polynomialsen
dc.titleRepairing Cartesian Codes with Linear Exact Repair Schemesen
dc.typeThesisen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen

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