Handle URI:
http://hdl.handle.net/10754/623516
Title:
Balanced Reed-Solomon codes for all parameters
Authors:
Halbawi, Wael; Liu, Zihan; Hassibi, Babak
Abstract:
We construct balanced and sparsest generator matrices for cyclic Reed-Solomon codes with any length n and dimension k. By sparsest, we mean that each row has the least possible number of nonzeros, while balanced means that the number of nonzeros in any two columns differs by at most one. Codes allowing such encoding schemes are useful in distributed settings where computational load-balancing is critical. The problem was first studied by Dau et al. who showed, using probabilistic arguments, that there always exists an MDS code over a sufficiently large field such that its generator matrix is both sparsest and balanced. Motivated by the need for an explicit construction with efficient decoding, the authors of the current paper showed that the generator matrix of a cyclic Reed-Solomon code of length n and dimension k can always be transformed to one that is both sparsest and balanced, when n and k are such that k/n (n-k+1) is an integer. In this paper, we lift this condition and construct balanced and sparsest generator matrices for cyclic Reed-Solomon codes for any set of parameters.
Citation:
Halbawi W, Liu Z, Hassibi B (2016) Balanced Reed-Solomon codes for all parameters. 2016 IEEE Information Theory Workshop (ITW). Available: http://dx.doi.org/10.1109/itw.2016.7606866.
Publisher:
Institute of Electrical and Electronics Engineers (IEEE)
Journal:
2016 IEEE Information Theory Workshop (ITW)
Conference/Event name:
2016 IEEE Information Theory Workshop, ITW 2016
Issue Date:
27-Oct-2016
DOI:
10.1109/itw.2016.7606866
Type:
Conference Paper
Sponsors:
This work was supported in part by the National Science Foundation under grants CNS-0932428, CCF-1018927, CCF-1423663 and CCF-1409204, by a grant from Qualcomm Inc., by NASAs Jet Propulsion Laboratory through the President and Directors Fund, and by King Abdullah University of Science and Technology.
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Full metadata record

DC FieldValue Language
dc.contributor.authorHalbawi, Waelen
dc.contributor.authorLiu, Zihanen
dc.contributor.authorHassibi, Babaken
dc.date.accessioned2017-05-15T10:35:05Z-
dc.date.available2017-05-15T10:35:05Z-
dc.date.issued2016-10-27en
dc.identifier.citationHalbawi W, Liu Z, Hassibi B (2016) Balanced Reed-Solomon codes for all parameters. 2016 IEEE Information Theory Workshop (ITW). Available: http://dx.doi.org/10.1109/itw.2016.7606866.en
dc.identifier.doi10.1109/itw.2016.7606866en
dc.identifier.urihttp://hdl.handle.net/10754/623516-
dc.description.abstractWe construct balanced and sparsest generator matrices for cyclic Reed-Solomon codes with any length n and dimension k. By sparsest, we mean that each row has the least possible number of nonzeros, while balanced means that the number of nonzeros in any two columns differs by at most one. Codes allowing such encoding schemes are useful in distributed settings where computational load-balancing is critical. The problem was first studied by Dau et al. who showed, using probabilistic arguments, that there always exists an MDS code over a sufficiently large field such that its generator matrix is both sparsest and balanced. Motivated by the need for an explicit construction with efficient decoding, the authors of the current paper showed that the generator matrix of a cyclic Reed-Solomon code of length n and dimension k can always be transformed to one that is both sparsest and balanced, when n and k are such that k/n (n-k+1) is an integer. In this paper, we lift this condition and construct balanced and sparsest generator matrices for cyclic Reed-Solomon codes for any set of parameters.en
dc.description.sponsorshipThis work was supported in part by the National Science Foundation under grants CNS-0932428, CCF-1018927, CCF-1423663 and CCF-1409204, by a grant from Qualcomm Inc., by NASAs Jet Propulsion Laboratory through the President and Directors Fund, and by King Abdullah University of Science and Technology.en
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)en
dc.subjectWelch-Berlekamp Algorithmen
dc.subjectReed-Solomon Codesen
dc.subjectError-Correcting Codesen
dc.subjectErasure Codesen
dc.subjectDistributed Storageen
dc.subjectLoad Balancingen
dc.titleBalanced Reed-Solomon codes for all parametersen
dc.typeConference Paperen
dc.identifier.journal2016 IEEE Information Theory Workshop (ITW)en
dc.conference.date2016-09-11 to 2016-09-14en
dc.conference.name2016 IEEE Information Theory Workshop, ITW 2016en
dc.conference.locationCambridge, GBRen
dc.contributor.institutionDepartment of Electrical Engineering, California Institute of Technology, Pasadena, 91125, United Statesen
dc.contributor.institutionDepartment of Information Engineering, The Chinese University of Hong Kong, Shatin, N.T., Hong Kongen
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