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    Balanced Reed-Solomon codes for all parameters

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    Type
    Conference Paper
    Authors
    Halbawi, Wael
    Liu, Zihan
    Hassibi, Babak
    Date
    2016-10-27
    Online Publication Date
    2016-10-27
    Print Publication Date
    2016-09
    Permanent link to this record
    http://hdl.handle.net/10754/623516
    
    Metadata
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    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.
    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.
    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
    DOI
    10.1109/itw.2016.7606866
    ae974a485f413a2113503eed53cd6c53
    10.1109/itw.2016.7606866
    Scopus Count
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