TY - GEN

T1 - Balanced Reed-Solomon codes for all parameters

AU - Halbawi, Wael

AU - Liu, Zihan

AU - Hassibi, Babak

N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: 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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2016/10/27

Y1 - 2016/10/27

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/623516

UR - http://ieeexplore.ieee.org/document/7606866/

UR - http://www.scopus.com/inward/record.url?scp=84999046790&partnerID=8YFLogxK

U2 - 10.1109/itw.2016.7606866

DO - 10.1109/itw.2016.7606866

M3 - Conference contribution

SN - 9781509010905

SP - 409

EP - 413

BT - 2016 IEEE Information Theory Workshop (ITW)

PB - Institute of Electrical and Electronics Engineers (IEEE)

ER -