Balanced Reed-Solomon codes for all parameters

Wael Halbawi, Zihan Liu, Babak Hassibi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

19 Scopus citations


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.
Original languageEnglish (US)
Title of host publication2016 IEEE Information Theory Workshop (ITW)
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Number of pages5
ISBN (Print)9781509010905
StatePublished - Oct 27 2016
Externally publishedYes

Bibliographical note

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.


Dive into the research topics of 'Balanced Reed-Solomon codes for all parameters'. Together they form a unique fingerprint.

Cite this