TY - GEN

T1 - Balanced Reed-Solomon codes

AU - Halbawi, Wael

AU - Liu, Zihan

AU - Hassibi, Babak

N1 - KAUST Repository Item: Exported on 2022-06-28
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 - 2016/8/11

Y1 - 2016/8/11

N2 - We consider the problem of constructing linear MDS error-correcting codes with generator matrices that are sparsest and balanced. In this context, sparsest means that every row has the least possible number of non-zero entries, and balanced means that every column contains the same number of non-zero entries. Codes with this structure minimize the maximal computation time of computing any code symbol, a property that is appealing to systems where computational load-balancing is critical. The problem was studied before by Dau et al. where it was shown that there always exists an MDS code over a sufficiently large field such that its generator matrix is both sparsest and balanced. However, the construction is not explicit and more importantly, the resulting MDS codes do not lend themselves to efficient error correction. With an eye towards explicit constructions with efficient decoding, we show in this paper 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, for all parameters n and k where k/n (n - k + 1) is an integer.

AB - We consider the problem of constructing linear MDS error-correcting codes with generator matrices that are sparsest and balanced. In this context, sparsest means that every row has the least possible number of non-zero entries, and balanced means that every column contains the same number of non-zero entries. Codes with this structure minimize the maximal computation time of computing any code symbol, a property that is appealing to systems where computational load-balancing is critical. The problem was studied before by Dau et al. where it was shown that there always exists an MDS code over a sufficiently large field such that its generator matrix is both sparsest and balanced. However, the construction is not explicit and more importantly, the resulting MDS codes do not lend themselves to efficient error correction. With an eye towards explicit constructions with efficient decoding, we show in this paper 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, for all parameters n and k where k/n (n - k + 1) is an integer.

UR - http://hdl.handle.net/10754/679378

UR - http://ieeexplore.ieee.org/document/7541436/

UR - http://www.scopus.com/inward/record.url?scp=84985920563&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2016.7541436

DO - 10.1109/ISIT.2016.7541436

M3 - Conference contribution

SN - 9781509018062

SP - 935

EP - 939

BT - 2016 IEEE International Symposium on Information Theory (ISIT)

PB - IEEE

ER -