Balanced Reed-Solomon codes

Wael Halbawi, Zihan Liu, Babak Hassibi

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

15 Scopus citations

Abstract

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.
Original languageEnglish (US)
Title of host publication2016 IEEE International Symposium on Information Theory (ISIT)
PublisherIEEE
Pages935-939
Number of pages5
ISBN (Print)9781509018062
DOIs
StatePublished - Aug 11 2016
Externally publishedYes

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