An explicit, coupled-layer construction of a high-rate MSR code with low sub-packetization level, small field size and d < (n − 1)

Abstract

This paper presents an explicit construction for an ((n &#x003D; 2qt, k &#x003D; 2q{t&#x2212;1), d &#x003D; n &#x2212; (q &#x002B; 1)), (&#x03B1; &#x003D; q(2q)<sup>t&#x2212;1</sup>,&#x03B2; &#x003D; &#x03B1;/q)) regenerating code over a field F<inf>q</inf> operating at the Minimum Storage Regeneration (MSR) point. The MSR code can be constructed to have rate k/n as close to 1 as desired, sub-packetization level &#x03B1; &#x2264; r<sup>n/r</sup> for r &#x003D; (n &#x2212; k), field size Q no larger than n and where all code symbols can be repaired with the same minimum data download. This is the first-known construction of such an MSR code for d &#x003C; (n &#x2212; 1).

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@article{Sasidharan2017AnEC, title={An explicit, coupled-layer construction of a high-rate MSR code with low sub-packetization level, small field size and d < (n − 1)}, author={Birenjith Sasidharan and Myna Vajha and P. Vijay Kumar}, journal={2017 IEEE International Symposium on Information Theory (ISIT)}, year={2017}, pages={2048-2052} }