Journal article

Improved Upper Bounds on Systematic-Length for Linear Minimum Storage Regenerating Codes

Kun Huang, Udaya Parampalli, Ming Xian

IEEE Transactions on Information Theory | Institute of Electrical and Electronics Engineers | Published : 2019

Abstract

In this paper, we revisit the problem of finding the longest systematic-length k for a linear minimum storage regenerating (MSR) code with optimal repair of only systematic part, for a given per-node storage capacity l and an arbitrary number of parity nodes r. We study the problem by following a geometric analysis of linear subspaces and operators. First, a simple quadratic bound is given, which implies that k = r + 2 is the largest number of systematic nodes in the scalar scenario. Second, an r-based-log bound is derived, which is superior to the upper bound on log-base 2 in the prior work. Finally, an explicit upper bound depending on the value of r 2 /l is introduced, which further exten..

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Grants

Funding Acknowledgements

U. Parampalli was supported in part by the Communications Sensing and Coding Research Network, in part by the International Research and Research Training Fund, and in part by the University of Melbourne, Melbourne, VIC, Australia.