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
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..View full abstract
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.