251. Improved Upper Bounds on Systematic-Length for Linear Minimum Storage Regenerating Codes.
- Author
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Kun Huang, Parampalli, Udaya, and Ming Xian
- Subjects
CODING theory ,SUBSPACES (Mathematics) ,VECTOR algebra ,FOUNDATIONS of arithmetic ,LINEAR programming - 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 extends the corresponding result in the literature. [ABSTRACT FROM AUTHOR]- Published
- 2019
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