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- W2969089074 abstract "An $(n,k,d)$ cooperative regenerating code provides the optimal-bandwidth repair for any $t~(t!>!1)$ node failures in a cooperative way. In particular, an MSCR (minimum storage cooperative regenerating) code retains the same storage overhead as an $(n,k)$ MDS code. Suppose each node stores $alpha $ symbols which indicates the sub-packetization level of the code. A scalar MSCR code attains the minimum sub-packetization, i.e., $alpha =d-k+t$ . By now, all existing constructions of scalar MSCR codes restrict to very special parameters, eg. $d=k$ or $k=2$ , etc. In a recent work, Ye and Barg construct MSCR codes for all $n,k,d,t$ , however, their construction needs $alpha approx text {exp}(n^{t})$ which is almost infeasible in practice. In this paper, we give an explicit construction of scalar MSCR codes for all $dgeq max {2k-1-t,k}$ , which covers all possible parameters except the case of $kleq dleq 2k-2-t$ when $k . Moreover, as a complementary result, for $k we prove the nonexistence of linear scalar MSCR codes that have invariant repair spaces. Our construction and most of the previous scalar MSCR codes all have invariant repair spaces and this property is appealing in practice because of convenient repair. In this sense, this work presents an almost full description of usual scalar MSCR codes." @default.
- W2969089074 created "2019-08-22" @default.
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- W2969089074 date "2020-02-01" @default.
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- W2969089074 title "Scalar MSCR Codes via the Product Matrix Construction" @default.
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- W2969089074 doi "https://doi.org/10.1109/tit.2019.2934114" @default.
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