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We propose a generic transformation that can convert any nonbinary $(n=k{+}r,k)$ maximum distance separable (MDS) code into another $(n,k)$ MDS code over the same field such that: 1) some arbitrarily chosen $r$ nodes have the optimal repair bandwidth and the optimal rebuilding access; 2) for the remaining $k$ nodes, the normalized repair bandwidth and the normalized rebuilding access (over the file size) are preserved; and 3) the sub-packetization level is increased only by a factor of $r$. Two immediate applications of this generic transformation are then presented. The first application is that we can transform any nonbinary MDS code with the optimal repair bandwidth or the optimal rebuilding access for the systematic nodes only, into a new MDS code which possesses the corresponding repair optimality for all nodes. The second application is that by applying the transformation multiple times, any nonbinary $(n,k)$ scalar MDS code can be converted into an $(n,k)$ MDS code with the optimal repair bandwidth and the optimal rebuilding access for all nodes, or only a subset of nodes, whose sub-packetization level is also optimal. [ABSTRACT FROM AUTHOR]

In this paper, we reinterpret the $(k+2,k)$ zigzag code in coding matrix and then propose an optimal exact repair strategy for its parity nodes, whose repair disk I/O approaches a lower bound derived in this paper. [ABSTRACT FROM PUBLISHER]

Piggybacking is an efficient method to decrease the repair bandwidth of maximum distance separable codes. In this paper, in order to reduce the repair bandwidth of parity nodes of the known minimum storage regenerating (MSR) codes with high rate, which is usually the whole amount of the original data, i.e., the maximal, a new systematic piggybacking design is proposed through an in-depth analysis of the design of piggybacking. As a result, new MSR codes are obtained with almost optimal repair bandwidth of parity nodes while retaining the optimal repair bandwidth of systematic nodes. Furthermore, MSR codes with balanced download during node repair process are presented based on the new piggybacking design. [ABSTRACT FROM PUBLISHER]

The newly presented $(k+m,k)$ Hadamard minimum storage regenerating (MSR) codes are a class of high rate storage codes with optimal repair property for single node failure. In this paper, we propose a new simple optimal repair strategy for $(k+m,k)$ Hadamard MSR codes, which can considerably reduce the computation compared with the original one during the node repair. [ABSTRACT FROM PUBLISHER]

In this paper, we present a generic framework for constructing systematic minimum storage regenerating codes with two parity nodes based on the invariant subspace technique. Codes constructed in our framework not only contain some best known codes as special cases, but also include some new codes with key properties, such as the optimal access property and the optimal update property. In particular, for a given storage capacity of an individual node, one of the new codes has the largest number of systematic nodes and two of the new codes have the largest number of systematic nodes with the optimal update property. [ABSTRACT FROM AUTHOR]

As a kind of erasure code, piggybacking has been applied in practice since it can significantly reduce the repair bandwidth of distributed storage systems. Currently, several efficient piggybacking designs have been proposed. In this paper, we propose a more efficient “one-to-one” piggybacking design (OOP) to further reduce the repair bandwidth. Different from the existing piggybacking designs, OOP adopts a simple encoding principle that one parity node only piggybacks symbols from one substripe. Particularly, OOP takes into account the efficient repair of systematic nodes and parity nodes simultaneously. It is shown that for OOP design, the optimal number of substripes is $(\sqrt {r-1}+r-1)$ , the average repair bandwidth ratio of systematic nodes can be as low as $\frac {2\sqrt {r-1}+1}{2\sqrt {r-1}+r}$ , and the average repair bandwidth ratio of parity nodes reaches $\left({\frac {\sqrt {r-1}+1}{r}+\frac {(r-1)^{2}-\sqrt {(r-1)^{3}}}{rk}}\right)$. In contrast to the existing piggybacking designs, OOP can further reduce the repair bandwidth of both system nodes and parity nodes. [ABSTRACT FROM AUTHOR]