A new piggybacking design for systematic MDS storage codes

Abstract

Distributed storage codes have important applications in the design of modern storage systems. In a distributed storage system, every storage node has a probability to fail and once an individual storage node fails, it must be reconstructed using the data stored in the surviving nodes. Computation load and network bandwidth are two important issues we need to concern when repairing a failed node. Generally speaking, the naive maximum distance separable (MDS) storage codes have low repair complexity but high repair bandwidth. On the contrary, minimum storage regenerating codes have low repair bandwidth but high repair complexity. Fortunately, the newly introduced piggybacked codes combine the advantages of both ones. The main result of this paper is a novel piggybacking design framework for $(k+r,k)$ systematic MDS storage codes, where k, r denote the number of systematic nodes and the number of parity nodes, respectively. In the new code, the average repair bandwidth rate for the systematic nodes, i.e., the ratio of the average repair bandwidth of a single failed systematic node and the amount of the original data, can be as low as $\sqrt{\frac{2}{r}}+\frac{1}{2r}+\frac{3}{k}+\frac{\sqrt{2r}}{k^2}$, which is roughly $\sqrt{\frac{2}{r}}+\frac{1}{2r}$ when the code has high rate $k\gg r$. For relatively large r (e.g., $r\ge 6$), this result significantly improves the previously known one which has average repair bandwidth rate roughly $\frac{r-1}{2r-1}$. In the meanwhile, every failed systematic node of the new code can be reconstructed quickly using the decoding algorithm of a classical MDS code, only with some additional additions over the underlying finite field.