EVENODD: An Efficient Scheme for Tolerating Double Disk Failures in RAID Architectures

We present a novel method, that we call EVENODD, for tolerating up to two disk failures in RAID architectures. EVENODD employs the addition of only two redundant disks and consists of simple exclusive-OR computations. This redundant storage is optimal, in the sense that two failed disks cannot be retrieved with less than two redundant disks. A major advantage of EVENODD is that it only requires parity hardware, which is typically present in standard RAID-5 controllers. Hence, EVENODD can be implemented on standard RAID-5 controllers without any hardware changes. The most commonly used scheme that employes optimal redundant storage (i.e., two extra disks) is based on Reed-Solomon (RS) error-correcting codes. This scheme requires computation over finite fields and results in a more complex implementation. For example, we show that the complexity of implementing EVENODD in a disk array with 15 disks is about 50% of the one required when using the RS scheme. The new scheme is not limited to RAID architectures: it can be used in any system requiring large symbols and relatively short codes, for instance, in multitrack magnetic recording. To this end, we also present a decoding algorithm for one column (track) in error

Self-Repairing Disk Arrays

As the prices of magnetic storage continue to decrease, the cost of replacing failed disks becomes increasingly dominated by the cost of the service call itself. We propose to eliminate these calls by building disk arrays that contain enough spare disks to operate without any human intervention during their whole lifetime. To evaluate the feasibility of this approach, we have simulated the behavior of two-dimensional disk arrays with n parity disks and n(n-1)/2 data disks under realistic failure and repair assumptions. Our conclusion is that having n(n+1)/2 spare disks is more than enough to achieve a 99.999 percent probability of not losing data over four years. We observe that the same objectives cannot be reached with RAID level 6 organizations and would require RAID stripes that could tolerate triple disk failures.Comment: Part of ADAPT Workshop proceedings, 2015 (arXiv:1412.2347

Zigzag Codes: MDS Array Codes with Optimal Rebuilding

MDS array codes are widely used in storage systems to protect data against erasures. We address the \emph{rebuilding ratio} problem, namely, in the case of erasures, what is the fraction of the remaining information that needs to be accessed in order to rebuild \emph{exactly} the lost information? It is clear that when the number of erasures equals the maximum number of erasures that an MDS code can correct then the rebuilding ratio is 1 (access all the remaining information). However, the interesting and more practical case is when the number of erasures is smaller than the erasure correcting capability of the code. For example, consider an MDS code that can correct two erasures: What is the smallest amount of information that one needs to access in order to correct a single erasure? Previous work showed that the rebuilding ratio is bounded between 1/2 and 3/4, however, the exact value was left as an open problem. In this paper, we solve this open problem and prove that for the case of a single erasure with a 2-erasure correcting code, the rebuilding ratio is 1/2. In general, we construct a new family of $r$-erasure correcting MDS array codes that has optimal rebuilding ratio of $\frac{e}{r}$ in the case of $e$ erasures, $1 \le e \le r$. Our array codes have efficient encoding and decoding algorithms (for the case $r=2$ they use a finite field of size 3) and an optimal update property.Comment: 23 pages, 5 figures, submitted to IEEE transactions on information theor