P-Code

Abstract

RAID-6 significantly outperforms the other RAID levels in disk-failure tolerance due to its ability to tolerate arbitrary two concurrent disk failures in a disk array. The underlying parity array codes have a significant impact on RAID-6's performance. In this paper, we propose a new XOR-based RAID-6 code, called the Partition Code (P-Code). P-Code is a very simple and flexible vertical code, making it easy to understand and implement. It works on a group of (prime-1) or (prime) disks, and its coding scheme is based on an equal partition of a specified two-integer-tuple set. P-Code has the following properties: (1) it is a Maximum-Distance-Separable (MDS) code, with optimal storage efficiency; (2) it has optimal construction and reconstruction computational complexity; (3) it has optimal update complexity (i.e., the number of parity blocks affected by a single data-block update is minimal). These optimal properties of P-Code are proven mathematically in this paper. While X-Code is provably optimal and RDP is proven optimal in computational complexity and storage efficiency, the latter in its current form is not optimal in update complexity. We propose a row-parity placement strategy for RDP to help it attain optimal update complexity. P-Code complements the other two optimal RAID-6 codes, X-code and the tweaked RDP, to provide a near-full set of optimal RAID-6 configurations of typical disk-array size (e.g., 4-20 disks). That is, for any prime in a typical array size range, P-code can be deployed for (prime-1) disks optimally, while X-code (or P-Code) and the tweaked RDP can be respectively deployed for (prime) and (prime+1) disks optimally. Moreover, P-code's potentially beneficial properties such as the flexible association between the blocks and their labels may find useful applications in distributed environments.