New EVENODD+ Codes with More Flexible Parameters and Lower Complexity
Panyu Zhu
TL;DR
The paper addresses robust binary MDS array codes for RAID-6 by introducing a new EVENODD+-style construction with parameterized per-column sizes. It defines an array of size $\tau(p-1) \times (k+2)$ that supports per-column storage equal to an odd-minus-one multiple of a positive integer, and it utilizes a set of common bits $S_{\mu}$ to manage parity updates. The authors prove the MDS property under the condition that $p$ is odd and every divisor aside from 1 exceeds $k-1$, and they provide decoding procedures for two erasures to establish reliability. They also present a comprehensive complexity analysis showing lower encoding/decoding/update costs compared to the original EVENODD+ codes, particularly when $\tau \ge k-1$, and they demonstrate asymptotically optimal update behavior. Overall, the work offers greater parameter flexibility with improved computational efficiency for double-disk failures in RAID-6 systems.
Abstract
EVENODD+ codes are binary maximum distance separable (MDS) array codes for correcting double disk failures in RAID-6 with asymptotically optimal encoding/decoding/update complexities. However, the number of bits stored in each disk of EVENODD+ codes should be an odd number minus one. In this paper, we present a new construction of EVENODD+ codes that have more flexible parameters. The number of bits stored in each disk of our codes is an odd minus one times any positive integer. Moreover, our codes not only have asymptotically optimal encoding/decoding/update complexities but also have lower encoding/decoding/update complexities than the existing EVENODD+ codes.