RAID-6 Codes Research Articles

Short Code: An Efficient RAID-6 MDS Code for Optimizing Degraded Reads and Partial Stripe Writes

As reliability requirements are increasingly important in both clusters and data centers, RAID-6, which can tolerate any two concurrent disk failures, has been widely used in modern storage systems. However, most existing RAID-6 codes cannot provide satisfied performance on both degraded reads and partial stripe writes, which are important performance metrics in storage systems. To address these problems, in this paper we propose a new RAID-6 MDS erasure code called Short Code, in order to optimize the degraded reads and partial stripe writes. In Short Code, we propose a novel short horizontal parity chain, which assures that all disks contribute to degraded reads while the continuous data elements are more likely to share the same horizontal chain for optimizing degraded reads. On the other hand, Short Code distributes all diagonal parities among disks for optimizing partial stripe writes. The proposed Short Code not only owns the optimal storage efficiency, but also keeps the optimal complexity for both encoding/decoding computations and update operations. The experiments show that Short Code achieves much higher speed on degraded reads and partial stripe writes than other popular RAID-6 codes, and provide acceptable performance on single disk failure recoveries and normal reads. Specifically, compared to RDP code, Short Code provides 6.1 to 26.3 percent higher speed on degraded reads and 36.2 to 80.3 percent higher speed on partial stripe writes with the same number of disks.

DCS: Diagonal Coding Scheme for Enhancing the Endurance of SSD-Based RAID Arrays

To guarantee high reliability, solid-state drive (SSD)-based storage systems require data redundancy schemes, e.g., redundant array of independent disks (RAID) schemes. Traditional RAID-5, RAID-6, and Reed-Solomon codes can tolerate one, two, and an arbitrary number of device failures, respectively. However, some SSDs under those redundant configurations may age much faster than others because of the high skewness and locality of workloads. The uneven aging rates may make some SSDs wear out very quickly and decrease the endurance of SSD-based RAID arrays. To address this problem, we first come up with a diagonal coding scheme (DCS) by distributing the updating dependencies evenly among devices to improve the system-level wear-leveling. DCS can efficiently improve the array endurance if requests are aligned with the stripe size, i.e., when data symbols in the same stripe receive the same number of writes, while the number could be different for different stripes. To relax the above assumption, we further propose an enhanced scheme, DCS+. With a buffer design, DCS+ can improve the wear-leveling among devices under general access patterns via triggering different responses to different kinds of requests. We conduct extensive trace-driven evaluations based on real-world workloads, and results show that our design efficiently enhances the endurance of SSD-based RAID arrays.

An efficient data layout scheme for better I/O balancing in RAID-6 storage systems

Among redundant arrays of independent disks (RAID)-6 codes, maximum distance separable (MDS) based RAID-6 codes are popular because they have the optimal storage efficiency. Although vertical MDS codes exhibit better load balancing compared to horizontal MDS codes in partial stripes, an I/O unbalancing problem still exists in some vertical codes. To address this issue, we propose a novel efficient data layout, uniform P-code (UPC), to support highly balanced I/Os among P-coded disk arrays (i.e., PC). In UPC, the nonuniformly distributed information symbols in each parity chain of P-code are moved along their columns to other rows, thus enabling the parity chain to keep original parity relationships and tolerate double disk failures. The UPC scheme not only achieves optimal storage efficiency, computational complexity, and update complexity, but also supports better I/O balancing in the context of large-scale storage systems. We also conduct a performance study on reconstruction algorithms using an analytical model. Besides extensive theoretical analysis, comparative performance experiments are conducted by replaying real-world workloads under various configurations. Experimental results illustrate that our UPC scheme significantly outperforms the PC scheme in terms of average user response time. In particular, in the case of a 12-disk array, the UPC scheme can improve the access performance of the RAID-6 storage system by 29.9% compared to the PC scheme.

A New Non-MDS RAID-6 Code to Support Fast Reconstruction and Balanced I/Os

RAID-6 is widely applied to tolerate double concurrent disk failures in both disk arrays and storage clusters. Among numerous erasure codes developed to implement RAID-6, Maximum Distance Separable (MDS) Codes are highly popular. Owing to the limitation of parity generating schemes used in MDS codes, RAID-6-based storage systems suffer from unbalance I/Os and low reconstruction performance. Out of consideration for high performance and reliability, we propose a new class of XOR-based RAID-6 code (i.e. |$V^{2}$|-Code), which improves both load balancing and reconstruction performance of the MDS RAID-6 codes. |$V^{2}$|-Code, a very simple yet flexible Non-MDS vertical code, can be easily implemented and deployed in storage systems. |$V^{2}$|-Code's unique features include lowest density code, steady parity chain length and well-balanced computation. We perform theoretical analysis and empirical evaluation of the coding scheme by running a wide range of workload under various configurations. Experimental results show that |$V^{2}$|-Code outperforms four popular codes (i.e. EVENODD, RDP, X-Code and Code-M) in terms of load balancing and reconstruction time. In the single-disk-failure and double-disk-failure cases, |$V^{2}$|-Code can speed up the reconstruction time of X-Code by a factor of up to 3.31 and 1.79, respectively.

MDR Codes: A New Class of RAID-6 Codes with Optimal Rebuilding and Encoding

As storage systems grow in size, device failures happen more frequently than ever before. Given the commodity nature of hard drives employed, a storage system needs to tolerate a certain number of disk failures while maintaining data integrity, and to recover lost data with minimal interference to normal disk I/O operations. RAID-6, which can tolerate up to two disk failures with the minimum redundancy, is becoming widespread. However, traditional RAID-6 codes suffer from high disk I/O overhead during recovery. In this paper, we propose a new family of RAID-6 codes, the Minimum Disk I/O Repairable (MDR) codes, which achieve the optimal disk I/O overhead for single failure recoveries. Moreover, we show that MDR codes can be encoded with the minimum number of bit-wise XOR operations. Simulation results show that MDR codes help to save about half of disk read operations than traditional RAID-6 codes, and thus can reduce the recovery time by up to 40%.

NCCloud: A Network-Coding-Based Storage System in a Cloud-of-Clouds

To provide fault tolerance for cloud storage, recent studies propose to stripe data across multiple cloud vendors. However, if a cloud suffers from a permanent failure and loses all its data, we need to repair the lost data with the help of the other surviving clouds to preserve data redundancy. We present a proxy-based storage system for fault-tolerant multiple-cloud storage called NCCloud, which achieves cost-effective repair for a permanent single-cloud failure. NCCloud is built on top of a network-coding-based storage scheme called the functional minimum-storage regenerating (FMSR) codes, which maintain the same fault tolerance and data redundancy as in traditional erasure codes (e.g., RAID-6), but use less repair traffic and, hence, incur less monetary cost due to data transfer. One key design feature of our FMSR codes is that we relax the encoding requirement of storage nodes during repair, while preserving the benefits of network coding in repair. We implement a proof-of-concept prototype of NCCloud and deploy it atop both local and commercial clouds. We validate that FMSR codes provide significant monetary cost savings in repair over RAID-6 codes, while having comparable response time performance in normal cloud storage operations such as upload/download.

Generalized X-code

Many RAID-6 codes have been proposed in the literature, but each has its limitations. Horizontal code has the ability to adapt to the arbitrary size of a disk array but its high computational complexity is a major shortcoming. In contrast, the computational complexity of vertical code (e.g. X-code) often achieves the theoretical optimality, but vertical code is limited to using a prime number as the size of the disk array In this article, we propose a novel efficient RAID-6 code for arbitrary size of disk array: generalized X-code. We move the redundant elements along their calculation diagonals in X-code onto two specific disks and change two data elements into redundant elements in order to realize our new code. The generalized X-code achieves optimal encoding and updating complexity and low decoding complexity; in addition, it has the ability to adapt to arbitrary size of disk array. Furthermore, we also provide a method for generalizing horizontal code to achieve optimal encoding and updating complexity while keeping the code's original ability to adapt to arbitrary size of disk array.

A Hybrid Approach to Failed Disk Recovery Using RAID-6 Codes

The current parallel storage systems use thousands of inexpensive disks to meet the storage requirement of applications. Data redundancy and/or coding are used to enhance data availability, for instance, Row-diagonal parity (RDP) and EVENODD codes, which are widely used in RAID-6 storage systems, provide data availability with up to two disk failures . To reduce the probability of data unavailability, whenever a single disk fails, disk recovery will be carried out. We find that the conventional recovery schemes of RDP and EVENODD codes for a single failed disk only use one parity disk. However, there are two parity disks in the system, and both can be used for single disk failure recovery. In this article, we propose a hybrid recovery approach that uses both parities for single disk failure recovery, and we design efficient recovery schemes for RDP code (RDOR-RDP) and EVENODD code (RDOR-EVENODD). Our recovery scheme has the following attractive properties: (1) “ read optimality ” in the sense that our scheme issues the smallest number of disk reads to recover a single failed disk and it reduces approximately 1/4 of disk reads compared with conventional schemes; (2) “ load balancing property ” in that all surviving disks will be subjected to the same (or almost the same) amount of additional workload in rebuilding the failed disk. We carry out performance evaluation to quantify the merits of RDOR-RDP and RDOR-EVENODD on some widely used disks with DiskSim. The offline experimental results show that RDOR-RDP and RDOR-EVENODD outperform the conventional recovery schemes of RDP and EVENODD codes in terms of total recovery time and recovery workload on individual surviving disk. However, the improvements are less than the theoretical value (approximately 25%), as RDOR-RDP and RDOR-EVENODD change the disk access pattern from purely sequential to a more random one compared with their conventional schemes.

Extending and analysis of X-Code

X-Code is one of the most important redundant array of independent disk (RAID)-6 codes which are capable of tolerating double disk failures. However, the code length of X-Code is restricted to be a prime number, and such code length restriction of X-Code limits its usage in the real storage systems. Moreover, as a vertical RAID-6 code, X-Code can not be extended easily to an arbitrary code length like horizontal RAID-6 codes. In this paper, a novel and efficient code shortening algorithm for X-Code is proposed to extend X-Code to an arbitrary length. It can be further proved that the code shortening algorithm maintains the maximum-distance-separable (MDS) property of X-Code, and namely, the shortened X-Code is still MDS code with the optimal space efficiency. In the context of the shortening algorithm for X-Code, an in-depth performance analysis on X-Code at consecutive code lengths is conducted, and the impacts of the code shortening algorithm on the performance of X-Code in various performance metrics are revealed.

Minimum density RAID-6 codes

RAID-6 codes protect disk array storage systems from two-disk failures. This article presents a complete treatment of a class of RAID-6 codes, called minimum density RAID-6 codes , that have an optimal blend of performance properties. There are two families of minimal density RAID-6 codes: Blaum-Roth codes and Liberation codes, and a separate special-purpose code called the Liber8tion code. The first of these have been known since the late 1990's, while the latter two are new constructions. In this article, we motivate, demonstrate, and evaluate the minimum density codes, comparing them to EVENODD and RDP codes, which represent the state-of-the-art in RAID-6. Following that, we prove that the codes indeed fit the RAID-6 methodology, and cite their implementation in an open-source library.