Row-diagonal Parity Research Articles

The Reconstruction of RDP-Based RAID-6 under Double Disk Failures: An In-depth Analysis

As the data volume increases rapidly, the necessity for data storage systems is also rising significantly. The RAID technologies have been widely applied in data storage, due to their reliability and reconstruction ability under disk failures. Furthermore, as the disks in RAIDs increase, disk failures occur more frequently, arousing a considerable amount of data loss. Given this situation, this paper proposes a reconstruction algorithm for double-disk failures and an extension coding scheme which is called RDP+ based on Row-diagonal parity (RDP) to address single-disk failures which are the most common fault at a higher efficiency, providing flexible reliability against disk failures. The simulation in MATLAB provided solid proof of the effectiveness and validity of the algorithm. Additionally, the performance analysis which evaluated RDP and its counterpart in terms of encoding complexity and reconstruction cost showed that RDP+ reduces the reconstruction cost while increasing the encoding complexity.

Performance Analysis of Row-Diagonal Parity (RDP) Algorithm in RAID 6 and Its Application in Cloud Computing

With the explosive growth of information, there is an increasing demand for storage technology, and cloud computing has become a major trend with the continuous development of new technologies. Therefore, this paper aims to find superior fault-tolerant coding schemes and explore their potential applications in the field of cloud computing. This paper provides a brief introduction to the background of RAID systems and fault-tolerant coding; elaborates on the principles and encoding process of the RDP algorithm in detail; deeply analyzes the application and performance of the RDP algorithm in RAID-6, and a comparison was made with RDP coding in cloud storage; and analyzes the development potential and specific application scenarios of the RDP algorithm in the field of cloud computing. Based on the above analysis and research, this paper affirms the development potential of the RDP algorithm in cloud storage based on cloud computing. It also proposes the research direction of the RDP algorithm in the field of cloud computing.

Performance Comparison and Analysis of RAID-6 Encoding and Scaling in Edge Computing Environments

In today's world where cloud computing is widely used, edge computing is starting to be used as a new type of data computing and management service. This paper first describes the importance of data reliability and storage fault tolerance for edge computing operating in multiple environments, and then focuses on RAID-6 to address the data storage requirements of edge computing. In this paper, the feasibility of RAID-6 for edge computing is discussed and two different RAID-6 coding algorithms are introduced. The better option for edge computing is explored through performance comparison. Among the two RAID-6 coding algorithms, it is considered that Row-Diagonal parity will be more suitable than EVENODD code for edge computing scenarios through comparison. But perhaps there are better coding algorithms with lower complexity that can again improve the performance of edge computing storage systems. An edge computing storage system using RAID-6 architecture would be very beneficial for a wide range of real-world application scenarios.

Several Efficient Alternative Solutions for RS Codes in RAID 6

The RAID-6 specification requires a storage system with multiple storage devices to be able to endure the failure of any two parities. RAID-6 can be implemented using a variety of erasure coding methods, but each has drawbacks, like low fault tolerance, bad writing performance low decoding speed, and so on. In this paper, we research a variety of materials, explore RAID 6 disks to comprehend their purpose and prerequisites, and understand how to decode RS codes. In order to help people find a decoding method that is more appropriate to their own systems and actual needs, we research and compare numerous high-quality alternating decoding techniques, and the RAID 6 Liberation codes and Row-Diagonal Parity emerge as the winners. We introduce their decoding methods briefly and list their advantages and disadvantages in this paper for people to request based on their needs. Finally, we compare different decoding methods, propose practical application scenarios and future development directions for these more efficient decoding methods, and also point out their existing shortcomings.

Triple-Disk Recovery RDP Coding: A Robust Solution for Data Storage in RAID Configurations

Data-intensive technologies require reliable and efficient storage solutions to ensure the integrity and availability of vast amounts of generated data. Redundant Arrays of Independent Disks (RAID) technology has emerged as a popular choice, offering fault tolerance and improved performance. Among RAID configurations, RAID-6 stands out for its ability to tolerate up to two disk failures. This is achieved through algorithms like Row-Diagonal Parity (RDP) coding, which introduces redundancy and enables data recovery. In this paper, we propose an innovative approach, namely Triple-Disk Recovery RDP (TDR-RDP), to enhance reliability based on RDP coding by accommodating three disk failures. We review the RDP algorithm, introduce the TDR-RDP coding scheme, elaborate on encoding and decoding processes, and address diverse types of triple disk failures along with their recovery strategies. Furthermore, we evaluate and compare the computing efficiency of TDR-RDP with the RDP algorithm, showcasing its practical feasibility. Overall, the TDR-RDP algorithm offers a compelling solution to bolster data storage reliability in RAID configurations, surpassing traditional RDP coding by ensuring resilience against triple disk failures and augmenting data-intensive technologies.

A Unified Form of EVENODD and RDP Codes and Their Efficient Decoding

Array codes are used widely in data storage systems such as redundant array of independent disks. The row-diagonal parity (RDP) codes and EVENODD codes are two popular double-parity array codes. The increasing capacity of hard disks demands better fault tolerance by using array codes with three or more parity disks. Although many extensions of RDP and EVENODD codes have been proposed, their main drawback is high decoding complexity. In this paper, we propose a unified form of RDP and EVENODD codes under which RDP codes can be treated as shortened EVENODD codes. Moreover, an efficient decoding algorithm based on an LU factorization of a Vandermonde matrix is proposed. The LU decoding method is applicable to all the erasure patterns of RDP and EVENODD codes with three parity columns. It is also applicable to the erasure decoding of RDP and EVENODD codes with more than three parity columns when the number of continuous surviving parity columns is no less than the number of erased information columns and the first parity column has not failed. The proposed efficient decoding algorithm is also applicable to other Vandermonde array codes, with less decoding complexity than that of the existing method.

Single Disk Recovery and Load Balancing Using Parity Declustering

In the recent scenario, capacity of the storage system increases significantly due to increasing demands. Data availability is a major concern in the context of storage systems. In order to achieve high data availability, a Maximum Distance Separable (MDS) code such as Row-Diagonal Parity (RDP) is used in RAID 6 storage systems. In order to ensure continuous availability of data, even a failure in a single disk cannot be tolerated and hence it must be recovered at the earliest. Existing RDOR-RDP, a modified scheme of RDP that achieves minimal disk I/O access and reduced recovery time when compared with conventional scheme but yet fails to achieve load balancing during the recovery process. In this work, Parity declustering based load balancing is proposed, which provides optimal recovery time when compared to RDOR-RDP.

On the MDS Condition of Blaum–Bruck–Vardy Codes With Large Number Parity Columns

Binary maximum distance separable (MDS) array codes are widely used in storage systems. EVENODD code and row-diagonal parity (RDP) code are two well-known binary MDS array codes with two parity columns. The Blaum–Bruck–Vardy (BBV) code is an extension of the double-erasure-correcting EVENODD code. It is known that the BBV code is always MDS for three parity columns, and sufficient conditions for up to eight parity columns to be MDS are also known. However, the MDS condition for more than eight parity columns is an open problem since then. In this letter, we study the MDS condition of BBV code and give a sufficient MDS condition of the BBV code with more than eight parity columns.

RDDP: An efficient MDS array code on toleration triple node failures in storage system

It is well known that erasure coding can be used in storage systems to efficiently store data while protecting against failures. Conventionally, the design of erasure codes has focused on the tradeoff between redundancy and reliability. Under this criterion, an maximum distance separable(MDS) code has optimal redundancy. In this paper, we address a new class of MDS array codes for tolerating triple node failures by extending the row diagonal parity(RDP) code, named the RDDP(row double diagonal parity) code. The RDDP code takes advantages of good performances of the RDP code with balanced I/O. A specific triple-erasure decoding algorithm to reduce decoding complexity is depicted by geometric graph, and it is easily implemented by software and hardware. The theoretical analysis shows that the comprehensive properties of the RDDP code are optimal, such as encoding and decoding efficiency, update efficiency and I/O balance performance.

A Data Placement Based on Toleration Triple Failures

随着存储介质的增多，单容错、双容错的数据布局方案已经无法满足现有分布式存储系统对可靠性要求。该文在双容错行对角奇偶校验(Row Diagonal Parity, RDP)码的基础上，提出一种新的扩展行对角奇偶校验 (Extending Row Diagonal Parity, E-RDP)码，能够容许任何3存储节点出错，具有最大距离可分(Maximum Distance Separable, MDS)编码特性，冗余率与纠错能力达到3容错编码最优。并采用不同斜率几何直线图描述编译码过程，给出了一种快速译码算法，易于软硬件实现。与其它纠删码数据布局方案进行比较，理论分析结果表明，E-RDP码的空间利用率、编译码效率、小写性能以及平衡性的综合性能达到最优，具有实用价值。

RAID triple parity

RAID triple parity (RTP) is a new algorithm for protecting against three-disk failures. It is an extension of the double failure correction Row-Diagonal Parity code. For any number of data disks, RTP uses only three parity disks. This is optimal with respect to the amount of redundant information required and accessed. RTP uses XOR operations and stores all data un-encoded. The algorithm's parity computation complexity is provably optimal. The decoding complexity is also much lower than that of existing comparable codes. This paper also describes a symmetric variant of the algorithm where parity computation is identical to triple reconstruction.

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.

Optimal recovery of single disk failure in RDP code storage systems

Modern storage systems use thousands of inexpensive disks to meet the storage requirement of applications. To enhance the data availability, some form of redundancy is used. For example, conventional RAID-5 systems provide data availability for single disk failure only, while recent advanced coding techniques such as row-diagonal parity (RDP) can provide data availability with up to two disk failures. To reduce the probability of data unavailability, whenever a single disk fails, disk recovery (or rebuild) will be carried out. We show that conventional recovery scheme of RDP code for a single disk failure is inefficient and suboptimal. In this paper, we propose an optimal and efficient disk recovery scheme, Row-Diagonal Optimal Recovery (RDOR), for single disk failure of RDP code that has the following properties: (1) it is read optimal in the sense that it issues the smallest number of disk reads to recover the failed disk; (2) it has the load balancing property that all surviving disks will be subjected to the same amount of additional workload in rebuilding the failed disk. We carefully explore the design state space and theoretically show the optimality of RDOR. We carry out performance evaluation to quantify the merits of RDOR on some widely used disks.

Higher reliability redundant disk arrays

Parity is a popular form of data protection in redundant arrays of inexpensive/independent disks (RAID) . RAID5 dedicates one out of N disks to parity to mask single disk failures, that is, the contents of a block on a failed disk can be reconstructed by exclusive-ORing the corresponding blocks on surviving disks. RAID5 can mask a single disk failure, and it is vulnerable to data loss if a second disk failure occurs. The RAID5 rebuild process systematically reconstructs the contents of a failed disk on a spare disk, returning the system to its original state, but the rebuild process may be unsuccessful due to unreadable sectors. This has led to two disk failure tolerant arrays (2DFTs) , such as RAID6 based on Reed-Solomon (RS) codes. EVENODD, RDP (Row-Diagonal-Parity), the X-code, and RM2 (Row-Matrix) are 2DFTs with parity coding. RM2 incurs a higher level of redundancy than two disks, while the X-code is limited to a prime number of disks. RDP is optimal with respect to the number of XOR operations at the encoding, but not for short write operations. For small symbol sizes EVENODD and RDP have the same disk access pattern as RAID6, while RM2 and the X-code incur a high recovery cost with two failed disks. We describe variations to RAID5 and RAID6 organizations, including clustered RAID, different methods to update parities, rebuild processing, disk scrubbing to eliminate sector errors, and the intra-disk redundancy (IDR) method to deal with sector errors. We summarize the results of recent studies of failures in hard disk drives. We describe Markov chain reliability models to estimate RAID mean time to data loss (MTTDL) taking into account sector errors and the effect of disk scrubbing. Numerical results show that RAID5 plus IDR attains the same MTTDL level as RAID6, while incurring a lower performance penalty. We conclude with a survey of analytic and simulation studies of RAID performance and tools and benchmarks for RAID performance evaluation.

Performance of Two-Disk Failure-Tolerant Disk Arrays

RAID5 disk arrays use the rebuild process to reconstruct the contents of a failed disk on a spare disk, but this process is unsuccessful if latent sector failures are encountered or a second disk failure occurs. The high cost of data loss has led to two-disk failure-tolerant (2DFT) arrays: RAID6, EVENODD, row-diagonal parity (RDP), and RM2. RAID6 uses Reed-Solomon (RS) codes, whereas the latter three use parity encoding. This paper is concerned with the performance from the viewpoint of disk accesses, which, with an appropriate choice of symbol sizes, is the same for RAID6, EVENODD, and RDP, rather than the computational cost (number of XOR operations). We compare the performance of 2DFTs with each other, as well as RAIDO and RAID5 in normal and degraded operating modes. We derive cost functions for processing discrete disk accesses. The mean response time can be obtained analytically with Poisson arrivals and first-come, first-served (FCFS) scheduling. A simulation is used for validation, calibrating the approximate fork-join response analysis, and shortest-access-time-first (SATF) scheduling. The response time for read requests in RAID6 and RM2 is higher than RAID5 and RAIDO and increases with the fraction of write requests. When there is a single disk failure, RM2 outperforms RAID6 since it has a smaller parity group size than RAID6, but RAID6 outperforms RM2 with two disk failures because of its costlier recovery process. Disk loads in RM2 and RAID6 in degraded mode are unbalanced, and a solution based on pseudorandom permutations is proposed for this purpose