In general, array codes consist of m x n arrays and in many cases, the arrays satisfy parity constraints along lines of different slopes (generally with a toroidal topology). Such codes are useful for RAID type of arc...
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In general, array codes consist of m x n arrays and in many cases, the arrays satisfy parity constraints along lines of different slopes (generally with a toroidal topology). Such codes are useful for RAID type of architectures, since they allow to replace finite field operations by XORs. We present expansions to traditional array codes of this type, like Blaum-Roth (BR) and extended evenodd codes, by adding parity on columns. This vertical parity allows for recovery of one or more symbols in a column locally, i.e., by using the remaining symbols in the column without invoking the rest of the array. Properties and applications of the new codes are discussed, in particular to Locally Recoverable (LRC) codes.
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-Bruc...
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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.
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 ...
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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.
In distributed storage systems that use coding, the issue of minimizing the communication required to rebuild a storage node after a failure arises. We consider the problem of repairing an erased node in a distributed...
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ISBN:
(纸本)9781424488650
In distributed storage systems that use coding, the issue of minimizing the communication required to rebuild a storage node after a failure arises. We consider the problem of repairing an erased node in a distributed storage system that uses an evenodd code. evenodd codes are maximum distance separable (MDS) array codes that are used to protect against erasures, and only require XOR operations for encoding and decoding. We show that when there are two redundancy nodes, to rebuild one erased systematic node, only 3/4 of the information needs to be transmitted. Interestingly, in many cases, the required disk I/O is also minimized.
Proper data placement schemes based on erasure correcting code are one of the most Important components for a highly available data storage system. In this paper, a new class of array codes are introduced which is cal...
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ISBN:
(纸本)9781424413119
Proper data placement schemes based on erasure correcting code are one of the most Important components for a highly available data storage system. In this paper, a new class of array codes are introduced which is called the V codes. The V codes are an Binary Maximum Distance Separable (MDS) codes and correct various double node failures,i.e. minimum column distance 3 and thus is optimal in terms of node failure recovery capability for a given data redundancy. We provide detailed v code's decoding algorithms for correcting various double node failures. We show that the decoding complexity of the V codes is much lower than those of the existing comparable codes, thus the V codes are practically very meaningful for storage systems that need higher reliability.
With the development of modern technology,people have more and more chance to use large storage *** is important to keep the reliability of the modern storage *** are different architectures to achieve the *** Array o...
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With the development of modern technology,people have more and more chance to use large storage *** is important to keep the reliability of the modern storage *** are different architectures to achieve the *** Array of Independent Disks(RAID) architectures are one efficient way to recover the storage system from disk *** different RAID data structures,RAID 6 refers to use two additional parity disks to allow the users to recover from up to two disk ***,there are different ways to perform the RAID *** example,the evenodd code uses an exclusive OR(XOR) operation to calculate *** has low storage requirements and simple *** Row Diagonal Parity(RDP)code is an upgraded version of the evenodd *** reduce the computational consumption of parity-check *** the other hand,the Reed-Solomon code has an efficient recovery algorithm and a quantitative calculation ***,there are other implementation methods with their advantage and limitations for the RAID 6 *** assist the application of RAID6,this paper aims to analyze,implement,and apply different RAID6 *** methodology of the paper is the exclusive literature review of published paper in the field in recent 10 to 20 years.
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