In recent years,a lot of XOR-based coding schemes have been developed to tolerate double disk failures in Redundant Array of Independent Disks (RAID) architectures,such as EVENODD-code,X-code,B-code and BG-HEDP. Despi...In recent years,a lot of XOR-based coding schemes have been developed to tolerate double disk failures in Redundant Array of Independent Disks (RAID) architectures,such as EVENODD-code,X-code,B-code and BG-HEDP. Despite those researches,the decades-old strategy of Reed-Solomon (RS) code remains the only popular space-optimal Maximum Distance Separable (MDS) code for all but the smallest storage systems. The reason is that all those XOR-based schemes are too difficult to be implemented,it mainly because the coding-circle of those codes vary with the number of disks. By contrast,the coding-circle of RS code is a constant. In order to solve this problem,we develop a new MDS code named Latin code and a cascading scheme based on Latin code. The cascading Latin scheme is a nearly MDS code (with only one or two more parity disks compared with the MDS ones). Nev-ertheless,it keeps the coding-circle of the basic Latin code (i.e. a constant) and the low encod-ing/decoding complexity similar to other parity array codes.展开更多
In distributed cloud storage systems, inevitably there exist multiple node failures at the same time. The existing methods of regenerating codes, including minimum storage regenerating(MSR) codes and minimum bandwidth...In distributed cloud storage systems, inevitably there exist multiple node failures at the same time. The existing methods of regenerating codes, including minimum storage regenerating(MSR) codes and minimum bandwidth regenerating(MBR) codes, are mainly to repair one single or several failed nodes, unable to meet the repair need of distributed cloud storage systems. In this paper, we present locally minimum storage regenerating(LMSR) codes to recover multiple failed nodes at the same time. Specifically, the nodes in distributed cloud storage systems are divided into multiple local groups, and in each local group(4, 2) or(5, 3) MSR codes are constructed. Moreover, the grouping method of storage nodes and the repairing process of failed nodes in local groups are studied. Theoretical analysis shows that LMSR codes can achieve the same storage overhead as MSR codes. Furthermore, we verify by means of simulation that, compared with MSR codes, LMSR codes can reduce the repair bandwidth and disk I/O overhead effectively.展开更多
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...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.展开更多
基于单容错编码的数据布局已经不能满足存储系统对可靠性越来越高的要求,而现有的基于多容错编码的数据布局普遍存在编码解码复杂,计算负载大等缺点。文中设计了一种基于双奇偶校验的双容错数据布局DP-RA ID。该布局只需要在磁盘数量为...基于单容错编码的数据布局已经不能满足存储系统对可靠性越来越高的要求,而现有的基于多容错编码的数据布局普遍存在编码解码复杂,计算负载大等缺点。文中设计了一种基于双奇偶校验的双容错数据布局DP-RA ID。该布局只需要在磁盘数量为素数的RA ID 5阵列系统中增加1个校验磁盘,通过水平和对角方向的双重奇偶校验实现双容错。该布局的双重校验条纹长度相同,结构简单,易于实现。而且该布局的编码解码算法简单,计算负载小。研究表明该布局与RA ID 5相比,写操作性能会有少许的下降,读操作性能不变,而可靠性大幅度提高。展开更多
基金Supported in part by the National High Technology Re-search and Development Program of China (2008 AA01Z-401)the National Science Foundation of China (No.60903028)+1 种基金Doctoral Fund of Ministry of Education of China (20070055054)Science and Technology De-velopment Plan of Tianjin (08JCYBJC13000)
文摘In recent years,a lot of XOR-based coding schemes have been developed to tolerate double disk failures in Redundant Array of Independent Disks (RAID) architectures,such as EVENODD-code,X-code,B-code and BG-HEDP. Despite those researches,the decades-old strategy of Reed-Solomon (RS) code remains the only popular space-optimal Maximum Distance Separable (MDS) code for all but the smallest storage systems. The reason is that all those XOR-based schemes are too difficult to be implemented,it mainly because the coding-circle of those codes vary with the number of disks. By contrast,the coding-circle of RS code is a constant. In order to solve this problem,we develop a new MDS code named Latin code and a cascading scheme based on Latin code. The cascading Latin scheme is a nearly MDS code (with only one or two more parity disks compared with the MDS ones). Nev-ertheless,it keeps the coding-circle of the basic Latin code (i.e. a constant) and the low encod-ing/decoding complexity similar to other parity array codes.
基金supported in part by the National Natural Science Foundation of China (61640006, 61572188)the Natural Science Foundation of Shaanxi Province, China (2015JM6307, 2016JQ6011)the project of science and technology of Xi’an City (2017088CG/RC051(CADX002))
文摘In distributed cloud storage systems, inevitably there exist multiple node failures at the same time. The existing methods of regenerating codes, including minimum storage regenerating(MSR) codes and minimum bandwidth regenerating(MBR) codes, are mainly to repair one single or several failed nodes, unable to meet the repair need of distributed cloud storage systems. In this paper, we present locally minimum storage regenerating(LMSR) codes to recover multiple failed nodes at the same time. Specifically, the nodes in distributed cloud storage systems are divided into multiple local groups, and in each local group(4, 2) or(5, 3) MSR codes are constructed. Moreover, the grouping method of storage nodes and the repairing process of failed nodes in local groups are studied. Theoretical analysis shows that LMSR codes can achieve the same storage overhead as MSR codes. Furthermore, we verify by means of simulation that, compared with MSR codes, LMSR codes can reduce the repair bandwidth and disk I/O overhead effectively.
基金supported by the National Basic Research Program of China (Grant Nos.2011CB302300, 2011CB302301)the National High-Technology Research and Development Program of China (Grant Nos.2009AA01A401,2009AA01A402)+1 种基金the National Natural Science Foundation of China (Grant Nos.60873028, 60933002, 61025008)the Changjiang Innovation Group of Education of China (Grant No.IRT0725)
文摘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.
文摘基于单容错编码的数据布局已经不能满足存储系统对可靠性越来越高的要求,而现有的基于多容错编码的数据布局普遍存在编码解码复杂,计算负载大等缺点。文中设计了一种基于双奇偶校验的双容错数据布局DP-RA ID。该布局只需要在磁盘数量为素数的RA ID 5阵列系统中增加1个校验磁盘,通过水平和对角方向的双重奇偶校验实现双容错。该布局的双重校验条纹长度相同,结构简单,易于实现。而且该布局的编码解码算法简单,计算负载小。研究表明该布局与RA ID 5相比,写操作性能会有少许的下降,读操作性能不变,而可靠性大幅度提高。
