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.

Cross-Rack Updates in Vertical Array Codes Storage Systems with High Fault Tolerance

Vertical array codes have less computational complexity and update complexity in comparison with horizontal array codes.However,the fault tolerance of the existing vertical array codes is in general lower than that of horizontal array codes.In addition,the cross-rack bandwidth is often the bottleneck of the update performance in erasure-coded storage systems.In this paper,we propose a cross-rack update(CRU)mechanism for vertical array codes intended to improve both the fault tolerance and update performance of erasure-coded storage systems.CRU builds on three parts:(i)stripe encoding,which can improve the fault tolerance of vertical code by encoding multiple sub-stripe;(ii)node grouping,which filters out the best combination of nodes to minimize cross-rack update traffic;(iii)selective logging,which can selectively log based on the location of data sub-blocks and parity sub-blocks to reduce disk I/O and cross-rack traffic.We evaluate CRU via trace-driven analysis and local cluster experiments.Evaluations show that CRU can significantly reduce cross-rack update traffic and improve system update throughput.