Extending and analysis of X-Code

• Published in: Journal of Shanghai University Vol. 15; no. 3; pp. 194 - 200
• Main Author: 金超 冯丹 刘景宁
• Format: Journal Article
• Language: English
• Published: Heidelberg Shanghai University Press 01.06.2011; Wuhan National Laboratory for Optoelectronics, School of Computer Science and Technology, Huazhong University of Science and Technology, Wuhan 430074, P. R. China
• Subjects: Algorithms; Arrays; Classical Mechanics; Code; Constrictions; Disks; Engineering; Environment; Information Technology; Life Sciences; Materials Science; Mathematical and Computational Engineering; Mechatronics; Optimization; Prime numbers; RAID; Redundant; Storage systems; 代码; 任意长度; 利用效率; 存储系统; 最大距离; 独立磁盘冗余阵列; code shortening; X-Code; vertical code; performance analysis; redundant array of independent disk (RAID)-6
• ISSN: 1007-6417; 1863-236X
• DOI: 10.1007/s11741-011-0720-2

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.