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
Embedded RAM blocks（BRAMs） in field programmable gate arrays（FPGAs） are susceptible to single event effects（SEEs） induced by environmental factors such as cosmic rays, heavy ions, alpha particles and so on. As t...Embedded RAM blocks（BRAMs） in field programmable gate arrays（FPGAs） are susceptible to single event effects（SEEs） induced by environmental factors such as cosmic rays, heavy ions, alpha particles and so on. As technology scales, the issue will be more serious. In order to tackle this issue, two different error correcting codes（ECCs）, the shortened Hamming codes and shortened BCH codes, are investigated in this paper. The concrete design methods of the codes are presented. Also, the codes are both implemented in flash-based FPGAs. Finally, the synthesis report and simulation results are presented in the paper. Moreover, heavy-ion experiments are performed,and the experimental results indicate that the error cross-section of the device using the shortened Hamming codes can be reduced by two orders of magnitude compared with the device without mitigation, and no errors are discovered in the experiments for the device using the shortened BCH codes.展开更多
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.
基金Supported by National Natural Science Foundation of China(11079045,11179003 and 11305233)
文摘Embedded RAM blocks（BRAMs） in field programmable gate arrays（FPGAs） are susceptible to single event effects（SEEs） induced by environmental factors such as cosmic rays, heavy ions, alpha particles and so on. As technology scales, the issue will be more serious. In order to tackle this issue, two different error correcting codes（ECCs）, the shortened Hamming codes and shortened BCH codes, are investigated in this paper. The concrete design methods of the codes are presented. Also, the codes are both implemented in flash-based FPGAs. Finally, the synthesis report and simulation results are presented in the paper. Moreover, heavy-ion experiments are performed,and the experimental results indicate that the error cross-section of the device using the shortened Hamming codes can be reduced by two orders of magnitude compared with the device without mitigation, and no errors are discovered in the experiments for the device using the shortened BCH codes.
