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This paper presents a class of binary Maximum Distance Separable (MDS) array codes for tolerating disk failures in Redundant Arrays of Inexpensive Disks (RAID) architecture based on circular permutation matrices. The size of the information part is m \times n, the size of the parity-check part is m \times 3, and the minimum distance is 4, where n is the number of information disks, the number of parity-check disks is 3, and (m+1) is a prime integer. In practical applications, m can be very large and n is from 20 to 50. The code rate is R = {\frac{n}{n+3}}. These codes can be used for tolerating three disk failures. The encoding and decoding of the Reed-Solomon-like codes are very fast. There need to be 3mn XOR operations for encoding and (3mn+9(m+1)) XOR operations for decoding.
Index Terms- Low-density-parity-check codes, MDS array codes, RAID, multiple disk failures, Reed-Solomon codes.
Jia-Chen Shen, Robert H. Deng, Gui-Liang Feng, Feng Bao, "New Efficient MDS Array Codes for RAID Part I: Reed-Solomon-Like Codes for Tolerating Three Disk Failures", IEEE Transactions on Computers, vol. 54, no. , pp. 1071-1080, September 2005, doi:10.1109/TC.2005.150
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