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RAID2: Hamming Codes MUKHTARULY Yeldos (ee_myx) CHENG Siu Ho (ee_csh) Wang Wei (ee_wwxab) WANG Su (ee_wsxab) David A Patterson Garth A. Gibson Randy Katz RAID = Redundant Array of Inexpensive Disks

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RAID2: Hamming Codes Bit-level striping with dedicated Hamming-code parity. RAID 2 can recover from 1 disk failure or repair corrupt data or parity when a corrupted bit's corresponding data and parity are good

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RAID2: Hamming Codes Characteristics/Advantages 1)"On the fly" data error correction 2)Extremely high data transfer rates possible 3)The higher the data transfer rate required, the better the ratio of data disks to ECC disks 4)Relatively simple controller design compared to RAID levels 3,4 & 5 Disadvantages 1)Very high ratio of ECC disks to data disks with smaller word sizes - inefficient 2)Entry level cost very high - requires very high transfer rate requirement to justify 3)Transaction rate is equal to that of a single disk at best (with spindle synchronization) 4)No commercial implementations exist / not commercially viable

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Richard Hamming RAID2: Hamming Codes Hamming code is a linear error- correcting code named after its inventor, Richard Hamming Detect up to two simultaneous bit errors Correct single-bit errors

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RAID2: Hamming Codes Hamming(7,4) code It encodes 4 data bits into 7 bits by adding three parity bits. Hamming(7,4) can detect and correct single-bit errors. With the addition of an overall parity bit, it can also detect (but not correct) double-bit errors.

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RAID2: Hamming Codes Hamming(8,4) code The same (7,4) example before but with an extra parity bit Example, 1011 is encoded into 01100110 blue digits are data red digits are parity from the Hamming(7,4) code green digit is the parity added by Hamming(8,4). The green digit makes the parity of the (7,4) code even.

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References http://www.websters-online-dictionary.org/definitions/Hamming+code?cx=partner-pub- 0939450753529744%3Av0qd01-tdlq&cof=FORID%3A9&ie=UTF-8&q=Hamming+code&sa=Search#922 http://www.websters-online-dictionary.org/definitions/Hamming+code?cx=partner-pub- 0939450753529744%3Av0qd01-tdlq&cof=FORID%3A9&ie=UTF-8&q=Hamming+code&sa=Search#922 http://en.wikipedia.org/wiki/RAID http://en.wikipedia.org/wiki/Raid2 http://en.wikipedia.org/wiki/Hamming_code http://www.sindominio.net/~apm/articulos/raid/ref/04_01_02.html MacKay, David J.C. (September 2003). Information Theory, Inference and Learning Algorithms. Cambridge: Cambridge University Press. ISBN 0-521-64298-1. D.K. Bhattacharryya, S. Nandi. "An efficient class of SEC-DED-AUED codes". 1997 International Symposium on Parallel Architectures, Algorithms and Networks (ISPAN '97): 410–415. doi:10.1109/ISPAN.1997.645128.

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