A New Minimum Density RAID-6 Code with a Word Size of Eight

RAID-6 storage systems protect k disks of data with twoparity disks so that the system of k+2 disks may toleratethe failure of any two disks. Coding techniques for RAID-6 systems are varied, but an important class of techniquesare those with minimum density, featuring an optimalcombination of encoding, decoding and modificationcomplexity. The word size of a code impacts both how thecode is laid out on each disk's sectors and how large k canbe. Word sizes which are powers of two are especiallyimportant, since they fit precisely into file systemblocks. Minimum density codes exist for many word sizeswith the notable exception of eight. This paper fills thatgap by describing new codes for this important word size.The description includes performancencoding,e properties as well asdetails of the discovery process.

[1]  Bin Zhou,et al.  Scalable Performance of the Panasas Parallel File System , 2008, FAST.

[2]  Jay J. Wylie,et al.  Determining Fault Tolerance of XOR-Based Erasure Codes Efficiently , 2007, 37th Annual IEEE/IFIP International Conference on Dependable Systems and Networks (DSN'07).

[3]  Ethan L. Miller,et al.  Pergamum: Replacing Tape with Energy Efficient, Reliable, Disk-Based Archival Storage , 2008, FAST.

[4]  James Lee Hafner,et al.  WEAVER codes: highly fault tolerant erasure codes for storage systems , 2005, FAST'05.

[5]  Jehoshua Bruck,et al.  X-Code: MDS Array Codes with Optimal Encoding , 1999, IEEE Trans. Inf. Theory.

[6]  James S. Plank.  A tutorial on Reed-Solomon coding for fault-tolerance in RAID-like systems , 1997 .

[7]  Mario Blaum,et al.  On Lowest Density MDS Codes , 1999, IEEE Trans. Inf. Theory.

[8]  Minghua Chen,et al.  Pyramid Codes: Flexible Schemes to Trade Space for Access Efficiency in Reliable Data Storage Systems , 2007, Sixth IEEE International Symposium on Network Computing and Applications (NCA 2007).

[9]  Francine Berman,et al.  Logistical computing and internetworking: middleware for the use of storage in communication , 2001, Proceedings Third Annual International Workshop on Active Middleware Services.

[10]  Peter F. Corbett,et al.  Row-Diagonal Parity for Double Disk Failure Correction (Awarded Best Paper!) , 2004, USENIX Conference on File and Storage Technologies.

[11]  Minghua Chen,et al.  On Optimizing XOR-Based Codes for Fault-Tolerant Storage Applications , 2007, 2007 IEEE Information Theory Workshop.

[12]  F. MacWilliams,et al.  The Theory of Error-Correcting Codes , 1977 .

[13]  Ben Y. Zhao,et al.  Maintenance-Free Global Data Storage , 2001, IEEE Internet Comput..

[14]  James S. Plank.  The RAID-6 Liberation Codes , 2008, FAST.

[15]  Jehoshua Bruck,et al.  EVENODD: An Efficient Scheme for Tolerating Double Disk Failures in RAID Architectures , 1995, IEEE Trans. Computers.

[16]  James Lee Hafner,et al.  HoVer Erasure Codes For Disk Arrays , 2006, International Conference on Dependable Systems and Networks (DSN'06).

[17]  James Lee Hafner,et al.  Matrix methods for lost data reconstruction in erasure codes , 2005, FAST'05.

[18]  Ying Ding,et al.  Note: Correction to the 1997 tutorial on Reed–Solomon coding , 2005, Softw. Pract. Exp..

[19]  Marek Karpinski,et al.  An XOR-based erasure-resilient coding scheme , 1995 .

[20]  James S. Plank,et al.  Small parity-check erasure codes - exploration and observations , 2005, 2005 International Conference on Dependable Systems and Networks (DSN'05).

[21]  Kai Li,et al.  Avoiding the Disk Bottleneck in the Data Domain Deduplication File System , 2008, FAST.