Abstract-We present a novel method, that we call EVEN ODD, for tolerating up to two disk failures in RAID architectures. EVEN ODD employs the addition of only two redundant disks and consists of simple exclusive-OR computations. This redundant storage is optimal, in the sense that two failed disks cannot be retrieved with less than two redundant disks. A major advantage of EVENODD is that it only requires parity hardware, which is typically present in standard RAID-S controllers. Hence, EVENODD can be implemented on standard RAID-S controllers without any hardware changes. The most commonly used scheme that employes optimal redundant storage (i.e., two extra disks) is based on Reed-Solomon (RS) error-correcting codes. This scheme requires computation over finite fields and results in a more complex implementation. For example, we show that the complexity of implementing EVENODD in a disk array with 15 disks is about 50% of the one required when using the RS scheme.The new scheme is not limited to RAID architectures: it can be used in any system requiring large symbols and relatively short codes, for instance, in multitrack magnetic recording. To this end, we also present a decoding algorithm for one column (track) in error.

We present a novel method, that we call EVEN-

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The storage hierarchy is a natural structure, given the set of available technologies and their price and performance characteristics. The physical structure of the storage subsystem is described, and the flow of data through the system is traced. The concept of a storage hierarchy is discussed, and the specific components of the IBM storage hierarchy from the processor highspeed buffer (HSB) to the on-line DASD configuration are described in detail. Trade-offs between technologies and the interactions among the levels of the hierarchy are discussed. In particular, the importance of the I/O boundary, processor storage volatility, and data sharing are highlighted. A continuous increase in virtual storage capacity can be seen in the evolution of large-scale operating systems, and MVS/ESA™ now provides the ultimate virtual capacity and function. New virtual structures available in MVS/ESA are discussed, and their relationship to the storage hierarchy is studied. The importance of storage to the performance and cost of a large processing system leads to a discussion of guidelines for storage configuration and data placement within the hierarchy. 95193. Mr. Brady joined IBM in 1961 as a systems engineer-scientific. He has held various positions in the Data Processing, Advanced Systems Development, Systems Products, Data Systems, and General Products Divisions. He was manager ofDSD systems technology and strategy, where he initiated the development of the Enterprise Systems Architecture and expanded storage. Mr. Brady is currently product manager ofGPD storage systems strategy and architecture, where he is responsible for performance analysis, architecture, and the development of new product opportunities. Mr. Brady graduated from Creighton University in 1961, with a B.S. degree in mathematics. He has done graduate work in mathematics and business administration and is a graduate of the

We present a novel method, that we call EVEN-