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.

A family of codes with a natural two-dimensional structure is presented, inspired by an application of RAID type of architectures whose units are solid state drives (SSDs). Arrays of SSDs behave differently to arrays of hard disk drives (HDDs), since hard errors in sectors are common and traditional RAID approaches (like RAID 5 or RAID 6) may be either insufficient or excessive. An efficient solution to this problem is given by the new codes presented, called partial-MDS (PMDS) codes.

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