This paper proposes a parity placement scheme, Row-Oblique Parity (ROP), for protecting against double disk failure in disk array systems. It stores all data unencoded, and uses only exclusive-or (XOR) operations to compute parity. ROP is provably optimal in computational complexity, both during construction and reconstruction. It is optimal in the capacity of redundant information stored and accessed. The simplicity of ROP allowed us to implement it within the current available RAID framework.

This paper presents two improved triple parity placement schemes, the HDD1 (Horizontal and Dual Diagonal) scheme and the HDD2 scheme, to enhance the reliability of a disk array system. Both the schemes can tolerate up to three column disk failures by using three types of parity information (horizontal, diagonal, and anti-diagonal parities) in a disk array. HDD1 scheme can decrease the frequency of bottlenecks because its horizontal and anti-diagonal parities are uniformly distributed over a disk array, with its diagonal parities placed in dedicated column disks. HDD2 scheme possesses one more column disks than HDD1 to store the horizontal parities and an additional diagonal parity; its anti-diagonal and diagonal parities are placed in the same way as in HDD1 scheme, only with a minor difference. The encoding and decoding algorithms of the two schemes are rather simple and straightforward, some steps of its procedure can even be executed in parallel, which makes the disk failure recovery faster.