Changsheng Xie

RAID-6 is widely used to tolerate concurrent failures of any two disks to provide a higher level of reliability with the support of erasure codes. Among many implementations, one class of codes called Maximum Distance Separable (MDS) codes aims to offer data protection against disk failures with optimal storage efficiency. Typical MDS codes contain horizontal and vertical codes. Due to the horizontal parity, in the case of partial stripe write (refers to I/O operations that write new data or update data to a subset of disks in an array) in a row, horizontal codes may get less I/O operations in most cases, but suffer from unbalanced I/O distribution. They also have limitation on high single write complexity. Vertical codes improve single write complexity compared to horizontal codes, while they still suffer from poor performance in partial stripe writes. In this paper, we propose a new XOR-based MDS array code, named Hybrid Code (H-Code), which optimizes partial stripe writes for RAID-6 by taking advantages of both horizontal and vertical codes. H-Code is a solution for an array of (p+1) disks, where p is a prime number. Unlike other codes taking a dedicated anti-diagonal parity strip, H-Code uses a special anti-diagonal parity layout and distributes the anti-diagonal parity elements among disks in the array, which achieves a more balanced I/O distribution. On the other hand, the horizontal parity of H-Code ensures a partial stripe write to continuous data elements in a row share the same row parity chain, which can achieve optimal partial stripe write performance. Not only within a row but also within a stripe, H-Code offers optimal partial stripe write complexity to two continuous data elements and optimal partial stripe write performance among all MDS codes to the best of our knowledge. Specifically, compared to RDP and EVENODD codes, H-Code reduces I/O cost by up to 15.54% and 22.17%. Overall, H-code has optimal storage efficiency, optimal encoding/decoding computational complexity, optimal complexity of both single write and partial stripe write.

With higher reliability requirements in clusters and data centers, RAID-6 has gained popularity due to its capability to tolerate concurrent failures of any two disks, which has been shown to be of increasing importance in large scale storage systems. Among various implementations of erasure codes in RAID-6, a typical set of codes known as Maximum Distance Separable (MDS) codes aim to offer data protection against disk failures with optimal storage efficiency. However, because of the limitation of horizontal parity or diagonal/anti-diagonal parities used in MDS codes, storage systems based on RAID-6 suffers from unbalanced I/O and thus low performance and reliability. To address this issue, in this paper, we propose a new parity called Horizontal-Diagonal Parity (HDP), which takes advantages of both horizontal and diagonal/anti-diagonal parities. The corresponding MDS code, called HDP code, distributes parity elements uniformly in each disk to balance the I/O workloads. HDP also achieves high reliability via speeding up the recovery under single or double disk failure. Our analysis shows that HDP provides better balanced I/O and higher reliability compared to other popular MDS codes.

As both NAND flash memory manufacturers and users are turning their attentions from planar architecture towards three-dimensional (3D) architecture, it becomes critical and urgent to understand the characteristics of 3D NAND flash memory. These characteristics, especially those different from planar NAND flash, can significantly affect design choices of flash management techniques. In this article, we present a characterization study on the state-of-the-art 3D floating gate (FG) NAND flash memory through comprehensive experiments on an FPGA-based 3D NAND flash evaluation platform. We make distinct observations on its performance and reliability, such as operation latencies and various error patterns, followed by careful analyses from physical and circuit-level perspectives. Although 3D FG NAND flash provides much higher storage densities than planar NAND flash, it faces new performance challenges of garbage collection overhead and program performance variations and more complicated reliability issues due to, e.g., distinct location dependence and value dependence of errors. We also summarize the differences between 3D FG NAND flash and planar NAND flash and discuss implications on the designs of NAND flash management techniques brought by the architecture innovation. We believe that our work will facilitate developing novel 3D FG NAND flash-oriented designs to achieve better performance and reliability.