Repair performance in hierarchical data centers is often bottlenecked by cross-rack network transfer. Recent theoretical results show that the cross-rack repair traffic can be minimized through repair layering, whose idea is to partition a repair operation into inner-rack and cross-rack layers. However, how repair layering should be implemented and deployed in practice remains an open issue. In this paper, we address this issue by proposing a practical repair layering framework called DoubleR. We design two families of practical double regenerating codes (DRC), which not only minimize the cross-rack repair traffic, but also have several practical properties that improve state-of-the-art regenerating codes. We implement and deploy DoubleR atop Hadoop Distributed File System (HDFS), and show that DoubleR maintains the theoretical guarantees of DRC and improves the repair performance of regenerating codes in both node recovery and degraded read operations.
Many constructions of erasure codes have been proposed to reduce the repair traffic. Regenerating codes @cite_54 are a special family of erasure codes that minimize the repair traffic and provably achieve the optimal trade-off between storage redundancy and repair traffic. Constructions of regenerating codes have been proposed, such as Interference Alignment codes @cite_49 @cite_5 @cite_57 , Product-Matrix codes @cite_52 , Zigzag codes @cite_23 , FMSR codes @cite_10 @cite_36 , PM-RBT codes @cite_35 , and Butterfly codes @cite_53 . As stated in , recent studies @cite_15 @cite_18 @cite_4 @cite_3 also propose MSR code constructions for general parameters.
@cite_35 @cite_18 @cite_4 @cite_36 @cite_54 @cite_53 @cite_52 @cite_3 @cite_57 @cite_49 @cite_23 @cite_5 @cite_15 @cite_10
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Distributed storage systems can store data with erasure coding to maintain data availability with low storage redundancy. One class of erasure coding is based on regenerating codes , which provably minimize the amount of data transferred for failure repair and realize the optimal tradeoff between the storage redundancy and the amount of traffic transferred for repair. Typical regenerating codes often require surviving storage nodes to encode their stored data for repair. In this paper, we study a framework called proxy-assisted regeneration, which offloads the repair process to a centralized proxy. We extend the previous applied work on proxy-assisted regeneration by providing theoretical validation. Specifically, we study a special class of regenerating codes called proxy-assisted minimum storage regenerating (PMSR) codes, which enable uncoded repair without the need of encoding in surviving nodes, while preserving the minimum storage redundancy and minimum amount of traffic transferred for repair. We formally prove the existence of PMSR codes for two configurations: 1) repairing single-node failures under double fault tolerance and 2) repairing double-node failures under triple fault tolerance. We also provide a semi-deterministic PMSR code construction for repairing single-node failures under double fault tolerance. Erasure codes, such as Reed-Solomon (RS) codes, are increasingly being deployed as an alternative to data-replication for fault tolerance in distributed storage systems. While RS codes provide significant savings in storage space, they can impose a huge burden on the I O and network resources when reconstructing failed or otherwise unavailable data. A recent class of erasure codes, called minimum-storage-regeneration (MSR) codes, has emerged as a superior alternative to the popular RS codes, in that it minimizes network transfers during reconstruction while also being optimal with respect to storage and reliability. However, existing practical MSR codes do not address the increasingly important problem of I O overhead incurred during reconstructions, and are, in general, inferior to RS codes in this regard. In this paper, we design erasure codes that are simultaneously optimal in terms of I O, storage, and network bandwidth. Our design builds on top of a class of powerful practical codes, called the product-matrix-MSR codes. Evaluations show that our proposed design results in a significant reduction the number of I Os consumed during reconstructions (a 5× reduction for typical parameters), while retaining optimality with respect to storage, reliability, and network bandwidth. A new class of exact-repair regenerating codes is constructed by stitching together shorter erasure correction codes, where the stitching pattern can be viewed as block designs. The proposed codes have the help-by-transfer property where the helper nodes simply transfer part of the stored data directly, without performing any computation. This embedded error correction structure makes the decoding process straightforward, and in some cases the complexity is very low. We show that this construction is able to achieve performance better than space-sharing between the minimum storage regenerating codes and the minimum repair-bandwidth regenerating codes, and it is the first class of codes to achieve this performance. In fact, it is shown that the proposed construction can achieve a nontrivial point on the optimal functional-repair tradeoff, and it is asymptotically optimal at high rate, i.e., it asymptotically approaches the minimum storage and the minimum repair-bandwidth simultaneously. Erasure coding techniques are used to increase the reliability of distributed storage systems while minimizing storage overhead. Also of interest is minimization of the bandwidth required to repair the system following a node failure. In a recent paper, characterize the tradeoff between the repair bandwidth and the amount of data stored per node. They also prove the existence of regenerating codes that achieve this tradeoff. In this paper, we introduce Exact Regenerating Codes, which are regenerating codes possessing the additional property of being able to duplicate the data stored at a failed node. Such codes require low processing and communication overheads, making the system practical and easy to maintain. Explicit construction of exact regenerating codes is provided for the minimum bandwidth point on the storage-repair bandwidth tradeoff, relevant to distributed-mail-server applications. A subspace based approach is provided and shown to yield necessary and sufficient conditions on a linear code to possess the exact regeneration property as well as prove the uniqueness of our construction. Also included in the paper, is an explicit construction of regenerating codes for the minimum storage point for parameters relevant to storage in peer-to-peer systems. This construction supports a variable number of nodes and can handle multiple, simultaneous node failures. All constructions given in the paper are of low complexity, requiring low field size in particular.