Centralized multi-node repair in distributed storage

Zorgui, Marwen; Wang, Zhiying

doi:10.1109/allerton.2016.7852289

Cited by 13 publications

(15 citation statements)

References 25 publications

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“…The broadcast repair model is theoretically equivalent to the centralized multi-node repair model studied in [6], [7]. Hence, the results that we derive, and codes that we construct for broadcast repair are directly applicable to the centralized repair model.…”

Section: Introductionmentioning

confidence: 80%

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Practical Functional Regenerating Codes for Broadcast Repair of Multiple Nodes

Mital

Kralevska

Ling

et al. 2019

2019 IEEE International Symposium on Information Theory (ISIT)

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A code construction and repair scheme for optimal functional regeneration of multiple node failures is presented, which is based on stitching together short MDS codes on carefully chosen sets of points lying on a linearized polynomial. The nodes are connected wirelessly, hence all transmissions by helper nodes during a repair round are available to all the nodes being repaired. The scheme is simple and practical because of low subpacketization, low I/O cost and low computational cost. Achievability of the minimum-bandwidth regenerating (MBR) point, as well as an interior point, on the optimal storage-repair bandwidth tradeoff curve is shown. The subspace properties derived in the paper provide insight into the general properties of functional regenerating codes.

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Section: Introductionmentioning

confidence: 80%

“…In [7], it is shown that the functional MBR point for repair of multiple nodes is not achievable under exact repair. Similarly, it is shown that under exact repair, the functional repair tradeoff interior points are also not achievable.…”

Section: Introductionmentioning

confidence: 99%

Practical Functional Regenerating Codes for Broadcast Repair of Multiple Nodes

Mital

Kralevska

Ling

et al. 2019

2019 IEEE International Symposium on Information Theory (ISIT)

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show abstract

“…Thus, a point r = 2e + p, p > p max is a corner point for any (k + e, k, k, e) system such that r ≤ k + e. For each 0 ≤ p ≤ p max , the point r = 2e + p is a corner point if and only if sign(β ′ r −β r ) = sign(N 2 (k)) > 0. From (19), Let k 0 be the solution to the linear equation N 1 (k) = 0. Then, after simplification, we have…”

Section: Lemma 3 the Mbcr Point Is A Corner Point For Rmentioning

confidence: 99%

“…Achievable points using Construction 2 for an (n, k, d, e) =(19,13,14,3) system. The x-axis is the normalized storage per nodeᾱ and the y-axis is the normalized bandwidthβ.…”

mentioning

confidence: 99%

On the Achievability Region of Regenerating Codes for Multiple Erasures

Zorgui

Wang

2018

2018 IEEE International Symposium on Information Theory (ISIT)

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We study the problem of centralized exact repair of multiple failures in distributed storage. We describe constructions that achieve a new set of interior points under exact repair. The constructions build upon the layered code construction by Tian et al in [1], designed for exact repair of single failure. We firstly improve upon the layered construction for general system parameters. Then, we extend the improved construction to support the repair of multiple failures, with varying number of helpers. In particular, we prove the optimality of one point on the functional repair tradeoff of multiple failures for some parameters. Finally, considering minimum bandwidth cooperative repair (MBCR) codes as centralized repair codes, we determine explicitly the best achievable region obtained by space-sharing among all known points, including the MBCR point.

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“…Moreover, there has been a M. Zorgui and Z. Wang are with the Center for Pervasive Communications and Computing, University of California at Irvine, Irvine, CA 92697 USA (e-mail: mzorgui@uci.edu, zhiying@uci.edu). Part of this work has been presented in the 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2016 [1] and IEEE International Symposium on Information Theory, 2017 [2]. growing literature focused on understanding the fundamental limits of exact-repair regenerating codes.…”

Section: Introductionmentioning

confidence: 99%

Centralized Multi-Node Repair Regenerating Codes

Zorgui

Wang

2019

IEEE Trans. Inform. Theory

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In a distributed storage system, recovering from multiple failures is a critical and frequent task that is crucial for maintaining the system's reliability and fault-tolerance. In this work, we focus on the problem of repairing multiple failures in a centralized way, which can be desirable in many data storage configurations, and we show that a significant repair traffic reduction is possible. First, the fundamental tradeoff between the repair bandwidth and the storage size for functional repair is established. Using a graph-theoretic formulation, the optimal tradeoff is identified as the solution to an integer optimization problem, for which a closed-form expression is derived. Expressions of the extreme points, namely the minimum storage multi-node repair (MSMR) and minimum bandwidth multi-node repair (MBMR) points, are obtained. Second, we describe a general framework for converting single erasure minimum storage regenerating codes to MSMR codes. The repair strategy for e failures is similar to that for single failure, however certain extra requirements need to be satisfied by the repairing functions for single failure. For illustration, the framework is applied to product-matrix codes and interference alignment codes. Furthermore, we prove that the functional MBMR point is not achievable for linear exact repair codes. We also show that exact-repair minimum bandwidth cooperative repair (MBCR) codes achieve an interior point, that lies near the MBMR point, when k ≡ 1 mod e, k being the minimum number of nodes needed to reconstruct the entire data. Finally, for k > 2e, e | k and e | d, where d is the number of helper nodes during repair, we show that the functional repair tradeoff is not achievable under exact repair, except for maybe a small portion near the MSMR point, which parallels the results for single erasure repair by Shah et al.

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Centralized multi-node repair in distributed storage

Cited by 13 publications

References 25 publications

Practical Functional Regenerating Codes for Broadcast Repair of Multiple Nodes

Practical Functional Regenerating Codes for Broadcast Repair of Multiple Nodes

On the Achievability Region of Regenerating Codes for Multiple Erasures

Centralized Multi-Node Repair Regenerating Codes

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