Explicit Maximally Recoverable Codes With Locality

Gopalan, Parikshit; Huang, Cheng; Jenkins, B. Keith; Yekhanin, Sergey

doi:10.1109/tit.2014.2332338

Cited by 155 publications

(193 citation statements)

References 17 publications

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“…As related work, let us mention a recent paper [6] that gives constructions of (1; s) PMDS codes trying to minimize the size of the field. In fact, (1; s) PMDS, called Maximally Recoverable codes in [6], satisfy also the requirements of Locally Repairable codes [10], [13].…”

Section: Discussionmentioning

confidence: 99%

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Partial MDS (PMDS) and Sector-Disk (SD) codes that tolerate the erasure of two random sectors

Blaum

Plank

Schwartz

et al. 2014

2014 IEEE International Symposium on Information Theory

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Abstract-Partial MDS (PMDS) codes are erasure codes combining local (row) correction with global additional correction of entries, while Sector-Disk (SD) codes are erasure codes that address the mixed failure mode of current RAID systems. It has been an open problem to construct general codes that have the PMDS and the SD properties, and previous work has relied on Monte-Carlo searches. In this paper, we present a general construction that addresses the case of any number of failed disks and in addition, two erased sectors. The construction requires a modest field size. This result generalizes previous constructions extending RAID 5 and RAID 6.

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Section: Discussionmentioning

confidence: 99%

“…In fact, (1; s) PMDS, called Maximally Recoverable codes in [6], satisfy also the requirements of Locally Repairable codes [10], [13]. Additionally, the recently-defined STAIR codes relax the failure-coverage of SD codes in order to allow for general constructions [8].…”

Section: Discussionmentioning

confidence: 99%

Partial MDS (PMDS) and Sector-Disk (SD) codes that tolerate the erasure of two random sectors

Blaum

Plank

Schwartz

et al. 2014

2014 IEEE International Symposium on Information Theory

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“…For h = 3, one gets a field of size q = O n 1.5 . In contrast to this, when h = 2, r = O(1), and k grows, constructions of [BHH13,GHJY14] yield codes over a field of optimal size O(n). In the setting of h = O(1), g = O(1), and growing k, constructions of [GHJY14] yield field of size n (g+h)/2 .…”

Section: Introductionmentioning

confidence: 91%

New constructions of SD and MR codes over small finite fields

Yekhanin

2016

2016 IEEE International Symposium on Information Theory (ISIT)

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Data storage applications require erasure-correcting codes with prescribed sets of dependencies between data symbols and redundant symbols. The most common arrangement is to have k data symbols and h redundant symbols (that each depends on all data symbols) be partitioned into a number of disjoint groups, where for each group one allocates an additional (local) redundant symbol storing the parity of all symbols in the group. A code as above is maximally recoverable, if it corrects all erasure patterns that are information theoretically correctable given the dependency constraints. A slightly weaker guarantee is provided by SD codes.One key consideration in the design of MR and SD codes is the size of the finite field underlying the code as using small finite fields facilitates encoding and decoding operations. In this paper we present new explicit constructions of SD and MR codes over small finite fields.

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“…The bounds on the failure tolerance of locally repairable codes, the codes with small locality, have been obtained in [7,12,16,20] and references therein. Furthermore, the constructions of locally repairable codes that are optimal with respect to these bounds are presented in [1,6,7,12,16,20,26]. Locally repairable codes that also minimize the repair bandwidth for repair of a code block are considered in [12,20].…”

Section: Background and Related Workmentioning

confidence: 99%

MDS Code Constructions with Small Sub-packetization and Near-optimal Repair Bandwidth

Rawat

Tamo

Guruswami

et al. 2017

Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms

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An (n, M ) vector code C ⊆ F n is a collection of M codewords where n elements (from the field F) in each of the codewords are referred to as code blocks. Assuming that F ∼ = B , the code blocks are treated as -length vectors over the base field B. Equivalently, the code is said to have the sub-packetization level . This paper addresses the problem of constructing MDS vector codes which enable exact reconstruction of each code block by downloading small amount of information from the remaining code blocks. The repair bandwidth of a code measures the information flow from the remaining code blocks during the reconstruction of a single code block. This problem naturally arises in the context of distributed storage systems as the node repair problem [4]. Assuming that M = |B| k , the repair bandwidth of an MDS vector code is lower bounded by (n − 1)/(n − k) · symbols (over the base field B) which is also referred to as the cut-set bound [4]. For all values of n and k, the MDS vector codes that attain the cut-set bound with the sub-packetization level = (n − k) n/(n−k) are known in the literature [23,36].This paper presents a construction for MDS vector codes which simultaneously ensures both small repair bandwidth and small sub-packetization level. The obtained codes have the smallest possible sub-packetization level = O(n − k) for an MDS vector code and the repair bandwidth which is at most twice the cut-set bound. The paper then generalizes this code construction so that the repair bandwidth of the obtained codes approach the cut-set bound at the cost of increased sub-packetization level. The constructions presented in this paper give MDS vector codes which are linear over the base field B.

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Explicit Maximally Recoverable Codes With Locality

Cited by 155 publications

References 17 publications

Partial MDS (PMDS) and Sector-Disk (SD) codes that tolerate the erasure of two random sectors

Partial MDS (PMDS) and Sector-Disk (SD) codes that tolerate the erasure of two random sectors

New constructions of SD and MR codes over small finite fields

MDS Code Constructions with Small Sub-packetization and Near-optimal Repair Bandwidth

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