On cooperative local repair in distributed storage

Rawat, Ankit Singh; Mazumdar, Arya; Vishwanath, Sriram

doi:10.1109/ciss.2014.6814152

Cited by 47 publications

(75 citation statements)

References 33 publications

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“…In the literature on locally repairable codes, a code is said to have (r, l)-locality if it allows l failed code symbols to be recovered by contacting at most r other intact code symbols. For any code of length n and dimension k with (r, l)-locality, the minimum distance d is bounded by the following inequality given in [8]:…”

Section: Our Contributionmentioning

confidence: 99%

“…We should mention that recovering multiple erasures by using a small number of queries have been studied in the locally repairable codes (LRCs) world [8], which is known as the cooperative local repair and motivated by the fact that distributed storage systems can experience multiple simultaneous failures. In the literature on locally repairable codes, a code is said to have (r, l)-locality if it allows l failed code symbols to be recovered by contacting at most r other intact code symbols.…”

Section: Our Contributionmentioning

confidence: 99%

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Locally correcting multiple bits and codes of high rate

2015

2015 IEEE Information Theory Workshop - Fall (ITW)

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Locally correctable codes are error-correcting codes that allow a single bit of the codeword to be recovered by looking up a small subset of the coordinates of the received word. In this work, we generalize the concept of traditional locally correcting to locally correcting multiple bits, and present a family of codes which allow multiple bits to be recovered with probability approaching 1 by visiting a small number of locations of the received word, even when a constant fraction of errors exist. Moreover, our codes are of high rate.

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Section: Our Contributionmentioning

confidence: 99%

Section: Our Contributionmentioning

confidence: 99%

Locally correcting multiple bits and codes of high rate

2015

2015 IEEE Information Theory Workshop - Fall (ITW)

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“…The notion of cooperative local repair was introduced as a generalization of the definition of local recovery in [15]. In this definition, instead of one server failure, provisions for multiple server failures are kept.…”

Section: A Collaborative Local Repair On Graphsmentioning

confidence: 99%

“…Furthermore, instead of a single node local repairability, multiple failures can also be considered. Such multiple failures and the corresponding cooperative local recovery model in distributed storage was recently introduced in [15]. In Section III we generalize this model as well on graphs.…”

Section: Introductionmentioning

confidence: 99%

Achievable schemes and limits for local recovery on a graph

Mazumdar

2014

2014 52nd Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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Recently, a graph-theoretic model for a singlefailure-recoverable distributed storage system was proposed. Unlike the usual local recovery model of codes for distributed storage, this model accounts for the fact that each server or storage node in a network is connectible to only some, and not all other, nodes. Here we provide bounds and constructive schemes for data storage in such networks. We also impose an additional requirement on the codes for such model -a minimum distance guarantee. The model is further generalized for multiple node failures and cooperative repairs.

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“…We should mention that recovering multiple erasures by using a small number of queries have been studied in the locally repairable codes (LRCs) world [29], which is known as the cooperative local repair and motivated by the fact that distributed storage systems can experience multiple simultaneous failures. In the literature on locally repairable codes, a code is said to have (r, l)-locality if it allows l failed code symbols to be recovered by contacting at most r other intact code symbols.…”

Section: Remarkmentioning

confidence: 99%

Local correction of codes of high rate

Wu¹

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This thesis is devoted to the study of locally correctable codes of high rate. We are mainly interested in new constructions of high-rate locally correctable codes, local correction of multiple bits, and the inner connection between the lifted Reed-Solomon codes and the multiplicity codes. Locally correctable codes (LCC) are error-correcting codes with efficient decoding schemes, which can recover any bit of a codeword by visiting a small number of locations of the codeword. LCCs have found numerous applications in complexity theory, cryptography and the theory of fault tolerant computation. Kopparty et. al. [4] presented the first family of high-rate locally correctable codes, which is known as the multiplicity codes, by considering the evaluations of multivariate polynomials together with their Hasse derivatives. After that work, Guo et al. [5], discovered another family of highrate locally correctable codes, the lifted Reed-Solomon codes, by considering lifting of multivariate polynomials. In this thesis, firstly, we extend the techniques of lifted Reed-Solomon codes by lifting multivariate polynomials on curves, and generalize the decoding on curve algorithm from Reed-Muller codes to these lifted codes to provide a correcting algorithm with success probability arbitrarily approaching 1. This gives a family of high-rate locally correctable codes which can be recovered with probability close to 1.

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On cooperative local repair in distributed storage

Cited by 47 publications

References 33 publications

Locally correcting multiple bits and codes of high rate

Locally correcting multiple bits and codes of high rate

Achievable schemes and limits for local recovery on a graph

Local correction of codes of high rate

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