Codes With Local Regeneration and Erasure Correction

Kamath, Govinda M.; Prakash, Naveen; Lalitha, V.; Kumar, P. Vijay

doi:10.1109/tit.2014.2329872

Cited by 172 publications

(225 citation statements)

References 28 publications

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“…Another line of work in distributed storage focuses on locality, the number of the code blocks contacted during the repair of a single code block, as a metric to characterize the efficiency of the repair process. 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].…”

Section: Background and Related Workmentioning

confidence: 99%

“…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%

“…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]. Here we note that the locally repairable codes are not MDS codes, and thus have extra storage overhead.…”

Section: Background and Related Workmentioning

confidence: 99%

See 2 more Smart Citations

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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Section: Background and Related Workmentioning

confidence: 99%

Section: Background and Related Workmentioning

confidence: 99%

Section: Background and Related Workmentioning

confidence: 99%

See 1 more Smart Citation

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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“…. , n} has (R, ∆) locality if there exists a subset S of nodes such that |S| ≤ R + ∆ − 1, j ∈ S and any node in S can be repaired by any |S| − ∆ + 1 nodes from S. The definition of (R, ∆) all-symbol locality was introduced in [9]. Remark 1.1: Usually the letters (n, k, d, r, δ) are used to denote the parameters of a LRC.…”

Section: B Locally Repairable Codesmentioning

confidence: 99%

“…Locally repairable codes for several parameter sets (N, K, D, R, ∆) are constructed in [6], [9], [21], [22], [11], [23]. In [6] it was proved that bound (2) is not achievable for all parameters (N, K, R).…”

Section: B Locally Repairable Codesmentioning

confidence: 99%

A connection between locally repairable codes and exact regenerating codes

Ernvall¹,

Westerbäck²,

Freij-Hollanti³

et al. 2016

2016 IEEE International Symposium on Information Theory (ISIT)

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Abstract-Typically, locally repairable codes (LRCs) and regenerating codes have been studied independently of each other, and it has not been clear how the parameters of one relate to those of the other. In this paper, a novel connection between locally repairable codes and exact regenerating codes is established. Via this connection, locally repairable codes are interpreted as exact regenerating codes. Further, some of these codes are shown to perform better than time-sharing codes between minimum bandwidth regenerating and minimum storage regenerating codes.

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Matroid Theory and Storage Codes: Bounds and Constructions

Freij-Hollanti

Hollanti

Westerbäck

2018

Network Coding and Subspace Designs

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Recent research on distributed storage systems (DSSs) has revealed interesting connections between matroid theory and locally repairable codes (LRCs). The goal of this chapter is to introduce the reader to matroids and polymatroids, and illustrate their relation to distributed storage systems. While many of the results are rather technical in nature, effort is made to increase accessibility via simple examples. The chapter embeds all the essential features of LRCs, namely locality, availability, and hierarchy alongside with related generalised Singleton bounds.

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Codes With Local Regeneration and Erasure Correction

Cited by 172 publications

References 28 publications

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

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

A connection between locally repairable codes and exact regenerating codes

Matroid Theory and Storage Codes: Bounds and Constructions

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