Optimal locally repairable codes with local minimum storage regeneration via rank-metric codes

Rawat, Ankit Singh; Silberstein, Natalia; Koyluoglu, O. Ozan; Vishwanath, Sriram

doi:10.1109/ita.2013.6502983

Cited by 8 publications

(21 citation statements)

References 30 publications

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“…Various codes have been proposed to reduce repair locality, such as scalar linear codes [6] [8] and vector codes [7] [9] [10]. In [6] [8], extra parity constraints are introduced into encoded symbols of an MDS code to enhance repair locality, and a trade-off is demonstrated between the minimum distance and the repair locality of the resulting code.…”

Section: Introductionmentioning

confidence: 99%

“…of one failed node, and explicit code construction based on a two-layer encoding structure is proposed for a specific set of parameters. Vector codes capable of repairing more than one failed node locally at the same time are proposed in [10]. Those vector codes with local repair property are called locally repairable codes (LRCs), and LRCs achieving the optimal minimum distance are said to be optimal.…”

Section: Introductionmentioning

confidence: 99%

“…Those vector codes with local repair property are called locally repairable codes (LRCs), and LRCs achieving the optimal minimum distance are said to be optimal. Optimal LRCs are also constructed in [10] featuring a two-layer encoding structure, where Gabidulin codes [11] are used in the first layer encoding. However, the adoption of Gabidulin codes leads to a finite field size growing exponentially with the number of nodes in the DSS.…”

Section: Introductionmentioning

confidence: 99%

“…Naturally, the construction in [10] can be viewed as a special case of ours, as Gabidulin codes are also a family of MDS codes. Compared to [10], our code is guaranteed to exist in a finite field with size proportional to the total number of nodes in the DSS. Our construction has flexible structures, and leads to codes proposed in [7] given the same set of parameters.…”

Section: Introductionmentioning

confidence: 99%

“…It has been widely used in the literature for different desired advantages in the DSS aside from [7] [10]. For example, fractional repetition codes are proposed in [12] from concatenation of an outer MDS code and an inner repetition code for uncoded repair process.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Two-layer locally repairable codes for distributed storage systems

Xie

Yan

2014

2014 IEEE International Conference on Communications (ICC)

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In this paper, we propose locally repairable codes (LRCs) with optimal minimum distance for distributed storage systems (DSS). A two-layer encoding structure is employed to ensure data reconstruction and the designated repair locality. The data is first encoded in the first layer by any existing maximum distance separable (MDS) codes, and then the encoded symbols are divided into non-overlapping groups and encoded by an MDS array code in the second layer. The encoding in the second layer provides enough redundancy for local repair, while the overall code performs recovery of the data based on redundancy from both layers. Our codes can be constructed over a finite field with size growing linearly with the total number of nodes in the DSS, and facilitate efficient degraded reads.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Two-layer locally repairable codes for distributed storage systems

Xie

Yan

2014

2014 IEEE International Conference on Communications (ICC)

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Non-linear MRD codes from cones over exterior sets

Durante,

Grimaldi,

Longobardi

2024

Des. Codes Cryptogr.

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By using the notion of a d-embedding $$\Gamma $$ Γ of a (canonical) subgeometry $$\Sigma $$ Σ and of exterior sets with respect to the h-secant variety $$\Omega _{h}({\mathcal {A}})$$ Ω h ( A ) of a subset $${\mathcal {A}}$$ A , $$ 0 \le h \le n-1$$ 0 ≤ h ≤ n - 1 , in the finite projective space $${\textrm{PG}}(n-1,q^n)$$ PG ( n - 1 , q n ) , $$n \ge 3$$ n ≥ 3 , in this article we construct a class of non-linear (n, n, q; d)-MRD codes for any $$ 2 \le d \le n-1$$ 2 ≤ d ≤ n - 1 . A code of this class $${\mathcal {C}}_{\sigma ,T}$$ C σ , T , where $$1\in T \subseteq {\mathbb {F}}_q^*$$ 1 ∈ T ⊆ F q ∗ and $$\sigma $$ σ is a generator of $$\textrm{Gal}({\mathbb {F}}_{q^n}|{\mathbb {F}}_q)$$ Gal ( F q n | F q ) , arises from a cone of $${\textrm{PG}}(n-1,q^n)$$ PG ( n - 1 , q n ) with vertex an $$(n-d-2)$$ ( n - d - 2 ) -dimensional subspace over a maximum exterior set $${\mathcal {E}}$$ E with respect to $$\Omega _{d-2}(\Gamma )$$ Ω d - 2 ( Γ ) . We prove that the codes introduced in Cossidente et al (Des Codes Cryptogr 79:597–609, 2016), Donati and Durante (Des Codes Cryptogr 86:1175–1184, 2018), Durante and Siciliano (Electron J Comb, 2017) are suitable punctured ones of $${\mathcal {C}}_{\sigma ,T}$$ C σ , T and we solve completely the inequivalence issue for this class showing that $${\mathcal {C}}_{\sigma ,T}$$ C σ , T is neither equivalent nor adjointly equivalent to the non-linear MRD codes $${\mathcal {C}}_{n,k,\sigma ,I}$$ C n , k , σ , I , $$I \subseteq {\mathbb {F}}_q$$ I ⊆ F q , obtained in Otal and Özbudak (Finite Fields Appl 50:293–303, 2018).

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Code constructions for multi-node exact repair in distributed storage

Zorgui

Wang

2018

Sci. China Inf. Sci.

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We study the problem of centralized exact repair of multiple failures in distributed storage. We present constructions that achieve a new set of interior points under exact repair. The constructions build upon the layered code construction by Tian et al., 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, for some parameters, we prove the optimality of one point in terms of the storage size and the repair bandwidth for multiple erasures. 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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Optimal locally repairable codes with local minimum storage regeneration via rank-metric codes

Cited by 8 publications

References 30 publications

Two-layer locally repairable codes for distributed storage systems

Two-layer locally repairable codes for distributed storage systems

Non-linear MRD codes from cones over exterior sets

Code constructions for multi-node exact repair in distributed storage

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