Constructions of Optimal Codes With Hierarchical Locality

Zhang, Guanghui; Liu, Hongwei

doi:10.1109/tit.2020.2977636

Cited by 19 publications

(15 citation statements)

References 17 publications

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“…Finding explicit constructions of optimal (r, δ)-LRCs is both of theoretical and practical significance. This general problem has attracted considerable attention, as exemplified by the respective works in [8], [27], [34], [19], [35], [36], [3], [5], [26], [13], [32], [6], [18], [23], [24], [17], [14], [33], [30], [15], [31].…”

Section: A Codes With Localitymentioning

confidence: 99%

“…In [3], the maximum length of optimal (r, δ)-LRCs was determined when (r +δ −1) is a divisor of the length n. Employing combinatorial structures, some families of optimal (r, δ)-LRCs with superlinear lengths were proposed very recently in [3], [20]. Another approach to designing optimal (r, δ)-LRCs of superlinear length is by a direct construction of suitable parity-check matrices, as was done, e.g., in [5], [35], [36].…”

Section: A Codes With Localitymentioning

confidence: 99%

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Three New Infinite Families of Optimal Locally Repairable Codes from Matrix-Product Codes

Luo,

Ezerman,

Ling

2021

Preprint

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Locally repairable codes have become a key instrument in large-scale distributed storage systems. This paper focuses on the construction of locally repairable codes with (r, δ)-locality that achieve the equality in the Singleton-type bound. We use matrix-product codes to propose two infinite families of q-ary optimal (r, δ) locally repairable codes of lengths up to q 2 + q. The ingredients in the matrix-product codes are either linear maximum distance separable codes or optimal locally repairable codes of small lengths. Further analysis and refinement yield a construction of another infinite family of optimal (r, δ) locally repairable codes. The codes in this third family have unbounded lengths not divisible by (r + δ − 1).The three families of optimal (r, δ) locally repairable codes constructed here are new. Previously constructed codes in the literature have not covered the same sets of parameters. Our construction proposals are flexible since one can easily vary r and δ to come up with particular parameters that can suit numerous scenarios.

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Section: A Codes With Localitymentioning

confidence: 99%

Section: A Codes With Localitymentioning

confidence: 99%

Three New Infinite Families of Optimal Locally Repairable Codes from Matrix-Product Codes

Luo,

Ezerman,

Ling

2021

Preprint

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“…• more than two errors in information symbol: In this case the complexity of procedures quantified by Υ 1I , Υ 2I , Υ 1P 1I can be added as the worst case: (16,6,23,9,2). (106)…”

Section: Complexity Estimation Of the Algorithmmentioning

confidence: 99%

“…More surprisingly, in recent years a new interest in these codes has risen in the research community. It is caused by the fact that they are extensively used in cloud technology, namely in distributed storage systems [5,6,7,8,9]. In [1] it was shown that RS codes could be extended not only three times, but even five times when they are constructed over certain finite fields.…”

Section: Introductionmentioning

confidence: 99%

Decoding Five Times Extended Reed Solomon Codes Using Syndromes

Farkas

Rakús

2020

cai

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Recently a new family of five times extended Reed Solomon codes constructed over certain finite fields GF (2 ζ ), where ζ ≥ 3 is an odd integer, was discovered. Until now only an erasure decoding algorithm for these codes was published. In this paper a new decoding algorithm is presented, which allows correcting up to two errors in a codeword from the five times extended Reed Solomon codes. The proposed decoding algorithm is based on syndrome usage.

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“…To allow different requirements for local recovery, hierarchical and unequal locality were introduced in [34] and [23], [42], respectively. Over the past decade, many bounds and constructions for LRCs have been introduced, e.g., [3], [6], [7], [9], [17], [20], [25], [32], [37], [40], [41] for (r, δ)-locality [4], [5], [22], [33], [38] for multiple repair sets, [10], [27], [34], [43] for hierarchical locality, and [23], [42] for unequal locality.…”

Section: Introductionmentioning

confidence: 99%