Construction of Fractional Repetition Codes with Variable Parameters for Distributed Storage Systems

Park, Hosung; Kim, Young Sik

doi:10.3390/e18120441

Cited by 12 publications

(19 citation statements)

References 23 publications

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“…For ζ = 1, we have an RDS with parameters (8, 6, 7, 1) as D = {0, 18,22,28,29,31, 43}, and its characteristic sequence is given as:…”

Section: Examplementioning

confidence: 99%

“…In [16], the existence of FR codes for each parameter set is shown by algorithm-based search, and some examples for each parameter set are provided. Many kinds of FR codes have been constructed mostly based on algebraic structures, combinatorial designs and graph theory [15,[17][18][19][20][21][22]. In [15], Steiner systems are used as a class of (v, (v − 1)/(k − 1), k) FR codes with β = 1 under the existence of Steiner system S(2, k, v).…”

Section: Introductionmentioning

confidence: 99%

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Construction of New Fractional Repetition Codes from Relative Difference Sets with λ=1

Kim

Park

2017

Entropy

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Abstract:Fractional repetition (FR) codes are a class of distributed storage codes that replicate and distribute information data over several nodes for easy repair, as well as efficient reconstruction. In this paper, we propose three new constructions of FR codes based on relative difference sets (RDSs) with λ = 1. Specifically, we propose new (q 2 − 1, q, q) FR codes using cyclic RDS with parameters (q + 1, q − 1, q, 1) constructed from q-ary m-sequences of period q 2 − 1 for a prime power q, (p 2 , p, p) FR codes using non-cyclic RDS with parameters (p, p, p, 1) for an odd prime p or p = 4 and (4 l , 2 l , 2 l ) FR codes using non-cyclic RDS with parameters (2 l , 2 l , 2 l , 1) constructed from the Galois ring for a positive integer l. They are differentiated from the existing FR codes with respect to the constructable code parameters. It turns out that the proposed FR codes are (near) optimal for some parameters in terms of the FR capacity bound. Especially, (8,3,3) and (9, 3, 3) FR codes are optimal, that is, they meet the FR capacity bound for all k. To support various code parameters, we modify the proposed (q 2 − 1, q, q) FR codes using decimation by a factor of the code length q 2 − 1, which also gives us new good FR codes.

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“…For ζ = 1, we have an RDS with parameters (8, 6, 7, 1) as D = {0, 18,22,28,29,31, 43}, and its characteristic sequence is given as:…”

Section: Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Construction of New Fractional Repetition Codes from Relative Difference Sets with λ=1

Kim

Park

2017

Entropy

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“…which completes the proof. We refer to the inequality in (15) as the dual bound on the supported file size. Moreover, the recursive bound applied to the dual code yields M ℓ (C t ) ≤ g ′ (ℓ) with g ′ (1) = 3, g ′ (2) = 5, g ′ (3) = 7, g ′ (4) = 9, g ′ (5) = 11, g ′ (6) = 12, g ′ (7) = 13, g ′ (8) = 14, g ′ (9) = g ′ (10) = 15.…”

Section: Dual Bound On Supported File Sizementioning

confidence: 99%

On the duality of fractional repetition codes

Zhu

Shum

2017

2017 IEEE Information Theory Workshop (ITW)

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Erasure codes have emerged as an efficient technology for providing data redundancy in distributed storage systems. However, it is a challenging task to repair the failed storage nodes in erasure-coded storage systems, which requires large quantities of network resources. In this paper, we study fractional repetition (FR) codes, which enable the minimal repair complexity and also minimum repair bandwidth during node repair. We focus on the duality of FR codes, and investigate the relationship between the supported file size of an FR code and its dual code. Furthermore, we present a dual bound on the supported file size of FR codes.

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“…For example, the Google file system [3] and Hadoop [4] adopt this approach. However, given that triplication requires thrice the storage space, a (14,10) Reed-Solomon code is deployed in their warehouse cluster in the case of Facebook [5]. Although RS codes are efficient for handling specified numbers of erasures, all of the code symbols must be communicated and reconstructed to repair erasures.…”

Section: Introductionmentioning

confidence: 99%

Overview of Binary Locally Repairable Codes for Distributed Storage Systems

Kim

2019

Electronics

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This paper summarizes the details of recently proposed binary locally repairable codes (BLRCs) and their features. The construction of codes over a small alphabet size of symbols is of particular interest for efficient hardware implementation. Therefore, BLRCs are highly noteworthy because no multiplication is required during the encoding, decoding, and repair processes. We explain the various construction approaches of BLRCs such as cyclic code based, bipartite graph based, anticode based, partial spread based, and generalized Hamming code based techniques. We also describe code generation methods based on modifications for linear codes such as extending, shorting, expurgating, and augmenting. Finally, we summarize and compare the parameters of the discussed constructions.

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Construction of Fractional Repetition Codes with Variable Parameters for Distributed Storage Systems

Cited by 12 publications

References 23 publications

Construction of New Fractional Repetition Codes from Relative Difference Sets with λ=1

Construction of New Fractional Repetition Codes from Relative Difference Sets with λ=1

On the duality of fractional repetition codes

Overview of Binary Locally Repairable Codes for Distributed Storage Systems

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