scholarly journals New Binary Locally Repairable Codes with Locality 2 and Uneven Availabilities for Hot Data

Entropy ◽  
2018 ◽  
Vol 20 (9) ◽  
pp. 636 ◽  
Author(s):  
Kang-Seok Lee ◽  
Hosung Park ◽  
Jong-Seon No
Keyword(s):  
Hamming Distance ◽  
Distributed Storage ◽  
Information Symbol ◽  
Local Repair ◽  
New Family ◽  
Minimum Hamming Distance ◽  
Other Information ◽  
Distributed Storage Systems ◽  
Locally Repairable Codes ◽  
High Information

In this paper, a new family of binary LRCs (BLRCs) with locality 2 and uneven availabilities for hot data is proposed, which has a high information symbol availability and low parity symbol availabilities for the local repair of distributed storage systems. The local repair of each information symbol for the proposed codes can be done not by accessing other information symbols but only by accessing parity symbols. The proposed BLRCs with k = 4 achieve the optimality on the information length for their given code length, minimum Hamming distance, locality, and availability in terms of the well-known theoretical upper bound.

Constructions of (r,t)-LRC Based on Totally Isotropic Subspaces in Symplectic Space Over Finite Fields

2020 ◽  
Vol 31 (03) ◽  
pp. 327-339
Author(s):  
Gang Wang ◽  
Min-Yao Niu ◽  
Fang-Wei Fu
Keyword(s):  
Finite Fields ◽  
Linear Codes ◽  
Distributed Storage ◽  
Symplectic Space ◽  
Information Rate ◽  
Local Repair ◽  
Distributed Storage Systems ◽  
Isotropic Subspaces ◽  
Locally Repairable Codes ◽  
Totally Isotropic Subspaces

Linear code with locality [Formula: see text] and availability [Formula: see text] is that the value at each coordinate [Formula: see text] can be recovered from [Formula: see text] disjoint repairable sets each containing at most [Formula: see text] other coordinates. This property is particularly useful for codes in distributed storage systems because it permits local repair of failed nodes and parallel access of hot data. In this paper, two constructions of [Formula: see text]-locally repairable linear codes based on totally isotropic subspaces in symplectic space [Formula: see text] over finite fields [Formula: see text] are presented. Meanwhile, comparisons are made among the [Formula: see text]-locally repairable codes we construct, the direct product code in Refs. [8], [11] and the codes in Ref. [9] about the information rate [Formula: see text] and relative distance [Formula: see text].

scholarly journals On the Single-Parity Locally Repairable Codes with Multiple Repairable Groups

Information ◽  
2018 ◽  
Vol 9 (11) ◽  
pp. 265
Author(s):  
Yanbo Lu ◽  
Xinji Liu ◽  
Shutao Xia
Keyword(s):  
Minimum Distance ◽  
Distributed Storage ◽  
Standard Form ◽  
Erasure Codes ◽  
New Family ◽  
Distributed Storage Systems ◽  
Locally Repairable Codes ◽  
Generator Matrices ◽  
Straightforward Proof

Locally repairable codes (LRCs) are a new family of erasure codes used in distributed storage systems which have attracted a great deal of interest in recent years. For an [ n , k , d ] linear code, if a code symbol can be repaired by t disjoint groups of other code symbols, where each group contains at most r code symbols, it is said to have availability- ( r , t ) . Single-parity LRCs are LRCs with a constraint that each repairable group contains exactly one parity symbol. For an [ n , k , d ] single-parity LRC with availability- ( r , t ) for the information symbols (single-parity LRCs), the minimum distance satisfies d ≤ n - k - ⌈ k t / r ⌉ + t + 1 . In this paper, we focus on the study of single-parity LRCs with availability- ( r , t ) for information symbols. Based on the standard form of generator matrices, we present a novel characterization of single-parity LRCs with availability t ≥ 1 . Then, a simple and straightforward proof for the Singleton-type bound is given based on the new characterization. Some necessary conditions for optimal single-parity LRCs with availability t ≥ 1 are obtained, which might provide some guidelines for optimal coding constructions.

Multiple Repair Localities with Distinct Erasure Tolerance

2016 ◽  
Vol 27 (06) ◽  
pp. 665-674
Author(s):  
Jiyong Lu ◽  
Jun Zhang ◽  
Xuan Guang ◽  
Fang-Wei Fu
Keyword(s):  
Lower Bound ◽  
Linear Code ◽  
Linear Codes ◽  
Storage Systems ◽  
Distributed Storage ◽  
Local Repair ◽  
Codeword Length ◽  
Information Set ◽  
Distributed Storage Systems ◽  
Failed Node

In distributed storage systems, codes with lower repair locality for each coordinate are much more desirable since they can reduce the disk I/O complexity for repairing a failed node. The ith coordinate of a linear code 𝒞 is said to have [Formula: see text] locality if there exist δi non-overlapping local repair sets of size no more than ri, where a local repair set of one coordinate is defined as the set of some other coordinates by which one can recover the value at this coordinate. In this paper, we consider linear codes with information [Formula: see text] locality, where there exists an information set I such that for each [Formula: see text], the ith coordinate has [Formula: see text] locality and [Formula: see text] and [Formula: see text]. We derive a lower bound on the codeword length n for any linear [n, k, d] code with information [Formula: see text] locality. Particularly, we indicate that some existing bounds can be deduced from our result by restrictions on parameters.

scholarly journals Overview of Binary Locally Repairable Codes for Distributed Storage Systems

Electronics ◽  
2019 ◽  
Vol 8 (6) ◽  
pp. 596 ◽  
Author(s):  
Young-Sik Kim ◽  
Chanki Kim ◽  
Jong-Seon No
Keyword(s):  
Code Generation ◽  
Hardware Implementation ◽  
Linear Codes ◽  
Cyclic Code ◽  
Storage Systems ◽  
Distributed Storage ◽  
Partial Spread ◽  
Hamming Code ◽  
Distributed Storage Systems ◽  
Locally Repairable Codes

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.

Analysis of a Stochastic Model of Replication in Large Distributed Storage Systems

2017 ◽  
Vol 45 (1) ◽  
pp. 51-51
Author(s):  
Wen Sun ◽  
Véronique Simon ◽  
Sébastien Monnet ◽  
Philippe Robert ◽  
Pierre Sens
Keyword(s):  
Stochastic Model ◽  
Storage Systems ◽  
Distributed Storage ◽  
Distributed Storage Systems
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