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Information 2018, 9(11), 265; https://doi.org/10.3390/info9110265

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

1,2
,
1,2
and
1,2,*
1
Graduate School at Shenzhen, Tsinghua University, Shenzhen 518055, China
2
Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China
*
Author to whom correspondence should be addressed.
Received: 25 September 2018 / Revised: 17 October 2018 / Accepted: 20 October 2018 / Published: 24 October 2018
(This article belongs to the Section Information Theory and Methodology)
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Abstract

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. View Full-Text
Keywords: Erasure codes; locally repairable codes; locality; availability; data reliability Erasure codes; locally repairable codes; locality; availability; data reliability
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Lu, Y.; Liu, X.; Xia, S. On the Single-Parity Locally Repairable Codes with Multiple Repairable Groups. Information 2018, 9, 265.

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