A Class of Binary Locally Repairable Codes

Shahabinejad, Mostafa; Khabbazian, Majid; Ardakani, Masoud

doi:10.1109/tcomm.2016.2581163

Cited by 33 publications

(18 citation statements)

References 26 publications

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“…Furthermore, mean-time to data-loss (MTTDL) associated with an LRC is inversely proportional to the average locality of the code 1 [12]. In other words, for two LRCs with the same values of (n, k, d)…”

Section: Importance Of the Resultsmentioning

confidence: 99%

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On the Average Locality of Locally Repairable Codes

Shahabinejad

Khabbazian

Ardakani

2018

IEEE Trans. Commun.

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A linear block code with dimension k, length n, and minimum distance d is called a locally repairable code (LRC) with locality r if it can retrieve any coded symbol by at most r other coded symbols. LRCs have been recently proposed and used in practice in distributed storage systems (DSSs) such as Windows Azure storage and Facebook HDFS-RAID. Theoretical bounds on the maximum locality of LRCs (r) have been established. The average locality of an LRC (r) directly affects the costly repair bandwidth, disk I/O, and number of nodes involved in the repair process of a missing data block. There is a gap in the literature studying r. In this paper, we establish a lower bound on r of arbitrary (n, k, d) LRCs. Furthermore, we obtain a tight lower bound on r for a practical case where the code rate (R = k n ) is greater than (1 − 1 √ n ) 2 . Finally, we design three classes of LRCs that achieve the obtained bounds on r. Comparing with the existing LRCs, our proposed codes improve the average locality without sacrificing such crucial parameters as the code rate or minimum distance.

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Section: Importance Of the Resultsmentioning

confidence: 99%

“…It is notable that linear block codes currently in use-e.g. the (16,10,5) code used in Facebook HDFS-RAID, the (16,12,4) code used in Windows Azure Storage, and the (9,6,4)…”

Section: B a Tight Lower Bound On R Of Lrcs Withmentioning

confidence: 99%

On the Average Locality of Locally Repairable Codes

Shahabinejad

Khabbazian

Ardakani

2018

IEEE Trans. Commun.

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“…In [124], the authors present a characterization of binary LR codes that achieve the Singleton bound (18). In [125], the authors present constructions of binary codes meeting the Singleton bound. These codes are a subclass of the codes characterized in [124] for the case d min ≤ 4.…”

Section: ) Construction Of Binary Codesmentioning

confidence: 99%

Erasure coding for distributed storage: an overview

Balaji

Krishnan

Vajha

et al. 2018

Sci. China Inf. Sci.

125

102

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In a distributed storage system, code symbols are dispersed across space in nodes or storage units as opposed to time. In settings such as that of a large data center, an important consideration is the efficient repair of a failed node. Efficient repair calls for erasure codes that in the face of node failure, are efficient in terms of minimizing the amount of repair data transferred over the network, the amount of data accessed at a helper node as well as the number of helper nodes contacted. Coding theory has evolved to handle these challenges by introducing two new classes of erasure codes, namely regenerating codes and locally recoverable codes as well as by coming up with novel ways to repair the ubiquitous Reed-Solomon code. This survey provides an overview of the efforts in this direction that have taken place over the past decade. I. INTRODUCTIONThis survey article deals with the use of erasure coding for the reliable and efficient storage of large amounts of data in settings such as that of a data center. The amount of data stored in a single data center can run into tens or hundreds of petabytes. Reliability of data storage is ensured in part by introducing redundancy in some form, ranging from simple replication to the use of more sophisticated erasure-coding schemes such as Reed-Solomon codes. Minimizing the storage overhead that comes with ensuring reliability is a key consideration in the choice of erasure-coding scheme. More recently a second problem has surfaced, namely, that of node repair.In [1], [2] the authors study the Facebook warehouse cluster and analyze the frequency of node failures as well as the resultant network traffic relating to node repair. It was observed in [1] that a median of 50 nodes are unavailable per day and that a median of 180TB of cross-rack traffic is generated as a result of node unavailability. It was also reported that 98.08% of the cases have exactly one block missing in a stripe. The erasure code that was deployed in this instance was an [n = 14, k = 10] Reed Solomon (RS) code. Here n denotes the block length of the code and k the dimension. The conventional repair of an [n, k] RS code is inefficient in that the repair of a single node, calls for contacting k other (helper) nodes and downloading k times the amount of data stored in the failed node, which is clearly inefficient. Thus there is significant practical interest in the design of erasure-coding techniques that offer both low overhead and which can also be repaired efficiently.Coding theorists have responded to this need by coming up with two new classes of codes, namely ReGenerating (RG) and Locally Recoverable (LR) codes. The focus in a RG code is on minimizing the amount of data download needed to repair a failed node, termed the repair bandwidth while LR codes seek to minimize the number of helper nodes contacted for node repair, termed the repair degree. In a different direction, coding theorists have also re-examined the problem of node repair in RS codes and have come up with new and more efficient ...

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“…In [43], the advantages of (n, k, d, r) = (15,10,4,6) BLRC are discussed and compared with (16,10,4,5) non-binary LRC, (14,10) RS code, and three-replication with four metrics including encoding complexity, repair complexity, mean time to data loss, and storage capacity. The authors of [43] further analyzed the advantages of BLRCs with a high Hamming distance and average locality [44,45]. In this section, we introduce bounds for BLRCs and various construction methods of BLRCs.…”

Section: Binary Locally Repairable Codesmentioning

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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A Class of Binary Locally Repairable Codes

Cited by 33 publications

References 26 publications

On the Average Locality of Locally Repairable Codes

On the Average Locality of Locally Repairable Codes

Erasure coding for distributed storage: an overview

Overview of Binary Locally Repairable Codes for Distributed Storage Systems

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