Bounds on the rate and minimum distance of codes with availability

Balaji, Sai A.; Kumar, P. Vijay

doi:10.1109/isit.2017.8007111

Cited by 25 publications

(26 citation statements)

References 25 publications

(66 reference statements)

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“…The above bound (27), derived in [111], is tighter than (26) as r increases for any fixed t. An upper bound on rate of an (n, k, r = 2, t) SA-LR code over F 2 that for large t, becomes tighter in comparison with the bounds in either (26) or (27), is presented in [144]. Also contained in [144], is an upper bound on the rate of an (n, k, r, 3) SA-LR code over F 2 which is tighter than the bound in either (27) or (26) for r > 72 and which makes use of the "transpose"-based rate equation appearing in [111].…”

Section: Parallel-recovery Lr Codesmentioning

confidence: 99%

Erasure coding for distributed storage: an overview

Balaji

Krishnan

Vajha

et al. 2018

Sci. China Inf. Sci.

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126

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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Section: Parallel-recovery Lr Codesmentioning

confidence: 99%

Erasure coding for distributed storage: an overview

Balaji

Krishnan

Vajha

et al. 2018

Sci. China Inf. Sci.

Self Cite

126

102

View full text Add to dashboard Cite

show abstract

“…Regenerating codes were proposed to decrease repair bandwidth of distributed storage systems by accessing more nodes and downloading less data from each node [1,2]. Locally repairable codes [3] improve the repairability of distributed storage system by decreasing number of nodes connected in the repair process. In a locally repairable code with strict (r, t)-availability [3], each symbol in a codeword is protected by t disjoint recovering sets of size r (r is locality of the code, t is availability of the code).…”

mentioning

confidence: 99%

“…Locally repairable codes [3] improve the repairability of distributed storage system by decreasing number of nodes connected in the repair process. In a locally repairable code with strict (r, t)-availability [3], each symbol in a codeword is protected by t disjoint recovering sets of size r (r is locality of the code, t is availability of the code). (n, k, r, t) q denotes [n, k] locally repairable codes with (r, t)-availability over F q .…”

mentioning

confidence: 99%

“…(n, k, r, t) q denotes [n, k] locally repairable codes with (r, t)-availability over F q . In [3], the author proposed a construction of locally repairable codes with strict (r, t)-availability over F 2 . Code length of the code is (r + 1) g , where g 1.…”

mentioning

confidence: 99%

“…In this study, we will give an extension to the construction in [3]. We propose a construction of locally repairable codes with strict (r, t)availability over any finite field (including F 2 ) for arbitrary r and t r. When n = (r + 1) 2 , t = 2, k ∈ [r + 1, 2r − 1] and q > n k+1 , our construction gives locally repairable codes with optimal minimum distance.…”

mentioning

confidence: 99%

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Locally repairable codes with strict availability from linear functions

Zhang

Kan

2018

Sci. China Inf. Sci.

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Locally repairable codes from combinatorial designs

Zhang

Kan

2020

Sci. China Inf. Sci.

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Locally repairable codes (LRCs) were proposed to reduce the repair degree in distributed storage systems. In particular, LRCs with availability are highly desirable for distributed storage systems, since this kind of codes provide the mechanism of local repair for code symbols and parallel reading of hot data. In this paper, we propose four types of (n, k, r, t)q LRCs from combinatorial designs. We introduce several constructions of LRCs with strict availability and some constructions of distance-optimal LRCs with information-symbol locality. Most of our constructions in this paper are over F 2 , i.e., they are suitable for implementation.

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Bounds on the rate and minimum distance of codes with availability

Cited by 25 publications

References 25 publications

Erasure coding for distributed storage: an overview

Erasure coding for distributed storage: an overview

Locally repairable codes with strict availability from linear functions

Locally repairable codes from combinatorial designs

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