An explicit, coupled-layer construction of a high-rate MSR code with low sub-packetization level, small field size and d &lt; (n − 1)

Sasidharan, Birenjith; Vajha, Myna; Kumar, P. Vijay

doi:10.1109/isit.2017.8006889

“…However, the flavor of their construction, which is not systematic in nature, differs from ours. Most recently, Ye and Barg [22], [23] show that [n, k, d] MSR codes can be explicitly constructed 4 over a small finite field and with a near optimal sub-packetization α. Birenjith et al [24] also construct explicit [n, k, d = n − 1] MSR codes with these properties. An interesting and related direction has been covered in [25] and [26] where MDS codes have been constructed that have a significantly reduced sub-packetization α at the expense of achieving only a near-optimal (and not the optimal) repair bandwidth.…”

Section: Subsequent Workmentioning

confidence: 99%

Minimum storage regenerating codes for all parameters

Goparaju

¹

,

Vardy

²

2016

2016 IEEE International Symposium on Information Theory (ISIT)

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Abstract-Regenerating codes for distributed storage have attracted much research interest in the past decade. Such codes trade the bandwidth needed to repair a failed node with the overall amount of data stored in the network. Minimum storage regenerating (MSR) codes are an important class of optimal regenerating codes that minimize (first) the amount of data stored per node and (then) the repair bandwidth. Specifically, an [n, k, d]-(α) MSR code C over F q stores a file F consisting of αk symbols over F q among n nodes, each storing α symbols, in such a way that:• the file F can be recovered by downloading the content of any k of the n nodes; and • the content of any failed node can be reconstructed by accessing any d of the remaining n − 1 nodes and downloading α/(d−k+1) symbols from each of these nodes. In practice, the file F is typically available in uncoded form on some k of the n nodes, known as systematic nodes, and the defining node-repair condition above can be relaxed to requiring the optimal repair bandwidth for systematic nodes only. Such codes are called systematic-repair MSR codes.Unfortunately, finite-α constructions of [n, k, d] MSR codes are known only for certain special cases: either low rate, namely k/n 0.5, or high repair connectivity, namely d = n − 1. Our main result in this paper is a finite-α construction of systematic-repair [n, k, d] MSR codes for all possible values of parameters n, k, d. We also introduce a generalized construction for [n, k] MSR codes to achieve the optimal repair bandwidth for all values of d simultaneously.

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“…We leave the optimization strategies of this kind to future work. We also refer the reader to [22]- [24], where MSR constructions with near-optimal sub-packetization parameter, e.g. α = r n/r , are introduced.…”

Section: ) Msr Codementioning

confidence: 99%

Minimum Storage Regenerating Codes for All Parameters

Goparaju

¹

,

Fazeli

²

,

Vardy

³

2017

IEEE Trans. Inform. Theory

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Abstract-Regenerating codes for distributed storage have attracted much research interest in the past decade. Such codes trade the bandwidth needed to repair a failed node with the overall amount of data stored in the network. Minimum storage regenerating (MSR) codes are an important class of optimal regenerating codes that minimize (first) the amount of data stored per node and (then) the repair bandwidth. Specifically, an [n, k, d]-(α) MSR code C over F q stores a file F consisting of αk symbols over F q among n nodes, each storing α symbols, in such a way that:• the file F can be recovered by downloading the content of any k of the n nodes; and • the content of any failed node can be reconstructed by accessing any d of the remaining n − 1 nodes and downloading α/(d−k+1) symbols from each of these nodes. In practice, the file F is typically available in uncoded form on some k of the n nodes, known as systematic nodes, and the defining node-repair condition above can be relaxed to requiring the optimal repair bandwidth for systematic nodes only. Such codes are called systematic-repair MSR codes.Unfortunately, finite-α constructions of [n, k, d] MSR codes are known only for certain special cases: either low rate, namely k/n 0.5, or high repair connectivity, namely d = n − 1. Our main result in this paper is a finite-α construction of systematic-repair [n, k, d] MSR codes for all possible values of parameters n, k, d. We also introduce a generalized construction for [n, k] MSR codes to achieve the optimal repair bandwidth for all values of d simultaneously.

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“…In particular, the problem of constructing high rate MSR codes, i.e., with a constant number of parity nodes, has received a great deal of attention [4,22,24,29,30]. Implementing our techniques for high rate MSR codes is one of our future research directions.…”

Section: Previous Workmentioning

confidence: 99%

Asymptotically Optimal Regenerating Codes Over Any Field

Raviv

¹

2018

IEEE Trans. Inform. Theory

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The study of regenerating codes has advanced tremendously in recent years. However, most known constructions require large field size, and hence may be hard to implement in practice. By using notions from the theory of extension fields, we obtain two explicit constructions of regenerating codes. These codes approach the cut-set bound as the reconstruction degree increases, and may be realized over any given field if the file size is large enough. Since distributed storage systems are the main purpose of regenerating codes, this file size restriction is trivially satisfied in most conceivable scenarios. The first construction attains the cut-set bound at the MBR point asymptotically for all parameters, whereas the second one attains the cut-set bound at the MSR point asymptotically for low-rate parameters.

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An explicit, coupled-layer construction of a high-rate MSR code with low sub-packetization level, small field size and d < (n − 1)

Cited by 53 publications

References 19 publications

Minimum storage regenerating codes for all parameters

Minimum storage regenerating codes for all parameters

Minimum Storage Regenerating Codes for All Parameters

Asymptotically Optimal Regenerating Codes Over Any Field

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