相关论文: A Repair Framework for Scalar MDS Codes
In a distributed storage systems (DSS) with $k$ systematic nodes, robustness against node failure is commonly provided by storing redundancy in a number of other nodes and performing repair mechanism to reproduce the content of the failed…
Consider a binary maximum distance separable (MDS) array code composed of an $m\times (k+r)$ array of bits with $k$ information columns and $r$ parity columns, such that any $k$ out of $k+r$ columns suffice to reconstruct the $k$…
Abundant high-rate (n, k) minimum storage regenerating (MSR) codes have been reported in the literature. However, most of them require contacting all the surviving nodes during a node repair process, resulting in a repair degree of d=n-1.…
This paper addresses the problem of constructing MDS codes that enable exact repair of each code block with small repair bandwidth, which refers to the total amount of information flow from the remaining code blocks during the repair…
Minimum storage regenerating (MSR) codes, with the MDS property and the optimal repair bandwidth, are widely used in distributed storage systems (DSS) for data recovery. In this paper, we consider the construction of $(n,k,l)$ MSR codes in…
High-rate minimum storage regenerating (MSR) codes are known to require a large sub-packetization level, which can make meta-data management difficult and hinder implementation in practical systems. A few maximum distance separable (MDS)…
This paper presents an explicit construction for an $((n,k,d=n-1), (\alpha,\beta))$ regenerating code over a field $\mathbb{F}_Q$ operating at the Minimum Storage Regeneration (MSR) point. The MSR code can be constructed to have rate $k/n$…
Reed-Solomon codes have found many applications in practical storage systems, but were until recently considered unsuitable for distributed storage applications due to the widely-held belief that they have poor repair bandwidth. The work of…
The repair bandwidth of a code is the minimum amount of data required to repair one or several failed nodes (erasures). For MDS codes, the repair bandwidth is bounded below by the so-called cut-set bound, and codes that meet this bound with…
In a distributed storage system based on erasure coding, an important problem is the \emph{repair problem}: If a node storing a coded piece fails, in order to maintain the same level of reliability, we need to create a new encoded piece and…
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…
A $(k+r,k,l)$ binary array code of length $k+r$, dimension $k$, and sub-packetization $l$ is composed of $l\times(k+r)$ matrices over $\mathbb{F}_2$, with every column of the matrix stored on a separate node in the distributed storage…
For scalar maximum distance separable (MDS) codes, the conventional repair schemes that achieve the cut-set bound with equality for the single-node repair have been proven to require a super-exponential sub-packetization level.As is well…
The minimum storage rack-aware regenerating (MSRR) code is a variation of regenerating codes that achieves the optimal repair bandwidth for a single node failure in the rack-aware model. The authors in~\cite{Chen-Barg2019}…
MDS codes are erasure-correcting codes that can correct the maximum number of erasures for a given number of redundancy or parity symbols. If an MDS code has $r$ parities and no more than $r$ erasures occur, then by transmitting all the…
Despite their exceptional error-correcting properties, Reed-Solomon (RS) codes have been overlooked in distributed storage applications due to the common belief that they have poor repair bandwidth: A naive repair approach would require the…
We present the construction of a family of erasure correcting codes for distributed storage that achieve low repair bandwidth and complexity at the expense of a lower fault tolerance. The construction is based on two classes of codes, where…
Maximum-distance separable (MDS) array codes with high rate and an optimal repair property were introduced recently. These codes could be applied in distributed storage systems, where they minimize the communication and disk access required…
A code construction and repair scheme for optimal functional regeneration of multiple node failures is presented, which is based on stitching together short MDS codes on carefully chosen sets of points lying on a linearized polynomial. The…
Distributed storage codes have important applications in the design of modern storage systems. In a distributed storage system, every storage node has a probability to fail and once an individual storage node fails, it must be reconstructed…