Related papers: Repairing Reed-Solomon Codes
It is well known that an (n,k) code can be used to store 'k' units of information in 'n' unit-capacity disks of a distributed data storage system. If the code used is maximum distance separable (MDS), then the system can tolerate any (n-k)…
Centralized repair refers to repairing $h\geq 2$ node failures using $d$ helper nodes in a centralized way, where the repair bandwidth is counted by the total amount of data downloaded from the helper nodes. A centralized MSR code is an MDS…
The newly presented $(k+2,k)$ Hadamard minimum storage regenerating (MSR) code is the first class of high rate storage code with optimal repair property for all single node failures. In this paper, we propose a new simple repair strategy,…
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 $k/n$…
List recovery of error-correcting codes has emerged as a fundamental notion with broad applications across coding theory and theoretical computer science. Folded Reed-Solomon (FRS) and univariate multiplicity codes are explicit…
Network codes designed specifically for distributed storage systems have the potential to provide dramatically higher storage efficiency for the same availability. One main challenge in the design of such codes is the exact repair problem:…
The reliability of erasure-coded distributed storage systems, as measured by the mean time to data loss (MTTDL), depends on the repair bandwidth of the code. Repair-efficient codes provide reliability values several orders of magnitude…
The $(n,k,d)$ regenerating code is a class of $(n,k)$ erasure codes with the capability to recover a lost code fragment from other $d$ existing code fragments. This paper concentrates on the design of exact regenerating codes at Minimum…
Distributed storage systems for large-scale applications typically use replication for reliability. Recently, erasure codes were used to reduce the large storage overhead, while increasing data reliability. A main limitation of…
We study the exact and optimal repair of multiple failures in codes for distributed storage. More particularly, we provide an explicit construction of exact minimum bandwidth coordinated regenerating codes (MBCR) for n=d+t,k,d >= k,t >= 1.…
Two widely studied models of multiple-node repair in distributed storage systems are centralized repair and cooperative repair. The centralized model assumes that all the failed nodes are recreated in one location, while the cooperative one…
MDS array codes are widely used in storage systems due to their computationally efficient encoding and decoding procedures. An MDS code with $r$ redundancy nodes can correct any $r$ node erasures by accessing all the remaining information…
We study the exact-repair tradeoff between storage and repair bandwidth in distributed storage systems (DSS). We give new inner bounds for the tradeoff region and provide code constructions that achieve these bounds.
We propose a generic transformation that can convert any nonbinary $(n=k+r,k)$ maximum distance separable (MDS) code into another $(n,k)$ MDS code over the same field such that 1) some arbitrarily chosen $r$ nodes have the optimal repair…
Distributed storage systems in the presence of a wiretapper are considered. A distributed storage system (DSS) is parameterized by three parameters (n, k,d), in which a file stored across n distributed nodes, can be recovered from any k out…
We investigate the problem of privately recovering a single erasure for Reed-Solomon codes with low communication bandwidths. For an $[n,k]_{q^\ell}$ code with $n-k\geq q^{m}+t-1$, we construct a repair scheme that allows a client to…
In an $(n,k,d)$ rack-aware storage model, the system consists of $n$ nodes uniformly distributed across $\bar{n}$ successive racks, such that each rack contains $u$ nodes of equal capacity and the reconstructive degree satisfies…
An $(n, M)$ vector code $\mathcal{C} \subseteq \mathbb{F}^n$ is a collection of $M$ codewords where $n$ elements (from the field $\mathbb{F}$) in each of the codewords are referred to as code blocks. Assuming that $\mathbb{F} \cong…
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.…
An $(n,k,l)$ MDS array code of length $n,$ dimension $k=n-r$ and sub-packetization $l$ is formed of $l\times n$ matrices over a finite field $F,$ with every column of the matrix stored on a separate node in a distributed storage system and…