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Regenerating codes enable trading off repair bandwidth for storage in distributed storage systems (DSS). Due to their distributed nature, these systems are intrinsically susceptible to attacks, and they may also be subject to multiple…
In distributed storage systems, cooperative regenerating codes tradeoff storage for repair bandwidth in the case of multiple node failures. In rack-aware distributed storage systems, there is no cost associated with transferring symbols…
In this paper, we present two constructions of degraded read friendly (DRF) MDS array codes with two parity nodes and a sub-packetization level of 2 over small finite fields, applicable for any arbitrary code length. The first construction…
Binary maximum distance separable (MDS) array codes are a special class of erasure codes for distributed storage that not only provide fault tolerance with minimum storage redundancy but also achieve low computational complexity. They are…
Maximum-distance-separable (MDS) codes are a class of erasure codes that are widely adopted to enhance the reliability of distributed storage systems (DSS). In (n, k) MDS coded DSS, the original data are stored into n distributed nodes in…
Regenerating codes are efficient methods for distributed storage in storage networks, where node failures are common. They guarantee low cost data reconstruction and repair through accessing only a predefined number of arbitrarily chosen…
In coding for distributed storage systems, efficient data reconstruction and repair through accessing a predefined number of arbitrarily chosen storage nodes is guaranteed by regenerating codes. Traditionally, code parameters, specially the…
Regenerating code is a class of code very suitable for distributed storage systems, which can maintain optimal bandwidth and storage space. Two types of important regenerating code have been constructed: the minimum storage regeneration…
In a distributed storage system, recovering from multiple failures is a critical and frequent task that is crucial for maintaining the system's reliability and fault-tolerance. In this work, we focus on the problem of repairing multiple…
We consider a set up where a file of size M is stored in n distributed storage nodes, using an (n,k) minimum storage regenerating (MSR) code, i.e., a maximum distance separable (MDS) code that also allows efficient exact-repair of any…
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…
In this paper, we propose two new constructions of exact-repair minimum storage regenerating (exact-MSR) codes. For both constructions, the encoded symbols are obtained by treating the message vector over GF(q) as a linearized polynomial…
We consider $(n,k,l)$ MDS codes of length $n$, dimension $k$, and subpacketization $l$ over a finite field $\mathbb{F}$. A codeword of such a code consists of $n$ column-vectors of length $l$ over $\mathbb{F}$, with the property that any…
$\epsilon$-Minimum Storage Regenerating ($\epsilon$-MSR) codes form a special class of Maximum Distance Separable (MDS) codes, providing mechanisms for exact regeneration of a single code block in their codewords by downloading slighly…
In large data centers, storage nodes are organized in racks, and the cross-rack transmission dominates the bandwidth cost. For the repair of single node failures, codes achieving the tradeoff between the storage redundancy and cross-rack…
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…
Several works have developed vector-linear maximum-distance separable (MDS) storage codes that min- imize the total communication cost required to repair a single coded symbol after an erasure, referred to as repair bandwidth (BW). Vector…
We consider the problem of designing [n; k] linear codes for distributed storage systems (DSS) that satisfy the (r, t)-Local Repair Property, where any t'(<=t) simultaneously failed nodes can be locally repaired, each with locality r. The…
To recover simultaneous multiple failures in erasure coded storage systems, Patrick Lee et al introduce concurrent repair based minimal storage regenerating codes to reduce repair traffic. The architecture of this approach is simpler and…
An $(n,k,\ell)$-vector MDS code is a $\mathbb{F}$-linear subspace of $(\mathbb{F}^\ell)^n$ (for some field $\mathbb{F}$) of dimension $k\ell$, such that any $k$ (vector) symbols of the codeword suffice to determine the remaining $r=n-k$…