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In the literature, all the known high-rate MDS codes with the optimal repair bandwidth possess a significantly large sub-packetization level, which may prevent the codes to be implemented in practical systems. To build MDS codes with small…
Fast and efficient failure recovery is a new challenge for cloud storage systems with a large number of storage nodes. A pivotal recovery metric upon the failure of a storage node is repair bandwidth cost which refers to the amount of data…
Efficient node repair is a central requirement in distributed storage systems, particularly in high-rate erasure-coded deployments where repair traffic directly affects network overhead and recovery cost. Piggybacking codes reduce the…
We construct maximally recoverable codes (corresponding to partial MDS codes) which are based on linearized Reed-Solomon codes. The new codes have a smaller field size requirement compared with known constructions. For certain asymptotic…
Maximum-distance separable (MDS) convolutional codes form an optimal family of convolutional codes, the study of which is of great importance. There are very few general algebraic constructions of MDS convolutional codes. In this paper, we…
Maximum Distance Separable (MDS) codes with a sparse and balanced generator matrix are appealing in distributed storage systems for balancing and minimizing the computational load. Such codes have been constructed via Reed-Solomon codes…
Array codes have been widely employed in storage systems, such as Redundant Arrays of Inexpensive Disks (RAID). The row-diagonal parity (RDP) codes and EVENODD codes are two popular double-parity array codes. As the capacity of hard disks…
Minimum storage regenerating (MSR) codes are a class of maximum distance separable (MDS) array codes capable of repairing any single failed node by downloading the minimum amount of information from each of the helper nodes. However, MSR…
Partial MDS (PMDS) codes are erasure codes combining local (row) correction with global additional correction of entries, while Sector-Disk (SD) codes are erasure codes that address the mixed failure mode of current RAID systems. It has…
Regenerating codes are a class of recently developed codes for distributed storage that, like Reed-Solomon codes, permit data recovery from any arbitrary k of n nodes. However regenerating codes possess in addition, the ability to repair a…
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 $k$…
$\epsilon$-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…
The explosion in the volumes of data being stored online has resulted in distributed storage systems transitioning to erasure coding based schemes. Local Reconstruction Codes (LRCs) have emerged as the codes of choice for these…
The Damerau-Levenshtein distance between two sequences is the minimum number of operations (deletions, insertions, substitutions, and adjacent transpositions) required to convert one sequence into another. Notwithstanding a long history of…
Scientific computing workflows generate enormous distributed data that is short-lived, yet critical for job completion time. This class of data is called intermediate data. A common way to achieve high data availability is to replicate…
In this paper, a new repair scheme for a modified construction of MDS codes is studied. The obtained repair scheme has optimal bandwidth for multiple failed nodes under the cooperative repair model. In addition, the repair scheme has…
A Maximum Distance Separable code over an alphabet $F$ is defined via an encoding function $C:F^k \rightarrow F^n$ that allows to retrieve a message $m \in F^k$ from the codeword $C(m)$ even after erasing any $n-k$ of its symbols. The…
The amount of digital data is rapidly growing. There is an increasing use of a wide range of computer systems, from mobile devices to large-scale data centers, and important for reliable operation of all computer systems is mitigating the…
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…
The complexity of software implementations of MDS erasure codes mainly depends on the efficiency of the finite field operations implementation. In this paper, we propose a method to reduce the complexity of the finite field multiplication…