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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.…
Data storage applications require erasure-correcting codes with prescribed sets of dependencies between data symbols and redundant symbols. The most common arrangement is to have $k$ data symbols and $h$ redundant symbols (that each depends…
Erasure correcting codes are widely used to ensure data persistence in distributed storage systems. This paper addresses the simultaneous repair of multiple failures in such codes. We go beyond existing work (i.e., regenerating codes by…
Residue codes have been traditionally used for compute error correction rather than storage error correction. In this paper, we use these codes for storage error correction with surprising results. We find that adapting residue codes to…
The repair problem in distributed storage addresses recovery of the data encoded using an erasure code, for instance, a Reed-Solomon (RS) code. We consider the problem of repairing a single node or multiple nodes in RS-coded storage systems…
This chapter deals with the topic of designing reliable and efficient codes for the storage and retrieval of large quantities of data over storage devices that are prone to failure. For long, the traditional objective has been one of…
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…
To help reliability of SSD arrays, Redundant Array of Independent Disks (RAID) are commonly employed. However, the conventional reliability models of HDD RAID cannot be applied to SSD arrays, as the nature of failures in SSDs are different…
This paper considers capacity-achieving coding for the clustered form of distributed storage that reflects practical storage networks. To reflect the clustered structure with limited cross-cluster communication bandwidths, nodes in the same…
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)…
Clustered distributed storage models real data centers where intra- and cross-cluster repair bandwidths are different. In this paper, exact-repair minimum-storage-regenerating (MSR) codes achieving capacity of clustered distributed storage…
We present the construction of a new family of erasure correcting codes for distributed storage that yield low repair bandwidth and low repair complexity. The construction is based on two classes of parity symbols. The primary goal of the…
As the size of data storing arrays of disks grows, it becomes vital to protect data against double disk failures. A popular method of protection is via the Reed-Solomon (RS) code with two parity words. In the present paper we construct…
Classical erasure codes, e.g. Reed-Solomon codes, have been acknowledged as an efficient alternative to plain replication to reduce the storage overhead in reliable distributed storage systems. Yet, such codes experience high overhead…
With the increase of huge amounts of data in volume, velocity, and variety, the need for capacity of Redundant Arrays of Inexpensive Disks (RAID) storage systems is dramatically growing. However, the probability of disk failures in RAID…
We consider the rack-aware storage system where $n=\bar{n}u$ nodes are organized in $\bar{n}$ racks each containing $u$ nodes, and any $k=\bar{k}u+u_0~(0\leq u_0<u)$ nodes can retrieve the original data file. More importantly, the…
Cooperative MSR codes are a kind of storage codes which enable optimal-bandwidth repair of any $h\geq2$ node erasures in a cooperative way, while retaining the minimum storage as an $[n,k]$ MDS code. Each code coordinate (node) is assumed…
Regenerating codes allow distributed storage systems to recover from the loss of a storage node while transmitting the minimum possible amount of data across the network. We present a systematic computer search for optimal systematic…
Distributed and cloud storage systems are used to reliably store large-scale data. Erasure codes have been recently proposed and used in real-world distributed and cloud storage systems such as Google File System, Microsoft Azure Storage,…
The high repair cost of (n,k) Maximum Distance Separable (MDS) erasure codes has recently motivated a new class of codes, called Regenerating Codes, that optimally trade off storage cost for repair bandwidth. In this paper, we address…