Related papers: Repairing Reed-Solomon Codes With Two Erasures
Generalized Reed-Solomon (RS) codes are a common choice for efficient, reliable error correction in memory and communications systems. These codes add $2t$ extra parity symbols to a block of memory, and can efficiently and reliably correct…
This paper presents a comprehensive study on the asymptotically optimal repair of Reed-Solomon (RS) codes with small sub-packetization, specifically tailored for rack-aware distributed storage systems. Through the utilization of multi-base…
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.…
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…
Algebraic decoding algorithms are commonly applied for the decoding of Reed-Solomon codes. Their main advantages are low computational complexity and predictable decoding capabilities. Many algorithms can be extended for correction of both…
We consider the repair scheme of Guruswami-Wootters for the Reed-Solomon code and ask: can we correctly repair a failed node in the presence of erroneous nodes? Equivalently, we consider the collection of downloaded traces as a code and…
Network transfer and disk read are the most time consuming operations in the repair process for node failures in erasure-code-based distributed storage systems. Recent developments on Reed-Solomon codes, the most widely used erasure codes…
Distributed storage systems for large clusters typically use replication to provide reliability. Recently, erasure codes have been used to reduce the large storage overhead of three-replicated systems. Reed-Solomon codes are the standard…
Maximum distance separable (MDS) codes are widely used in distributed storage, but naively repairing a single failure in an $(n,k)$ MDS code requires downloading the full contents of $k$ surviving nodes. Minimum storage regenerating (MSR)…
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…
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…
Codes in the sum-rank metric have various applications in error control for multishot network coding, distributed storage and code-based cryptography. Linearized Reed-Solomon (LRS) codes contain Reed-Solomon and Gabidulin codes as…
This paper presents two repair schemes for low-rate Reed-Solomon (RS) codes over prime fields that can repair any node by downloading a constant number of bits from each surviving node. The total bandwidth resulting from these schemes is…
A simple algorithm for decoding both errors and erasures of Reed-Solomon codes is described.
Cooperative regenerating codes are regenerating codes designed to tradeoff storage for repair bandwidth in case of multiple node failures. Minimum storage cooperative regenerating (MSCR) codes are a class of cooperative regenerating codes…
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…
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…
Erasure codes provide a storage efficient alternative to replication based redundancy in (networked) storage systems. They however entail high communication overhead for maintenance, when some of the encoded fragments are lost and need to…
In this paper, we address the node repair problem of Reed-Solomon (RS) coded distributed storage systems. Specifically, to overcome the challenges of multiple-node failures of RS codes under the rack-aware storage model, we employ good…
Regenerating codes are a class of codes proposed for providing reliability of data and efficient repair of failed nodes in distributed storage systems. In this paper, we address the fundamental problem of handling errors and erasures during…