Related papers: Repairing Reed-Solomon Codes With Two Erasures
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…
Erasure codes are an integral part of many distributed storage systems aimed at Big Data, since they provide high fault-tolerance for low overheads. However, traditional erasure codes are inefficient on reading stored data in degraded…
Large-scale systems with arrays of solid state disks (SSDs) have become increasingly common in many computing segments. To make such systems resilient, we can adopt erasure coding such as Reed-Solomon (RS) code as an alternative to…
An erasure code is said to be a code with sequential recovery with parameters $r$ and $t$, if for any $s \leq t$ erased code symbols, there is an $s$-step recovery process in which at each step we recover exactly one erased code symbol by…
We study the problem of centralized exact repair of multiple failures in distributed storage. We describe constructions that achieve a new set of interior points under exact repair. The constructions build upon the layered code construction…
Error-correcting codes are a method for representing data, so that one can recover the original information even if some parts of it were corrupted. The basic idea, which dates back to the revolutionary work of Shannon and Hamming about a…
We prove that Reed-Solomon (RS) codes with random evaluation points are list recoverable up to capacity with optimal output list size, for any input list size. Namely, given an input list size $\ell$, a designated rate $R$, and any…
Maximum-distance separable (MDS) array codes with high rate and an optimal repair property were introduced recently. These codes could be applied in distributed storage systems, where they minimize the communication and disk access required…
We consider the repair problem for Reed--Solomon (RS) codes, evaluated on an $\mathbb{F}_q$-linear subspace $U\subseteq\mathbb{F}_{q^m}$ of dimension $d$, where $q$ is a prime power, $m$ is a positive integer, and $\mathbb{F}_q$ is the…
For communication systems with heavy burst noise, an optimal Forward Error Correction (FEC) scheme is expected to have a large burst error correction capacity while simultaneously owning moderate random error correction capability. This…
In this paper we study array-based codes over graphs for correcting multiple node failures. These codes have applications to neural networks, associative memories, and distributed storage systems. We assume that the information is stored on…
Repair performance in hierarchical data centers is often bottlenecked by cross-rack network transfer. Recent theoretical results show that the cross-rack repair traffic can be minimized through repair layering, whose idea is to partition a…
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…
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…
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…
A locally recoverable code is an error-correcting code such that any erasure in a coordinate of a codeword can be recovered from a set of other few coordinates. In this article we introduce a model of local recoverable codes that also…
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 construct constant-sized ensembles of linear error-correcting codes over any fixed alphabet that can correct a given fraction of adversarial erasures at rates approaching the Singleton bound arbitrarily closely. We provide several…
Distributed storage systems support failures of individual devices by the use of replication or erasure correcting codes. While erasure correcting codes offer a better storage efficiency than replication for similar fault tolerance, they…
Data availability is critical in distributed storage systems, especially when node failures are prevalent in real life. A key requirement is to minimize the amount of data transferred among nodes when recovering the lost or unavailable data…