Related papers: Repairing Reed-Solomon Codes With Multiple Erasure…
Recently Reed-Solomon (RS) codes were shown to possess a repair scheme that supports repair of failed nodes with optimal repair bandwidth. In this paper, we extend this result in two directions. First, we propose a new repair scheme for the…
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…
Reed-Solomon (RS) codes are widely used in distributed storage systems. In this paper, we study the repair bandwidth and sub-packetization size of RS codes. The repair bandwidth is defined as the amount of transmitted information from…
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…
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…
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…
The minimum storage rack-aware regenerating (MSRR) code is a variation of regenerating codes that achieves the optimal repair bandwidth for a single node failure in the rack-aware model. The authors in~\cite{Chen-Barg2019}…
Constructing Reed-Solomon (RS) codes that can correct insertion and deletion (ins-del) errors has been the focus of several recent studies. However, efficient decoding algorithms for such codes have received less attention and remain a…
The piggybacking framework for designing erasure codes for distributed storage has empirically proven to be very useful, and has been used to design codes with desirable properties, such as low repair bandwidth and complexity. However, the…
A distributed storage system stores data across multiple nodes, with the primary objective of enabling efficient data recovery even in the event of node failures. The main goal of an exact repair scheme is to recover the data from a failed…
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…
Repairing Reed-Solomon codes with low bandwidth is a central challenge in distributed storage. Following the trace-repair framework of Guruswami and Wootters (2017), recent works by Lin (2023) and Liu-Wan-Xing (2024) provided significant…
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…
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)…
A simple algorithm for decoding both errors and erasures of Reed-Solomon codes is described.
The paper is devoted to the problem of erasure coding in distributed storage. We consider a model of storage that assumes that nodes are organized into equally sized groups, called racks, that within each group the nodes can communicate…
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…
We study the problem of efficiently computing on encoded data. More specifically, we study the question of low-bandwidth computation of functions $F:\mathbb{F}^k \to \mathbb{F}$ of some data $x \in \mathbb{F}^k$, given access to an encoding…
Distributed storage systems often introduce redundancy to increase reliability. When coding is used, the repair problem arises: if a node storing encoded information fails, in order to maintain the same level of reliability we need to…
In distributed storage systems that employ erasure coding, the issue of minimizing the total {\it repair bandwidth} required to exactly regenerate a storage node after a failure arises. This repair bandwidth depends on the structure of the…