Related papers: Repairing Reed-Solomon Codes With Two Erasures
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 this paper, we discuss codes for distributed storage systems with hierarchical repair properties. Specifically, we devote attention to the repair problem of the rack-aware storage model with locality, aiming to enhance the system's…
Petabyte-scale distributed storage systems are currently transitioning to erasure codes to achieve higher storage efficiency. Classical codes like Reed-Solomon are highly sub-optimal for distributed environments due to their high overhead…
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…
Distributed storage systems provide reliable access to data through redundancy spread over individually unreliable nodes. Application scenarios include data centers, peer-to-peer storage systems, and storage in wireless networks. Storing…
MDS array codes are widely used in storage systems to protect data against erasures. We address the \emph{rebuilding ratio} problem, namely, in the case of erasures, what is the fraction of the remaining information that needs to be…
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…
Minimum-Storage Regenerating (MSR) codes have emerged as a viable alternative to Reed-Solomon (RS) codes as they minimize the repair bandwidth while they are still optimal in terms of reliability and storage overhead. Although several MSR…
A new class of exact-repair regenerating codes is constructed by combining two layers of erasure correction codes together with combinatorial block designs, e.g., Steiner systems, balanced incomplete block designs and t-designs. The…
In order to provide high data reliability, distributed storage systems disperse data with redundancy to multiple storage nodes. Regenerating codes is a new class of erasure codes to introduce redundancy for the purpose of improving the data…
In this work, we present linear exact repair schemes for one or two erasures in decreasing monomial-Cartesian codes DM-CC, a family of codes which provides a framework for polar codes. In the case of two erasures, the positions of the…
Erasure coding techniques are used to increase the reliability of distributed storage systems while minimizing storage overhead. Also of interest is minimization of the bandwidth required to repair the system following a node failure. In a…
Maximum distance separable (MDS) codes facilitate the achievement of elevated levels of fault tolerance in storage systems while incurring minimal redundancy overhead. Reed-Solomon (RS) codes are typical MDS codes with the sub-packetization…
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…
Codes over rings, especially over Galois rings, have been extensively studied for nearly three decades due to their similarity to linear codes over finite fields. A distributed storage system uses a linear code to encode a large file across…
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 derive a lower bound on the amount of information accessed to repair failed nodes within a single rack from any number of helper racks in the rack-aware storage model that allows collective information processing in the nodes that share…
Distributed storage systems for large-scale applications typically use replication for reliability. Recently, erasure codes were used to reduce the large storage overhead, while increasing data reliability. A main limitation of…
MDS array codes are widely used in storage systems to protect data against erasures. We address the \emph{rebuilding ratio} problem, namely, in the case of erasures, what is the the fraction of the remaining information that needs to be…
We consider the decoding of linear and array codes from errors when we are only allowed to download a part of the codeword. More specifically, suppose that we have encoded $k$ data symbols using an $(n,k)$ code with code length $n$ and…