Related papers: Locally Repairable Codes
Locally repairable codes with availability have become essential components in modern large-scale distributed cloud storage systems and numerous other applications. In this paper, we focus on the construction of locally repairable codes…
An $(n,r,h,a,q)$-Local Reconstruction Code (LRC) is a linear code over $\mathbb{F}_q$ of length $n$, whose codeword symbols are partitioned into $n/r$ local groups each of size $r$. Each local group satisfies `$a$' local parity checks to…
A code is said to be a Locally Recoverable Code (LRC) with availability if every coordinate can be recovered from multiple disjoint sets of other coordinates called recovering sets. The vector of sizes of recovering sets of a coordinate is…
This paper studies the problem of code symbol availability: a code symbol is said to have $(r, t)$-availability if it can be reconstructed from $t$ disjoint groups of other symbols, each of size at most $r$. For example, $3$-replication…
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…
Distributed data storage systems are essential to deal with the need to store massive volumes of data. In order to make such a system fault-tolerant, some form of redundancy becomes crucial, incurring various overheads - most prominently in…
Regeneration codes with exact-repair property for distributed storage systems is studied in this paper. For exact- repair problem, the achievable points of ({\alpha},{\beta}) tradeoff match with the outer bound only for minimum storage…
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…
Erasure codes are an efficient means of storing data across a network in comparison to data replication, as they tend to reduce the amount of data stored in the network and offer increased resilience in the presence of node failures. The…
Maximally Recoverable Local Reconstruction Codes (LRCs) are codes designed for distributed storage to provide maximum resilience to failures for a given amount of storage redundancy and locality. An $(n,r,h,a,g)$-MR LRC has $n$ coordinates…
A locally recoverable code is an error-correcting code such that any erasure in a single coordinate of a codeword can be recovered from a small subset of other coordinates. In this article we develop an algorithm that computes a recovery…
Linear erasure codes with local repairability are desirable for distributed data storage systems. An [n, k, d] code having all-symbol (r, \delta})-locality, denoted as (r, {\delta})a, is considered optimal if it also meets the minimum…
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…
Consider a systematic linear code where some (local) parity symbols depend on few prescribed symbols, while other (heavy) parity symbols may depend on all data symbols. Local parities allow to quickly recover any single symbol when it is…
This paper investigates the use of redundancy and self repairing against node failures in distributed storage systems, using various strategies. In replication method, access to one replication node is sufficient to reconstruct a lost node,…
Constructions of optimal locally repairable codes (LRCs) achieving Singleton-type bound have been exhaustively investigated in recent years. In this paper, we consider new bounds and constructions of Singleton-optimal LRCs with minmum…
Constructions of optimal locally repairable codes (LRCs) in the case of $(r+1) \nmid n$ and over small finite fields were stated as open problems for LRCs in [I. Tamo \emph{et al.}, "Optimal locally repairable codes and connections to…
A locally repairable code is called Singleton-optimal if it achieves the Singleton-type bound. Such codes are of great theoretic interest in the study of locally repairable codes. In the recent years there has been a great amount of work on…
We consider the problem of constructing an erasure code for storage over a network when the data sources are distributed. Specifically, we assume that there are n storage nodes with limited memory and k<n sources generating the data. We…
We consider the problem of constructing codes that can correct deletions that are localized within a certain part of the codeword that is unknown a priori. Namely, the model that we study is when at most $k$ deletions occur in a window of…