Related papers: Locally Recoverable codes from rational maps
Locally repairable codes enables fast repair of node failure in a distributed storage system. The code symbols in a codeword are stored in different storage nodes, such that a disk failure can be recovered by accessing a small fraction of…
Reed-Muller codes are among the most important classes of locally correctable codes. Currently local decoding of Reed-Muller codes is based on decoding on lines or quadratic curves to recover one single coordinate. To recover multiple…
A Locally Recoverable Code is a code such that the value of any single coordinate of a codeword can be recovered from the values of a small subset of other coordinates. When we have $\delta$ non overlapping subsets of cardinality $r_i$ that…
Locally repairable codes (LRC) have recently been a subject of intense research due to theoretical appeal and their application in distributed storage systems. In an LRC, any coordinate of a codeword can be recovered by accessing only few…
This paper presents and analyzes a novel concatenated coding scheme for enabling error resilience in two distributed storage settings: one being storage using existing regenerating codes and the second being storage using locally repairable…
Modern large-scale distributed storage systems use erasure codes to protect against node failures with low storage overhead. In practice, the failure rate and other factors of storage devices in the system may vary significantly over time,…
This work focuses on sequential locally recoverable codes (SLRCs), a special family of locally repairable codes, capable of correcting multiple code symbol erasures, which are commonly used for distributed storage systems. First, we…
Erasure list decoding was introduced to correct a larger number of erasures with output of a list of possible candidates. In the present paper, we consider both random linear codes and algebraic geometry codes for list decoding erasure…
We study the Singleton-type bound that provides an upper limit on the minimum distance of locally repairable codes. We present an improved bound by carefully analyzing the combinatorial structure of the repair sets. Thus, we show the…
In a {\em locally recoverable} or {\em repairable} code, any symbol of a codeword can be recovered by reading only a small (constant) number of other symbols. The notion of local recoverability is important in the area of distributed…
We propose locally rewritable codes (LWC) for resistive memories inspired by locally repairable codes (LRC) for distributed storage systems. Small values of repair locality of LRC enable fast repair of a single failed node since the lost…
Locally Decodable Codes (LDCs) are error correcting codes that admit efficient decoding of individual message symbols without decoding the entire message. Unfortunately, known LDC constructions offer a sub-optimal trade-off between rate,…
We introduce a fast iterative non-local shrinkage algorithm to recover MRI data from undersampled Fourier measurements. This approach is enabled by the reformulation of current non-local schemes as an alternating algorithm to minimize a…
In this work, we give locally repairable regenerating code (LRRC) [1]-[3], [5], [6] constructions that can protect the file size promised by the graph analysis of the modified family helper selection (MFHS) scheme [1] at the…
This paper considers the classical error correcting problem which is frequently discussed in coding theory. We wish to recover an input vector $f \in \R^n$ from corrupted measurements $y = A f + e$. Here, $A$ is an $m$ by $n$ (coding)…
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…
The problem of recovering from qubit erasures has recently gained attention as erasures occur in many physical systems such as photonic systems, trapped ions, superconducting qubits and circuit quantum electrodynamics. While several…
In this article, we construct codes with hierarchical locality using natural geometric structures in Artin-Schreier surfaces of the form $y^p-y=f(x,z)$. Our main theorem describes the codes, their hierarchical structure and recovery…
Decoding error-correctiong codes by methods of mathematical optimization, most importantly linear programming, has become an important alternative approach to both algebraic and iterative decoding methods since its introduction by Feldman…
Codes for storage systems aim to minimize the repair locality, which is the number of disks (or nodes) that participate in the repair of a single failed disk. Simultaneously, the code must sustain a high rate, operate on a small finite…