English
Related papers

Related papers: Locally recoverable codes on algebraic curves

200 papers

Typically, locally repairable codes (LRCs) and regenerating codes have been studied independently of each other, and it has not been clear how the parameters of one relate to those of the other. In this paper, a novel connection between…

Information Theory · Computer Science 2016-11-22 Toni Ernvall , Thomas Westerbäck , Ragnar Freij-Hollanti , Camilla Hollanti

Recently, locally repairable codes (LRCs) with local erasure correction constraints that are unequal and disjoint have been proposed. In this work, we study the same topic and provide some improved and additional results.

Information Theory · Computer Science 2017-04-10 Geonu Kim , Jungwoo Lee

Employing underlying geometric and algebraic structures allows for constructing bespoke codes for local recovery of erasures. We survey techniques for enriching classical codes with additional machinery, such as using lines or curves in…

Information Theory · Computer Science 2024-02-06 Kathryn Haymaker , Hiram H. López , Beth Malmskog , Gretchen L. Matthews , Fernando Piñero

Locally recoverable codes deal with the task of reconstructing a lost symbol by relying on a portion of the remaining coordinates smaller than an information set. We consider the case of codes over finite chain rings, generalizing known…

Information Theory · Computer Science 2024-01-11 Giulia Cavicchioni , Eleonora Guerrini , Alessio Meneghetti

In this work we present a class of locally recoverable codes, i.e. codes where an erasure at a position $P$ of a codeword may be recovered from the knowledge of the entries in the positions of a recovery set $R_P$. The codes in the class…

Information Theory · Computer Science 2021-07-29 Cícero Carvalho , Victor G. L. Neumann

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…

Information Theory · Computer Science 2016-11-17 Viveck Cadambe , Arya Mazumdar

In distributed storage systems, locally repairable codes (LRCs) are designed to reduce disk I/O and repair costs by enabling recovery of each code symbol from a small number of other symbols. To handle multiple node failures,…

Information Theory · Computer Science 2023-07-11 Jing Qiu , Fang-Wei Fu

An $[n,k]$ code $\mathcal{C}$ is said to be locally recoverable in the presence of a single erasure, and with locality parameter $r$, if each of the $n$ code symbols of $\mathcal{C}$ can be recovered by accessing at most $r$ other code…

Information Theory · Computer Science 2017-02-20 S. B. Balaji , Ganesh R. Kini , P. Vijay Kumar

The locally repairable code (LRC) studied in this paper is an $[n,k]$ linear code of which the value at each coordinate can be recovered by a linear combination of at most $r$ other coordinates. The central problem in this work is to…

Information Theory · Computer Science 2014-09-04 Anyu Wang , Zhifang Zhang

This paper develops a new family of locally recoverable codes for distributed storage systems, Sequential Locally Recoverable Codes (SLRCs) constructed to handle multiple erasures in a sequential recovery approach. We propose a new…

Information Theory · Computer Science 2025-03-05 Akram Baghban , Mehdi Ghiyasvand

We consider linear cyclic codes with the locality property, or locally recoverable codes (LRC codes). A family of LRC codes that generalize the classical construction of Reed-Solomon codes was constructed in a recent paper by I. Tamo and A.…

Information Theory · Computer Science 2017-02-10 Itzhak Tamo , Alexander Barg , Sreechakra Goparaju , Robert Calderbank

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,…

Information Theory · Computer Science 2023-08-15 Xiangliang Kong

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…

Information Theory · Computer Science 2025-07-14 Akram Baghban , Marc Newman , Anna-Lena Horlemann , Mehdi Ghiyasvand

Locally repairable codes (LRCs) have gained significant interest for the design of large distributed storage systems as they allow a small number of erased nodes to be recovered by accessing only a few others. Several works have thus been…

Information Theory · Computer Science 2019-06-07 Matthias Grezet , Ragnar Freij-Hollanti , Thomas Westerbäck , Camilla Hollanti

When a node in a distributed storage system fails, it needs to be promptly repaired to maintain system integrity. While typical erasure codes can provide a significant storage advantage over replication, they suffer from poor repair…

Information Theory · Computer Science 2018-07-10 Geonu Kim , Jungwoo Lee

Locally repairable codes are widely applicable in contemporary large-scale distributed cloud storage systems and various other areas. By making use of some algebraic structures of elliptic curves, Li et al. developed a series of $q$-ary…

Information Theory · Computer Science 2025-02-19 Junjie Huang , Chang-An Zhao

This paper studies bounds and constructions of locally repairable codes (LRCs) with multiple localities so-called multiple-locality LRCs (ML-LRCs). In the simplest case of two localities some code symbols of an ML-LRC have a certain…

Information Theory · Computer Science 2016-01-13 Alexander Zeh , Eitan Yaakobi

Locally repairable codes (LRCs) are error correcting codes used in distributed data storage. A traditional approach is to look for codes which simultaneously maximize error tolerance and minimize storage space consumption. However, this…

Information Theory · Computer Science 2015-12-21 Antti Pöllänen

Locally repairable codes (LRCs) are ingeniously designed distributed storage codes with a (usually small) fixed set of helper nodes participating in repair. Since most existing LRCs assume exact repair and allow full exchange of the stored…

Information Theory · Computer Science 2016-05-06 Imad Ahmad , Chih-Chun Wang

As an important coding scheme in modern distributed storage systems, locally repairable codes (LRCs) have attracted a lot of attentions from perspectives of both practical applications and theoretical research. As a major topic in the…

Information Theory · Computer Science 2021-01-01 Xiangliang Kong , Xin Wang , Gennnian Ge