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Related papers: Capacity of Locally Recoverable Codes

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Considerable interest has been paid in recent literature to codes combining local and global properties for erasure correction. Applications are in cloud type of implementations, in which fast recovery of a failed storage device is…

Information Theory · Computer Science 2016-02-09 Mario Blaum , Steven R. Hetzler

Maximally recoverable codes are a class of codes which recover from all potentially recoverable erasure patterns given the locality constraints of the code. In earlier works, these codes have been studied in the context of codes with…

Information Theory · Computer Science 2021-05-10 D. Shivakrishna , Aaditya M. Nair , V. Lalitha

This paper studies a Shannon-theoretic version of the generalized distribution preserving quantization problem where a stationary and memoryless source is encoded subject to a distortion constraint and the additional requirement that the…

Information Theory · Computer Science 2015-07-10 Naci Saldi , Tamás Linder , Serdar Yüksel

Locally repairable codes (LRC) for distribute storage allow two approaches to locally repair multiple failed nodes: 1) parallel approach, by which each newcomer access a set of $r$ live nodes $(r$ is the repair locality$)$ to download data…

Information Theory · Computer Science 2015-11-20 Wentu Song , Chau Yuen

Locally repairable convolutional codes (LRCCs) for distributed storage systems (DSSs) are introduced in this work. They enable local repair, for a single node erasure (or more generally, $ \partial - 1 $ erasures per local group), and…

Information Theory · Computer Science 2020-12-08 Umberto Martínez-Peñas , Diego Napp

The two-receiver broadcast packet erasure channel with feedback and memory is studied. Memory is modeled using a finite-state Markov chain representing a channel state. The channel state is unknown at the transmitter, but observations of…

Information Theory · Computer Science 2015-06-25 Michael Heindlmaier , Shirin Saeedi Bidokhti

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…

Information Theory · Computer Science 2022-05-20 Sivakanth Gopi , Venkatesan Guruswami

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. We study Locally Recoverable Algebraic Geometry codes arising from…

Information Theory · Computer Science 2018-06-08 Carlos Munuera , Wanderson Tenório , Fernando Torres

We construct Locally Recoverable Codes (LRCs) with availability $2$ from a family of fibered surfaces. To obtain the locality and availability properties, and to estimate the minimum distance of the codes, we combine techniques coming from…

Algebraic Geometry · Mathematics 2025-12-10 Cecília Salgado , Lara Vicino

Distributed storage systems need to store data redundantly in order to provide some fault-tolerance and guarantee system reliability. Different coding techniques have been proposed to provide the required redundancy more efficiently than…

Information Theory · Computer Science 2016-11-15 Lluis Pamies-Juarez , Henk D. L. Hollmann , Frédérique Oggier

Locally repairable codes (LRCs) are error correcting codes used in distributed data storage. Besides a global level, they enable errors to be corrected locally, reducing the need for communication between storage nodes. There is a close…

Information Theory · Computer Science 2016-05-24 Antti Pöllänen , Thomas Westerbäck , Ragnar Freij-Hollanti , Camilla Hollanti

We consider the problem of designing [n; k] linear codes for distributed storage systems (DSS) that satisfy the (r, t)-Local Repair Property, where any t'(<=t) simultaneously failed nodes can be locally repaired, each with locality r. The…

Information Theory · Computer Science 2015-07-30 Wentu Song , Chau Yuen

Motivated by distributed storage applications, we investigate the degree to which capacity achieving encodings can be efficiently updated when a single information bit changes, and the degree to which such encodings can be efficiently…

Information Theory · Computer Science 2013-10-08 Arya Mazumdar , Venkat Chandar , Gregory W. Wornell

In distributed storage systems, locally repairable codes (LRCs) are introduced to realize low disk I/O and repair cost. In order to tolerate multiple node failures, the LRCs with \emph{$(r, \delta)$-locality} are further proposed. Since hot…

Information Theory · Computer Science 2017-05-03 Bin Chen , Shu-Tao Xia , Jie Hao

Locally recoverable codes (LRCs) with locality parameter $r$ can recover any erased code symbol by accessing $r$ other code symbols. This local recovery property is of great interest in large-scale distributed classical data storage systems…

Information Theory · Computer Science 2024-11-05 Sandeep Sharma , Vinayak Ramkumar , Itzhak Tamo

Error-correcting codes that admit local decoding and correcting algorithms have been the focus of much recent research due to their numerous theoretical and practical applications. An important goal is to obtain the best possible tradeoffs…

Data Structures and Algorithms · Computer Science 2018-09-19 Jeremiah Blocki , Venkata Gandikota , Elena Grigorescu , Samson Zhou

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

Locally repairable codes(LRCs) play important roles in distributed storage systems(DSS). LRCs with small locality have their own advantages since fewer available symbols are needed in the recovery of erased symbols. In this paper, we prove…

Information Theory · Computer Science 2022-07-08 Yuan Gao , Siman Yang

A code over a finite field is called locally recoverable code (LRC) if every coordinate symbol can be determined by a small number (at most r, this parameter is called locality) of other coordinate symbols. For a linear code with length n,…

Information Theory · Computer Science 2019-10-22 Hao Chen , Jian Weng , Weiqi Luo

A code over a finite alphabet is called locally recoverable (LRC code) if every symbol in the encoding is a function of a small number (at most r) other symbols. A family of linear LRC codes that generalize the classic construction of…

Information Theory · Computer Science 2015-05-12 Alexander Barg , Itzhak Tamo , Serge Vladut