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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

Locally repairable codes (LRCs) have recently been widely used in distributed storage systems and the LRCs with $(r,\delta)$-locality ($(r,\delta)$-LRCs) attracted a lot of interest for tolerating multiple erasures. Ge et al. constructed…

Information Theory · Computer Science 2023-04-28 Yaxin Wang , Siman Yang

Locally recoverable (LRC) codes have recently been a focus point of research in coding theory due to their theoretical appeal and applications in distributed storage systems. In an LRC code, any erased symbol of a codeword can be recovered…

Information Theory · Computer Science 2018-05-16 Abhishek Agarwal , Alexander Barg , Sihuang Hu , Arya Mazumdar , Itzhak Tamo

Recent studies have delved into the construction of locally repairable codes (LRCs) with optimal minimum distance from function fields. In this paper, we present several novel constructions by extending the findings of optimally designed…

Information Theory · Computer Science 2025-02-03 Yunlong Zhu , Chang-An Zhao

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 is called a $q$-query locally decodable code (LDC) if there is a randomized decoding algorithm that, given an index $i$ and a received word $w$ close to an encoding of a message $x$, outputs $x_i$ by querying only at most $q$…

Computational Complexity · Computer Science 2019-12-03 Arnab Bhattacharyya , L. Sunil Chandran , Suprovat Ghoshal

In this work we propose RELDEC, a novel approach for sequential decoding of moderate length low-density parity-check (LDPC) codes. The main idea behind RELDEC is that an optimized decoding policy is subsequently obtained via reinforcement…

Information Theory · Computer Science 2023-07-28 Salman Habib , Allison Beemer , Joerg Kliewer

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

A locally testable code (LTC) is an error correcting code with a property tester. The tester tests if a word is codeword by reading constant random bits and rejects the word with probability proportional to the distance from the word to the…

Information Theory · Computer Science 2022-01-31 Ting-Chun Lin , Min-Hsiu Hsieh

Locally repairable codes (LRCs) have emerged as an important coding scheme in distributed storage systems (DSSs) with relatively low repair cost by accessing fewer non-failure nodes. Theoretical bounds and optimal constructions of LRCs have…

Information Theory · Computer Science 2023-03-14 Weijun Fang , Fang-Wei Fu , Bin Chen , Shu-Tao Xia

Classical locally recoverable codes, which permit highly efficient recovery from localized errors as well as global recovery from larger errors, provide some of the most useful codes for distributed data storage in practice. In this paper,…

Quantum Physics · Physics 2023-11-16 Louis Golowich , Venkatesan Guruswami

Locally recoverable codes (LRCs) are classical error-correcting codes widely used in large scale distributed and cloud storage systems. Quantum locally recoverable codes (quantum LRCs) are the quantum counterpart of classical LRCs. They…

Information Theory · Computer Science 2025-08-06 Carlos Galindo , Fernando Hernando , Carlos Munuera , Diego Ruano

In a digital communication system, information is sent from one place to another over a noisy communication channel. It may be possible to detect and correct errors that occur during the transmission if one encodes the original information…

Information Theory · Computer Science 2017-08-21 Banu Kabakulak , Z. Caner Taşkın , Ali Emre Pusane

We show that locally repairable codes (LRCs) can be list decoded efficiently beyond the Johnson radius for a large range of parameters by utilizing the local error correction capabilities. The new decoding radius is derived and the…

Information Theory · Computer Science 2018-05-09 Lukas Holzbaur , Antonia Wachter-Zeh

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

A locally recoverable (LRC) code is a code over a finite field $\mathbb{F}_q$ such that any erased coordinate of a codeword can be recovered from a small number of other coordinates in that codeword. We construct LRC codes correcting more…

Information Theory · Computer Science 2024-05-01 Carlos Galindo , Fernando Hernando , Carlos Munuera

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…

Information Theory · Computer Science 2016-07-29 Abhishek Agarwal , Arya Mazumdar

We prove that 3-query linear locally correctable codes over the Reals of dimension $d$ require block length $n>d^{2+\lambda}$ for some fixed, positive $\lambda >0$. Geometrically, this means that if $n$ vectors in $R^d$ are such that each…

Computational Complexity · Computer Science 2013-11-21 Zeev Dvir , Shubhangi Saraf , Avi Wigderson

A linear block code with dimension $k$, length $n$, and minimum distance $d$ is called a locally repairable code (LRC) with locality $r$ if it can retrieve any coded symbol by at most $r$ other coded symbols. LRCs have been recently…

Information Theory · Computer Science 2017-01-25 Mostafa Shahabinejad , Majid Khabbazian , Masoud Ardakani

For a systematic erasure code, update complexity (UC) is defined as the maximum number of parity blocks needed to be changed when some information blocks are updated. Locally repairable codes (LRCs) have been recently proposed and used in…

Information Theory · Computer Science 2016-07-18 Mehrtash Mehrabi , Mostafa Shahabinejad , Masoud Ardakani , Majid Khabbazian