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Streaming codes are a class of packet-level erasure codes that are designed with the goal of ensuring recovery in low-latency fashion, of erased packets over a communication network. It is well-known in the streaming code literature, that…

Information Theory · Computer Science 2021-09-08 Vinayak Ramkumar , Myna Vajha , P. Vijay Kumar

In this paper, we discuss codes for distributed storage systems with hierarchical repair properties. Specifically, we devote attention to the repair problem of the rack-aware storage model with locality, aiming to enhance the system's…

Information Theory · Computer Science 2024-01-30 Yumeng Yang , Han Cai , Xiaohu Tang

In this paper, locally repairable codes with all-symbol locality are studied. Methods to modify already existing codes are presented. Also, it is shown that with high probability, a random matrix with a few extra columns guaranteeing the…

Information Theory · Computer Science 2014-08-04 Toni Ernvall , Thomas Westerbäck , Camilla Hollanti

We extend the notion of locality from the Hamming metric to the rank and subspace metrics. Our main contribution is to construct a class of array codes with locality constraints in the rank metric. Our motivation for constructing such codes…

Information Theory · Computer Science 2019-05-07 Swanand Kadhe , Salim El Rouayheb , Iwan Duursma , Alex Sprintson

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

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

This paper considers data secrecy in distributed storage systems (DSSs) using maximally recoverable locally repairable codes (MR-LRCs). Conventional MR-LRCs are in general not secure against eavesdroppers who can observe the transmitted…

Information Theory · Computer Science 2024-05-13 Tim Janz , Hedongliang Liu , Rawad Bitar , Frank R. Kschischang

In this work it is shown 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 corresponding decoding radius…

Information Theory · Computer Science 2020-09-16 Lukas Holzbaur , Sven Puchinger , Antonia Wachter-Zeh

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…

Number Theory · Mathematics 2024-11-15 Jennifer Berg , Beth Malmskog , Mckenzie West

Classical locally recoverable codes (LRCs) have become indispensable in distributed storage systems. They provide efficient recovery in terms of localized errors. Quantum LRCs have very recently been introduced for their potential…

Information Theory · Computer Science 2023-12-19 Gaojun Luo , Bocong Chen , Martianus Frederic Ezerman , San Ling

This paper presents a new alphabet-dependent bound for codes with hierarchical locality. Then, the complete list of possible localities is derived for a class of codes obtained by deleting specific columns from a Simplex code. This list is…

Information Theory · Computer Science 2019-07-04 Matthias Grezet , Camilla Hollanti

Wide Locally Recoverable Codes (LRCs) have recently been proposed as a solution for achieving high reliability, good performance, and ultra-low storage cost in distributed storage systems. However, existing wide LRCs struggle to balance…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-05-19 Liangliang Xu , Fengming Tang , Tingting Chen , Qiliang Li , Min Lyu , Gennian Ge

Aiming to recover the data from several concurrent node failures, linear $r$-LRC codes with locality $r$ were extended into $(r, \delta)$-LRC codes with locality $(r, \delta)$ which can enable the local recovery of a failed node in case of…

Information Theory · Computer Science 2022-02-22 Li Xu , Zhengchun Zhou , Jun Zhang , Sihem Mesnager

In this work, we give the first construction of high-rate locally list-recoverable codes. List-recovery has been an extremely useful building block in coding theory, and our motivation is to use these codes as such a building block. In…

Information Theory · Computer Science 2017-06-13 Brett Hemenway , Noga Ron-Zewi , Mary Wootters

Maximum distance separable (MDS) are constructed to required specifications. The codes are explicitly given over finite fields with efficient encoding and decoding algorithms. Series of such codes over finite fields with ratio of distance…

Information Theory · Computer Science 2021-10-27 Ted Hurley , Donny Hurley , Barry Hurley

In recent years, locally repairable codes (LRCs) have attracted considerable attention owing to their pivotal role in distributed storage systems. Since binary linear locally repairable codes can significantly reduce the complexity of both…

Information Theory · Computer Science 2026-05-07 Hengfeng Jin , Fang-Wei Fu

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

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…

An erasure code is said to be a code with sequential recovery with parameters $r$ and $t$, if for any $s \leq t$ erased code symbols, there is an $s$-step recovery process in which at each step we recover exactly one erased code symbol by…

Information Theory · Computer Science 2018-01-23 Balaji Srinivasan Babu , Ganesh R. Kini , P. Vijay Kumar

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