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Related papers: Erasure codes with simplex locality

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Optimal locally repairable codes with information locality are considered. Optimal codes are constructed, whose length is also order-optimal with respect to a new bound on the code length derived in this paper. The length of the constructed…

Information Theory · Computer Science 2020-02-07 Han Cai , Moshe Schwartz

We consider locally repairable codes over small fields and propose constructions of optimal cyclic and linear codes in terms of the dimension for a given distance and length. Four new constructions of optimal linear codes over small fields…

Information Theory · Computer Science 2016-11-17 Alexander Zeh , Eitan Yaakobi

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

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

In this paper, we study the notion of {\em codes with hierarchical locality} that is identified as another approach to local recovery from multiple erasures. The well-known class of {\em codes with locality} is said to possess hierarchical…

Information Theory · Computer Science 2015-01-28 Birenjith Sasidharan , Gaurav Kumar Agarwal , P. Vijay Kumar

In coding for distributed storage systems, efficient data reconstruction and repair through accessing a predefined number of arbitrarily chosen storage nodes is guaranteed by regenerating codes. Traditionally, code parameters, specially the…

Information Theory · Computer Science 2018-01-01 Kaveh Mahdaviani , Soheil Mohajer , Ashish Khisti

In this paper we extend the notion of {\em locally repairable} codes to {\em secret sharing} schemes. The main problem that we consider is to find optimal ways to distribute shares of a secret among a set of storage-nodes (participants)…

Information Theory · Computer Science 2016-08-15 Abhishek Agarwal , Arya Mazumdar

In this paper, we study codes with locality that can recover from two erasures via a sequence of two local, parity-check computations. By a local parity-check computation, we mean recovery via a single parity-check equation associated to…

Information Theory · Computer Science 2014-01-28 N. Prakash , V. Lalitha , P. Vijay Kumar

Linear erasure codes with local repairability are desirable for distributed data storage systems. An [n, k, d] code having all-symbol (r, \delta})-locality, denoted as (r, {\delta})a, is considered optimal if it also meets the minimum…

Information Theory · Computer Science 2013-07-09 Wentu Song , Son Hoang Dau , Chau Yuen , Tiffany Jing Li

We present simple constructions of optimal erasure-correcting LRC codes by exhibiting their parity-check matrices. When the number of local parities in a parity group plus the number of global parities is smaller than the size of the parity…

Information Theory · Computer Science 2015-12-22 Mario Blaum

Consider a distributed coding for computing problem with constant decoding locality, i.e., with a vanishing error probability, any single sample of the function can be approximately recovered by probing only constant number of compressed…

Information Theory · Computer Science 2024-03-01 Deheng Yuan , Tao Guo , Zhongyi Huang , Shi Jin

We consider the problem of erasure/list decoding using certain classes of simplified decoders. Specifically, we assume a class of erasure/list decoders, such that a codeword is in the list if its likelihood is larger than a threshold. This…

Information Theory · Computer Science 2016-11-17 Nir Weinberger , Neri Merhav

In recent years, several classes of codes are introduced to provide some fault-tolerance and guarantee system reliability in distributed storage systems, among which locally repairable codes (LRCs for short) play an important role. However,…

Information Theory · Computer Science 2017-11-21 Jingxue Ma , Gennian Ge

Erasure correcting codes are widely used to ensure data persistence in distributed storage systems. This paper addresses the simultaneous repair of multiple failures in such codes. We go beyond existing work (i.e., regenerating codes by…

Information Theory · Computer Science 2013-09-18 Anne-Marie Kermarrec , Gilles Straub , Nicolas Le Scouarnec

In this paper, the repair problem for erasures beyond locality in locally repairable codes is explored under a practical system setting, where a rack-aware storage system consists of racks, each containing a few parity checks. This is…

Information Theory · Computer Science 2024-07-29 Han Cai , Ying Miao , Moshe Schwartz , Xiaohu Tang

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

Distributed storage systems for large clusters typically use replication to provide reliability. Recently, erasure codes have been used to reduce the large storage overhead of three-replicated systems. Reed-Solomon codes are the standard…

This thesis makes several significant contributions to the theory of both Regenerating (RG) and Locally Recoverable (LR) codes. The two principal contributions are characterizing the optimal rate of an LR code designed to recover from $t$…

Information Theory · Computer Science 2018-06-13 S. B. Balaji , P. Vijay Kumar

In distributed storage systems that employ erasure coding, the issue of minimizing the total {\it repair bandwidth} required to exactly regenerate a storage node after a failure arises. This repair bandwidth depends on the structure of the…

Information Theory · Computer Science 2011-06-10 Dimitris S. Papailiopoulos , Alexandros G. Dimakis

We investigate adaptive single-trial error/erasure decoding of binary codes whose decoder is able to correct e errors and t erasures if le+t<=d-1. Thereby, d is the minimum Hamming distance of the code and 1<l<=2 is the tradeoff parameter…

Information Theory · Computer Science 2010-05-03 Christian Senger , Vladimir R. Sidorenko , Steffen Schober , Martin Bossert , Victor V. Zyablov