Locally Repairable Convolutional Codes With Sliding Window Repair

Please use this identifier to cite or link to this item: http://hdl.handle.net/10045/108411
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Title: Locally Repairable Convolutional Codes With Sliding Window Repair
Authors: Martínez-Peñas, Umberto | Napp, Diego
Research Group/s: Grupo de Álgebra y Geometría (GAG)
Center, Department or Service: Universidad de Alicante. Departamento de Matemáticas
Keywords: Convolutional codes | Distributed storage | Locally repairable codes | Locally repairable convolutional codes | Sliding-window repair | Sum-rank metric
Knowledge Area: Álgebra
Issue Date: Aug-2020
Publisher: IEEE
Citation: IEEE Transactions on Information Theory. 2020, 66(8): 4935-4947. https://doi.org/10.1109/TIT.2020.2977638
Abstract: 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, ∂−1 erasures per local group), and sliding-window global repair, which can correct erasure patterns with up to dcj−1 erasures in every window of j+1 consecutive blocks of n nodes, where dcj−1 is the j th column distance of the code. The parameter j can be adjusted, for a fixed LRCC, according to different catastrophic erasure patterns, requiring only to contact n(j+1)−dcj+1 nodes, plus less than μn other nodes, in the storage system, where μ is the memory of the code. A Singleton-type bound is provided for dcj−1 . If it attains such a bound, an LRCC can correct the same number of catastrophic erasures in a window of length n(j+1) as an optimal locally repairable block code of the same rate and locality, and with block length n(j+1) . In addition, the LRCC is able to perform the flexible and somehow local sliding-window repair by adjusting j . Furthermore, by adjusting and/or sliding the window, the LRCC can potentially correct more erasures in the original window of n(j+1) nodes than an optimal locally repairable block code of the same rate and locality, and length n(j+1) . Finally, the concept of partial maximum distance profile (partial MDP) codes is introduced. Partial MDP codes can correct all information-theoretically correctable erasure patterns for a given locality, local distance and information rate. An explicit construction of partial MDP codes whose column distances attain the provided Singleton-type bound, up to certain parameter j=L , is obtained based on known maximum sum-rank distance convolutional codes.
Sponsor: This work was supported in part by the Independent Research Fund Denmark under Grant DFF-7027-00053B, in part by the Generalitat Valenciana under Grant AICO/2017/128, and in part by the Universitat d’Alacant under Grant VIGROB-287.
URI: http://hdl.handle.net/10045/108411
ISSN: 0018-9448 (Print) | 1557-9654 (Online)
DOI: 10.1109/TIT.2020.2977638
Language: eng
Type: info:eu-repo/semantics/article
Rights: © 2020 IEEE
Peer Review: si
Publisher version: https://doi.org/10.1109/TIT.2020.2977638
Appears in Collections:INV - GAG - Artículos de Revistas

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