IEICE TRANSACTIONS on Fundamentals
Construction of Singleton-Type Optimal LRCs from Existing LRCs and Near-MDS Codes
Summary :
Modern large scale distributed storage systems play a central role in data center and cloud storage, while node failure in data center is common. The lost data in failure node must be recovered efficiently. Locally repairable codes (LRCs) are designed to solve this problem. The locality of an LRC is the number of nodes that participate in recovering the lost data from node failure, which characterizes the repair efficiency. An LRC is called optimal if its minimum distance attains Singleton-type upper bound [1]. In this paper, using basic techniques of linear algebra over finite field, infinite optimal LRCs over extension fields are derived from a given optimal LRC over base field(or small field). Next, this paper investigates the relation between near-MDS codes with some constraints and LRCs, further, proposes an algorithm to determine locality of dual of a given linear code. Finally, based on near-MDS codes and the proposed algorithm, those obtained optimal LRCs are shown.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E106-A No.8 pp.1051-1056
- Publication Date
- 2023/08/01
- Publicized
- 2023/01/31
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.2022EAP1107
- Type of Manuscript
- PAPER
- Category
- Coding Theory
Authors
Qiang FU
Air Force Engineering University
Buhong WANG
Air Force Engineering University
Ruihu LI
Air Force Engineering University
Ruipan YANG
Air Force Engineering University
Keyword
Latest Issue
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Qiang FU, Buhong WANG, Ruihu LI, Ruipan YANG, "Construction of Singleton-Type Optimal LRCs from Existing LRCs and Near-MDS Codes" in IEICE TRANSACTIONS on Fundamentals,
vol. E106-A, no. 8, pp. 1051-1056, August 2023, doi: 10.1587/transfun.2022EAP1107.
Abstract: Modern large scale distributed storage systems play a central role in data center and cloud storage, while node failure in data center is common. The lost data in failure node must be recovered efficiently. Locally repairable codes (LRCs) are designed to solve this problem. The locality of an LRC is the number of nodes that participate in recovering the lost data from node failure, which characterizes the repair efficiency. An LRC is called optimal if its minimum distance attains Singleton-type upper bound [1]. In this paper, using basic techniques of linear algebra over finite field, infinite optimal LRCs over extension fields are derived from a given optimal LRC over base field(or small field). Next, this paper investigates the relation between near-MDS codes with some constraints and LRCs, further, proposes an algorithm to determine locality of dual of a given linear code. Finally, based on near-MDS codes and the proposed algorithm, those obtained optimal LRCs are shown.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2022EAP1107/_p
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@ARTICLE{e106-a_8_1051,
author={Qiang FU, Buhong WANG, Ruihu LI, Ruipan YANG, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Construction of Singleton-Type Optimal LRCs from Existing LRCs and Near-MDS Codes},
year={2023},
volume={E106-A},
number={8},
pages={1051-1056},
abstract={Modern large scale distributed storage systems play a central role in data center and cloud storage, while node failure in data center is common. The lost data in failure node must be recovered efficiently. Locally repairable codes (LRCs) are designed to solve this problem. The locality of an LRC is the number of nodes that participate in recovering the lost data from node failure, which characterizes the repair efficiency. An LRC is called optimal if its minimum distance attains Singleton-type upper bound [1]. In this paper, using basic techniques of linear algebra over finite field, infinite optimal LRCs over extension fields are derived from a given optimal LRC over base field(or small field). Next, this paper investigates the relation between near-MDS codes with some constraints and LRCs, further, proposes an algorithm to determine locality of dual of a given linear code. Finally, based on near-MDS codes and the proposed algorithm, those obtained optimal LRCs are shown.},
keywords={},
doi={10.1587/transfun.2022EAP1107},
ISSN={1745-1337},
month={August},}
Copy
TY - JOUR
TI - Construction of Singleton-Type Optimal LRCs from Existing LRCs and Near-MDS Codes
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1051
EP - 1056
AU - Qiang FU
AU - Buhong WANG
AU - Ruihu LI
AU - Ruipan YANG
PY - 2023
DO - 10.1587/transfun.2022EAP1107
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E106-A
IS - 8
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - August 2023
AB - Modern large scale distributed storage systems play a central role in data center and cloud storage, while node failure in data center is common. The lost data in failure node must be recovered efficiently. Locally repairable codes (LRCs) are designed to solve this problem. The locality of an LRC is the number of nodes that participate in recovering the lost data from node failure, which characterizes the repair efficiency. An LRC is called optimal if its minimum distance attains Singleton-type upper bound [1]. In this paper, using basic techniques of linear algebra over finite field, infinite optimal LRCs over extension fields are derived from a given optimal LRC over base field(or small field). Next, this paper investigates the relation between near-MDS codes with some constraints and LRCs, further, proposes an algorithm to determine locality of dual of a given linear code. Finally, based on near-MDS codes and the proposed algorithm, those obtained optimal LRCs are shown.
ER -
English
