The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Dans cet article, nous étudions comment obtenir des codes binaires réparables localement (LRC) avec une bonne localité et une bonne disponibilité à partir de codes binaires Simplex. Nous proposons dans un premier temps un code Combinaison ayant la matrice génératrice avec toutes les colonnes de poids positifs inférieurs ou égaux à une valeur donnée. Un tel code peut également être obtenu en perforant toutes les colonnes de poids supérieurs à une valeur donnée à partir d'un code simplex binaire. Nous appelons par block-punching une telle méthode de ponction. De plus, nous suggérons une méthode de perforation heuristique, appelée perforation de sous-blocs, qui perce quelques colonnes supplémentaires de poids le plus élevé du code combiné. Nous déterminons la distance minimale, la localité, la disponibilité, la localité commune des informations, la disponibilité commune des informations des codes combinés sous forme fermée. Nous démontrons également l'optimalité des codes proposés avec certains choix de paramètres en fonction de certaines bornes bien connues.
Jung-Hyun KIM
Samsung Electronics
Min Kyu SONG
Yonsei University
Hong-Yeop SONG
Yonsei University
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Jung-Hyun KIM, Min Kyu SONG, Hong-Yeop SONG, "Block-Punctured Binary Simplex Codes for Local and Parallel Repair in Distributed Storage Systems" in IEICE TRANSACTIONS on Fundamentals,
vol. E101-A, no. 12, pp. 2374-2381, December 2018, doi: 10.1587/transfun.E101.A.2374.
Abstract: In this paper, we investigate how to obtain binary locally repairable codes (LRCs) with good locality and availability from binary Simplex codes. We first propose a Combination code having the generator matrix with all the columns of positive weights less than or equal to a given value. Such a code can be also obtained by puncturing all the columns of weights larger than a given value from a binary Simplex Code. We call by block-puncturing such puncturing method. Furthermore, we suggest a heuristic puncturing method, called subblock-puncturing, that punctures a few more columns of the largest weight from the Combination code. We determine the minimum distance, locality, availability, joint information locality, joint information availability of Combination codes in closed-form. We also demonstrate the optimality of the proposed codes with certain choices of parameters in terms of some well-known bounds.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E101.A.2374/_p
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@ARTICLE{e101-a_12_2374,
author={Jung-Hyun KIM, Min Kyu SONG, Hong-Yeop SONG, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Block-Punctured Binary Simplex Codes for Local and Parallel Repair in Distributed Storage Systems},
year={2018},
volume={E101-A},
number={12},
pages={2374-2381},
abstract={In this paper, we investigate how to obtain binary locally repairable codes (LRCs) with good locality and availability from binary Simplex codes. We first propose a Combination code having the generator matrix with all the columns of positive weights less than or equal to a given value. Such a code can be also obtained by puncturing all the columns of weights larger than a given value from a binary Simplex Code. We call by block-puncturing such puncturing method. Furthermore, we suggest a heuristic puncturing method, called subblock-puncturing, that punctures a few more columns of the largest weight from the Combination code. We determine the minimum distance, locality, availability, joint information locality, joint information availability of Combination codes in closed-form. We also demonstrate the optimality of the proposed codes with certain choices of parameters in terms of some well-known bounds.},
keywords={},
doi={10.1587/transfun.E101.A.2374},
ISSN={1745-1337},
month={December},}
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TY - JOUR
TI - Block-Punctured Binary Simplex Codes for Local and Parallel Repair in Distributed Storage Systems
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2374
EP - 2381
AU - Jung-Hyun KIM
AU - Min Kyu SONG
AU - Hong-Yeop SONG
PY - 2018
DO - 10.1587/transfun.E101.A.2374
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E101-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2018
AB - In this paper, we investigate how to obtain binary locally repairable codes (LRCs) with good locality and availability from binary Simplex codes. We first propose a Combination code having the generator matrix with all the columns of positive weights less than or equal to a given value. Such a code can be also obtained by puncturing all the columns of weights larger than a given value from a binary Simplex Code. We call by block-puncturing such puncturing method. Furthermore, we suggest a heuristic puncturing method, called subblock-puncturing, that punctures a few more columns of the largest weight from the Combination code. We determine the minimum distance, locality, availability, joint information locality, joint information availability of Combination codes in closed-form. We also demonstrate the optimality of the proposed codes with certain choices of parameters in terms of some well-known bounds.
ER -