Block-Punctured Binary Simplex Codes for Local and Parallel Repair in Distributed Storage Systems

Jung-Hyun KIM  Min Kyu SONG  Hong-Yeop SONG  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E101-A   No.12   pp.2374-2381
Publication Date: 2018/12/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E101.A.2374
Type of Manuscript: Special Section PAPER (Special Section on Signal Design and Its Applications in Communications)
Category: Information Theory
distributed storage systems,  locally repairable codes,  locality,  availability,  simplex codes,  

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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.