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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
Publication Date: 2018/12/01
Online ISSN: 1745-1337
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.