Some Constructions for Fractional Repetition Codes with Locality 2

Mi-Young NAM  Jung-Hyun KIM  Hong-Yeop SONG  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E100-A   No.4   pp.936-943
Publication Date: 2017/04/01
Online ISSN: 1745-1337
Type of Manuscript: Special Section PAPER (Special Section on Signal Design and Its Applications in Communications)
Category: Coding Theory
Keyword: 
regenerating codes,  fractional repetition codes,  locality,  locally repairable codes,  

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Summary: 
In this paper, we examine the locality property of the original Fractional Repetition (FR) codes and propose two constructions for FR codes with better locality. For this, we first derive the capacity of the FR codes with locality 2, that is the maximum size of the file that can be stored. Construction 1 generates an FR code with repetition degree 2 and locality 2. This code is optimal in the sense of achieving the capacity we derived. Construction 2 generates an FR code with repetition degree 3 and locality 2 based on 4-regular graphs with girth g. This code is also optimal in the same sense.