Bounds and Constructions of Codes with Multiple Localities
Information Theory
2016-01-13 v1 Discrete Mathematics
Networking and Internet Architecture
Combinatorics
math.IT
Abstract
This paper studies bounds and constructions of locally repairable codes (LRCs) with multiple localities so-called multiple-locality LRCs (ML-LRCs). In the simplest case of two localities some code symbols of an ML-LRC have a certain locality while the remaining code symbols have another one. We extend two bounds, the Singleton and the alphabet-dependent upper bound on the dimension of Cadambe--Mazumdar for LRCs, to the case of ML-LRCs with more than two localities. Furthermore, we construct Singleton-optimal ML-LRCs as well as codes that achieve the extended alphabet-dependent bound. We give a family of binary ML-LRCs based on generalized code concatenation that is optimal with respect to the alphabet-dependent bound.
Cite
@article{arxiv.1601.02763,
title = {Bounds and Constructions of Codes with Multiple Localities},
author = {Alexander Zeh and Eitan Yaakobi},
journal= {arXiv preprint arXiv:1601.02763},
year = {2016}
}