List Decoding of Locally Repairable Codes
Information Theory
2018-05-09 v2 math.IT
Abstract
We show that locally repairable codes (LRCs) can be list decoded efficiently beyond the Johnson radius for a large range of parameters by utilizing the local error correction capabilities. The new decoding radius is derived and the asymptotic behavior is analyzed. We give a general list decoding algorithm for LRCs that achieves this radius along with an explicit realization for a class of LRCs based on Reed-Solomon codes (Tamo-Barg LRCs). Further, a probabilistic algorithm for unique decoding of low complexity is given and its success probability analyzed.
Cite
@article{arxiv.1801.04229,
title = {List Decoding of Locally Repairable Codes},
author = {Lukas Holzbaur and Antonia Wachter-Zeh},
journal= {arXiv preprint arXiv:1801.04229},
year = {2018}
}