List Decoding of Locally Repairable Codes

Lukas Holzbaur; Antonia Wachter-Zeh

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arXiv · 1801.04229

List Decoding of Locally Repairable Codes

Lukas Holzbaur·Antonia Wachter-Zeh

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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.

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Lukas Holzbaur, Antonia Wachter-Zeh. 2018-01-12. List Decoding of Locally Repairable Codes. https://arxiv.org/abs/1801.04229

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