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Hypergraph-Based Binary Locally Repairable Codes With Availability
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DOI：10.1109/LCOMM.2017.2730183.png)
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Abstract
En 中文
We study a hypergraph-based code construction for binary locally repairable codes (LRCs) with availability. A symbol of a code is said to have (r, t)-availability if it can be recovered from t disjoint repair sets of other symbols, each set of size at most r. We refer a systematic code to an LRC with (r, t)(i)-availability if its information symbols have (r, t)-availability and a code to an LRC with (r, t)(a)-availability if its all symbols have (r, t)-availability. We construct binary LRCs with (r, t)(i)-availability from linear r-uniform t-regular hypergraphs. As a special case, we also construct binary LRCs with (r, t)(a)-availability from labeled linear r-uniform t-regular hypergraphs. Moreover, we extend the hypergraph-based codes to increase the minimum distance. All the proposed codes achieve a well-known Singleton-like bound with equality.
Keywords:
Distributed storage systems
locally repairable codes
hypergraphs
graph-based codes
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