Hypergraph-Based Binary Locally Repairable Codes with Availability

Jung Hyun Kim, Hong Yeop Song

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Article number8000383
Pages (from-to)2332-2335
Number of pages4
JournalIEEE Communications Letters
Volume21
Issue number11
DOIs
Publication statusPublished - 2017 Nov

Fingerprint

Hypergraph
Availability
Binary
Repair
Minimum Distance
Disjoint
Equality

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Computer Science Applications
  • Electrical and Electronic Engineering

Cite this

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abstract = "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.",
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Hypergraph-Based Binary Locally Repairable Codes with Availability. / Kim, Jung Hyun; Song, Hong Yeop.

In: IEEE Communications Letters, Vol. 21, No. 11, 8000383, 11.2017, p. 2332-2335.

Research output: Contribution to journalArticle

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