Applications of polymatroid theory to distributed storage systems

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A4 Artikkeli konferenssijulkaisussa
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2016-04-04

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Department of Mathematics and Systems Analysis
Department of Communications and Networking

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Mcode

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en

Pages

7
231-237

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2015 53rd Annual Allerton Conference on Communication, Control, and Computing, Allerton 2015

Abstract

In this paper, a link between polymatroid theory and locally repairable codes (LRCs) is established. The codes considered here are completely general in that they are subsets of An, where A is an arbitrary finite set. Three classes of LRCs are considered, both with and without availability, and for both information-symbol and all-symbol locality. The parameters and classes of LRCs are generalized to polymatroids, and a generalized Singelton bound on the parameters for these three classes of polymatroids and LRCs is given. This result generalizes the earlier Singleton-type bounds given for LRCs. Codes achieving these bounds are coined perfect, as opposed to the more common term optimal used earlier, since they might not always exist. Finally, new constructions of perfect linear LRCs are derived from gammoids, which are a special class of matroids. Matroids, for their part, form a subclass of polymatroids and have proven useful in analyzing and constructing linear LRCs.

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DOI

10.1109/ALLERTON.2015.7447009

Citation

Westerbäck, T, Freij-Hollanti, R & Hollanti, C 2016, Applications of polymatroid theory to distributed storage systems . in 2015 53rd Annual Allerton Conference on Communication, Control, and Computing, Allerton 2015 ., 7447009, IEEE, pp. 231-237, Allerton Conference on Communication, Control, and Computing, Monticello, Illinois, United States, 29/09/2015 . https://doi.org/10.1109/ALLERTON.2015.7447009

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https://urn.fi/URN:NBN:fi:aalto-201708036359

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[article-cris] Perustieteiden korkeakoulu / SCI