Applications of polymatroid theory to distributed storage systems

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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.

Original languageEnglish
Title of host publication2015 53rd Annual Allerton Conference on Communication, Control, and Computing, Allerton 2015
Number of pages7
ISBN (Electronic)978-1-5090-1824-6
ISBN (Print)9781509018239
Publication statusPublished - 4 Apr 2016
MoE publication typeA4 Article in a conference publication
EventAllerton Conference on Communication, Control, and Computing - Monticello, United States
Duration: 29 Sept 20152 Oct 2015
Conference number: 53


ConferenceAllerton Conference on Communication, Control, and Computing
Abbreviated titleAllerton
Country/TerritoryUnited States


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