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.
| Original language | English |
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| Title of host publication | 2015 53rd Annual Allerton Conference on Communication, Control, and Computing, Allerton 2015 |
| Publisher | IEEE |
| Pages | 231-237 |
| Number of pages | 7 |
| ISBN (Electronic) | 978-1-5090-1824-6 |
| ISBN (Print) | 9781509018239 |
| DOIs | |
| Publication status | Published - 4 Apr 2016 |
| MoE publication type | A4 Article in a conference publication |
| Event | Allerton Conference on Communication, Control, and Computing - Monticello, United States Duration: 29 Sept 2015 → 2 Oct 2015 Conference number: 53 |
Conference
| Conference | Allerton Conference on Communication, Control, and Computing |
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| Abbreviated title | Allerton |
| Country/Territory | United States |
| City | Monticello |
| Period | 29/09/2015 → 02/10/2015 |