Bounds on the maximal minimum distance of linear locally repairable codes
Loading...
Access rights
openAccess
URL
Journal Title
Journal ISSN
Volume Title
A4 Artikkeli konferenssijulkaisussa
This publication is imported from Aalto University research portal.
View publication in the Research portal (opens in new window)
View/Open full text file from the Research portal (opens in new window)
Other link related to publication (opens in new window)
View publication in the Research portal (opens in new window)
View/Open full text file from the Research portal (opens in new window)
Other link related to publication (opens in new window)
Date
2016-08-10
Major/Subject
Mcode
Degree programme
Language
en
Pages
5
1586-1590
1586-1590
Series
Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory, Volume 2016-August, IEEE International Symposium on Information Theory
Abstract
Locally repairable codes (LRCs) are error correcting codes used in distributed data storage. Besides a global level, they enable errors to be corrected locally, reducing the need for communication between storage nodes. There is a close connection between almost affine LRCs and matroid theory which can be utilized to construct good LRCs and derive bounds on their performance. A generalized Singleton bound for linear LRCs with parameters (n; k; d; r; δ) was given in [N. Prakash et al., 'Optimal Linear Codes with a Local-Error-Correction Property', IEEE Int. Symp. Inf. Theory]. In this paper, a LRC achieving this bound is called perfect. Results on the existence and nonexistence of linear perfect (n; k; d; r; δ)-LRCs were given in [W. Song et al., 'Optimal locally repairable codes', IEEE J. Sel. Areas Comm.]. Using matroid theory, these existence and nonexistence results were later strengthened in [T. Westerbäck et al., 'On the Combinatorics of Locally Repairable Codes', Arxiv: 1501.00153], which also provided a general lower bound on the maximal achievable minimum distance dmax(n; k; r; δ) that a linear LRC with parameters (n; k; r; δ) can have. This article expands the class of parameters (n; k; d; r; δ) for which there exist perfect linear LRCs and improves the lower bound for dmax(n; k; r; δ). Further, this bound is proved to be optimal for the class of matroids that is used to derive the existence bounds of linear LRCs.Description
Keywords
Other note
Citation
Pöllänen, A, Westerbäck, T, Freij-Hollanti, R & Hollanti, C 2016, Bounds on the maximal minimum distance of linear locally repairable codes . in Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory . vol. 2016-August, 7541566, IEEE International Symposium on Information Theory, IEEE, pp. 1586-1590, IEEE International Symposium on Information Theory, Barcelona, Spain, 10/07/2016 . https://doi.org/10.1109/ISIT.2016.7541566