In this letter, we investigate a class of codes with the following property: any decodable set of erased symbols can be repaired from any single set of several disjoint symbol sets with small cardinality. We refer such codes to locally repairable codes (LRCs) with joint availability. In particular, if information symbols of a code have this property, then we refer the code to an LRC with joint information availability. We propose two alphabet-dependent bounds for LRCs with joint information availability. From the bounds, we rederive some well-known bounds for LRCs. Based on the relation between LRCs and batch codes, we also present an alternative proof of an existing bound for batch codes. Finally, we show the achievability and tightness of the proposed bounds using graph-based codes.
Bibliographical noteFunding Information:
Manuscript received March 8, 2017; revised April 10, 2017; accepted April 25, 2017. Date of publication April 27, 2017; date of current version August 10, 2017. This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (No. 2013R1A1A2062061). The associate editor coordinating the review of this letter and approving it for publication was J. Li. (Corresponding author: Hong-Yeop Song.) The authors are with the Department of Electrical and Electronic Engineering, Yonsei University, Seoul 120-749, South Korea (e-mail: firstname.lastname@example.org). Digital Object Identifier 10.1109/LCOMM.2017.2699968
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All Science Journal Classification (ASJC) codes
- Modelling and Simulation
- Computer Science Applications
- Electrical and Electronic Engineering