Codes With Hierarchical Locality
arXiv:1501.06683
Abstract
In this paper, we study the notion of {\em codes with hierarchical locality} that is identified as another approach to local recovery from multiple erasures. The well-known class of {\em codes with locality} is said to possess hierarchical locality with a single level. In a {\em code with two-level hierarchical locality}, every symbol is protected by an inner-most local code, and another middle-level code of larger dimension containing the local code. We first consider codes with two levels of hierarchical locality, derive an upper bound on the minimum distance, and provide optimal code constructions of low field-size under certain parameter sets. Subsequently, we generalize both the bound and the constructions to hierarchical locality of arbitrary levels.
12 pages, submitted to ISIT 2015
References in corpus (7)
- A family of optimal locally recoverable codes
- Repair Locality with Multiple Erasure Tolerance
- Locally Repairable Codes with Multiple Repair Alternatives
- Binary Cyclic Codes that are Locally Repairable
- Optimal Locally Repairable Codes via Rank-Metric Codes
- Codes with Locality for Two Erasures
- An Integer Programming Based Bound for Locally Repairable Codes
Cited by in corpus (4)
- Erasure Coding for Distributed Storage: An Overview
- A Study on the Impact of Locality in the Decoding of Binary Cyclic Codes
- A Tight Rate Bound and Matching Construction for Locally Recoverable Codes with Sequential Recovery From Any Number of Multiple Erasures
- Locality and Availability of Array Codes Constructed from Subspaces