Abstract
In this paper, a new family of binary LRCs (BLRCs) with locality 2 and uneven availabilities for hot data is proposed, which has a high information symbol availability and low parity symbol availabilities for the local repair of distributed storage systems. The local repair of each information symbol for the proposed codes can be done not by accessing other information symbols but only by accessing parity symbols. The proposed BLRCs with achieve the optimality on the information length for their given code length, minimum Hamming distance, locality, and availability in terms of the well-known theoretical upper bound.
Highlights
Distributed storage systems (DSSs) which efficiently store information on several distributed nodes have been proposed [1,2]
A bound for (n, k, r, d) locally repairable codes (LRCs) was introduced [16] to take the symbol size q into account compared to the bound in Equation (1)
The explicit constructions of the family of binary LRCs (BLRCs) in earlier works [16,17] achieve the bound in Equation (2)
Summary
Distributed storage systems (DSSs) which efficiently store information on several distributed nodes have been proposed [1,2]. It is well known that traditional erasure codes, such as Reed–Solomon (RS) codes, are not optimal for DSSs, because DSSs have different performance criteria These erasure codes do not have the optimal performance in local repair, which is one of the important criteria for DSSs. Local repair refers to a repair process that reconstructs the original data of an erasure symbol (node) using a small number of other symbols. Locality refers to the number of symbols (nodes) participating in the local repair Each of these metrics is considered in DSSs for different purposes, and their fundamental bounds for optimality have not been completely determined yet. Most local repair groups of the proposed BLRCs have one information symbol and two parity symbols and we do not need to access other information symbols for the local repair of each information symbol This property is desirable for information symbols in hot data storage systems.
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