Multiple Repair Localities with Distinct Erasure Tolerance
Jiyong Lu, Jun Zhang, Xuan Guang, Fang‐Wei Fu · International Journal of Foundations of Computer Science · 2016
In distributed storage systems, codes with lower repair locality for each coordinate are much more desirable since they can reduce the disk I/O complexity for repairing a failed node. The ith coordinate of a linear code 𝒞 is said to have [Formula: see text] locality if there exist δi non-overlapping local repair sets of size no more than ri, where a local repair set of one coordinate is defined as the set of some other coordinates by which one can recover the value at this coordinate. In this paper, we consider linear codes with information [Formula: see text] locality, where there exists an information set I such that for each [Formula: see text], the ith coordinate has [Formula: see text] locality and [Formula: see text] and [Formula: see text]. We derive a lower bound on the codeword length n for any linear [n, k, d] code with information [Formula: see text] locality. Particularly, we indicate that some existing bounds can be deduced from our result by restrictions on parameters.