Repair Locality with Multiple Erasure Tolerance
Abstract
In distributed storage systems, erasure codes with locality r is preferred because a coordinate can be recovered by accessing at most r other coordinates which in turn greatly reduces the disk I/O complexity for small r. However, the local repair may be ineffective when some of the r coordinates accessed for recovery are also erased. To overcome this problem, we propose the (r,δ)c-locality providing δ -1 local repair options for a coordinate. Consequently, the repair locality r can tolerate δ-1 erasures in total. We derive an upper bound on the minimum distance d for any linear [n,k] code with information (r,δ)c-locality. For general parameters, we prove existence of the codes that attain this bound when n≥ k(r(δ-1)+1), implying tightness of this bound. Although the locality (r,δ) defined by Prakash et al provides the same level of locality and local repair tolerance as our definition, codes with (r,δ)c-locality are proved to have more advantage in the minimum distance. In particular, we construct a class of codes with all symbol (r,δ)c-locality where the gain in minimum distance is (r) and the information rate is close to 1.