Repair Locality With Multiple Erasure Tolerance

In distributed storage systems, erasure codes with locality r are preferred because a coordinate can be locally repaired 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 not be performed when some of the r coordinates are also erased. To overcome this problem, we propose the (r, delta) c-locality providing delta-1 nonoverlapping local repair groups of size no more than r for a coordinate. Consequently, the repair locality r can tolerate delta-1 erasures in total. We derive an upper bound on the minimum distance for any linear [n, k] code with information (r, delta) c-locality. Then, we prove existence of the codes that attain this bound when n = k(r(delta-1) + 1). Although the locality (r, delta) defined by Prakash et al. provides the same level of locality and local repair tolerance as our definition, codes with (r, delta) c-locality attaining the bound are proved to have more advantage in the minimum distance. In particular, we construct a class of codes with all symbol (r, delta) c-locality where the gain in minimum distance is Omega (v r) and the information rate is close to 1.