On the erasure recoverability of MDS codes under concurrent updates

We consider a fault-tolerant distributed storage system that protects data on k disks using a systematic linear (n, k) MDS code. In such a system, updates to data blocks require corresponding updates to check blocks. Concurrent fault-prone access by multiple writers can drive the system into an inconsistent state with reduced tolerance for disk failures. We show tight bounds on the erasure recoverability of an (n, k) MDS code in this scenario. The bounds depend not just on the minimum distance of the code, but also on the maximum number of concurrent faulty writers and the manner in which they attempt to update the check blocks (one at a time/all at once.)