A New Design of Binary MDS Array Codes with Asymptotically Weak-Optimal Repair
share
Binary maximum distance separable (MDS) array codes are a special class of erasure codes for distributed storage that not only provide fault tolerance with minimum storage redundancy but also achieve low computational complexity. They are constructed by encoding k information columns into r parity columns, in which each element in a column is a bit, such that any k out of the k+r columns suffice to recover all information bits. In addition to providing fault tolerance, it is critical to improve repair performance in practical applications. If one column of an MDS code is failed, it is known that we need to download at least 1/(d-k+1) fraction of the data stored in each of d healthy columns. If this lower bound is achieved for the repair of the failure column from accessing arbitrary d healthy columns, we say that the MDS code has optimal repair. However, if such lower bound is only achieved by d specific healthy columns, then we say the MDS code has weak-optimal repair. Existing binary MDS array codes that achieve high data rate (i.e., k/(k+r)>1/2) and optimal repair of information column only support double fault tolerance (i.e., r=2), which is insufficient for failure-prone distributed storage environments in practice. This paper fills the void by proposing two explicit constructions of binary MDS array codes with more parity columns (i.e., r≥ 3) that achieve asymptotically weak-optimal repair, where k+1≤ d≤ k+(r-1)/2. Codes in the first construction have odd number of parity columns and asymptotically weak-optimal repair for any one information failure, while codes in the second construction have even number of parity columns and asymptotically weak-optimal repair for any one column failure.
READ FULL TEXT