A class of binary MDS array codes with asymptotically weak-optimal repair

摘要

Binary maximum distance separable（MDS） array codes contain k information columns and r parity columns in which each entry is a bit that can tolerate r arbitrary erasures. When a column in an MDS code fails, it has been proven that we must download at least half of the content from each helper column if k + 1 columns are selected as the helper columns. If the lower bound is achieved such that the k + 1 helper columns can be selected from any k + r-1 surviving columns, then the repair is an optimal repair.Otherwise, if the lower bound is achieved with k + 1 specific helper columns, the repair is a weak-optimal repair. This paper proposes a class of binary MDS array codes with k 3 and r 2 that asymptotically achieve weak-optimal repair of an information column with k + 1 helper columns. We show that there exist many encoding matrices such that the corresponding binary MDS array codes can asymptotically achieve weak-optimal repair for repairing any information column.