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

作者：Hou, Hanxu^*; Han, Yunghsiang S.

来源：Science China Information Sciences, 2018, 61(10): 100302.

DOI：10.1007/s11432-018-9485-7

• MDS codes
• binary MDS array codes
• optimal repair
• encoding matrix
• asymptotically weak-optimal repair

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 a (c) 3/4 3 and r a (c) 3/4 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.

• 出版日期2018-10
• 单位东莞理工学院