Constructions of Binary MDS Array Codes With Optimal Repair/Access Bandwidth

Maximum distance separable (MDS) codes are commonly deployed in distributed storage systems as they provide the maximum failure tolerance for some given redundancy. The repair problem of MDS codes has drawn much attention and various constructions of MDS array codes with optimal repair bandwidth have been proposed in the last decade. However, few of the existing codes are constructed over the binary field. In this paper, we propose new constructions of binary MDS array codes with optimal repair (or access) bandwidth for single-node failure. Specifically, by stacking multiple Blaum-Roth code instances of which the parity-check matrices are judiciously designed, we obtain three families of binary MDS array codes with optimal repair bandwidth; using the permutation matrices as building blocks, we also construct two families of binary MDS array codes with optimal access bandwidth. Moreover, error-resilient capability while achieving the lower bound on repair (or access) bandwidth is obtained when the number of helper nodes
$d < n-1$
. All the codes in this paper are constructed over a particular ring of binary polynomials. Consequently, computation operations involved in the encoding, decoding and node repair procedures for these codes are only XORs and cyclic shifts, avoiding complex multiplications and divisions over large finite fields.