Triple-Fault-Tolerant Binary MDS Array Codes with Lower Encoding Complexity
Hanxu Hou, Linqi Song · 2023
In this paper, we present a new construction of maximal distance separable (MDS) array codes with three parity columns. We present an efficient encoding algorithm for our new codes and show that our new codes have lower encoding complexity than all the existing MDS codes under the same parameters. The essential reasons of obtaining lower encoding complexity for our codes are of two-folds: (i) our codes are well-designed in a cyclic polynomial ring with only cyclic shifts and XORs being involved in the operations; (ii) our codes are designed based on the efficient schedule algorithm that can minimize the number of operations in the coding procedure. Moreover, our codes can support much more parameters compared with the existing MDS array codes, such as the EVENODD codes and STAR codes. We also present an efficient decoding method for the proposed codes.