Side Encoding for MDS Array Codes.

This paper considers the parity-check matrix of a maximum distance separable (MDS) array code as a superposition of two matrices, block diagonal matrix A and side matrix S. By matching their entries, the syndrome calculation of the matrix A can share computations with that of the side matrix S. Then, a low-complexity encoding, referred to as side encoding, is proposed to encode matched MDS array codes efficiently. Moreover, it can combine with the Reed-Muller transform-based (RMTB) Reed-Solomon encoding algorithm to reduce the encoding complexity further. The analysis indicates that for the MDS array code [1] with four parity nodes, the number of multiplications is reduced by 85.4% and 52.6% compared to the traditional encoding and only RMTB encoding, respectively.