New Reed-Solomon Codes with All XOR Operation for Better En/Decoding Performance

Reed-Solomon (RS) codes are widely used in storage systems to ensure data reliability. In this paper, we first propose a new construction of RS codes with between three to five parity symbols over a special finite field of size 256. We show that all the operations involved in the encoding/decoding process can be implemented by XOR and cyclic shift. Second, we present a fast encoding/decoding algorithm for our codes by designing a modified Reed-Muller (RM) transform that has both small computational complexity and space complexity. We show that our codes have much lower space complexity and nearly the same computational complexity, compared with the existing RM-based RS codes. Simulation results demonstrate that our codes improve encoding and decoding throughput by 34.06% and 31.66%, respectively, under evaluated parameters, compared with existing RM-based RS codes.