RS (255, 249) Codec Based on All Primitive Polynomials Over GF($$2^8$$)

Abstract

Reed–Solomon (RS) codes are generally employed to detect and correct errors in digital transmission and storage systems. The primitive polynomial has a great role to design any RS codes. In this chapter, a RS (255, 249) codec has been designed and implemented based on sixteen primitive polynomials over GF(\(2^8\)) field. The details of theoretical and FPGA synthesis results of the RS (255, 249) codec are presented here. The area in terms of lookup tables and delay of RS (255, 249) codec have been observed for sixteen primitive polynomials. The RS (255, 249) codec based on primitive polynomial, PP3 = \(x^{8} +x^{5} +x^{3} +x^{2} +1\), has consumed lowest area compared to all other primitive polynomials. This codec architecture can be employed in M-ary phase-shift keying modulation scheme and ultra-wideband application.