Low complexity Reed-Solomon encoder using globally optimized finite field multipliers

This paper proposes a new approach to implement a low complexity Reed-Solomon (RS) encoder of DTV systems. Based on a reported optimization algorithm which yields low complexity constant finite field multipliers for Galois fields GF(2ⁿ), the new compact RS encoder is constructed with 15 optimized finite field multipliers, of which the redundant operations are reduced to minimize the number of modulo 2 additions or XOR gates. Hence the 15 multipliers partly share the same hardware operations. A significant improvement on complexity is clearly shown with FPGA implementation.