An architecture for a universal Reed-Solomon encoder using a triangular basis multiplication algorithm

Reed-Solomon (RS) codes have many practical applications. The complexity of RS encoders and decoders depends on arithmetic operations in the finite field over which the code is defined. In this paper, using a triangular basis multiplication algorithm a universal GF(2^m) multiplier is presented. The multiplier can be used for different values of m. The maximum value of m is determined by the length of the registers associated with the multiplier. The multiplier provides bit-serial and pipeline operations. Using this multiplier, an RS encoder is presented which can be used for different finite fields and variable redundancy