A Low Power Error Detection in the Syndrome Calculator Block for Reed-Solomon Codes: RS(204,188)

Reed-Solomon (RS) codes have been widely adopted in many modern communication systems. This paper describes a new method for error detection in the syndrome calculator block of RS decoders. The main feature of this method is to prove that it is possible to compute only a few syndrome coefficients — less than half — to detect whether the codeword is correct. The theoretical estimate of the probability that the new algorithm failed is shown to depend on the number of syndrome coefficients computed. The algorithm is tested using the RS(204,188) code with the first four coefficients. With a bit error rate of 1×10^-4, this method reduces the power consumption by 6% compared to the basic RS(204,188) decoder. The error detection algorithm for the syndrome calculator block does not require modification of the basic hardware implementation of the syndrome coefficients computation. The algorithm significantly reduces the computation complexity of the syndrome calculator block, thus lowering the power needed.