Rs Decoder For Edcme Algorithm-based Ip Core Design

As a maximum distance separate code, RS code can efficiently correct burst errors as well as random errors. RS code has been widely used in various communication and digital storage systems.The most important part in the RS decoder is the key equation solver.In this paper, we make research on the EDCME algorithm. In the ME algorithm, there are degree computation and degree comparation circuits.There are no degree computation and degree comparation circuits in the EDCME algorithm, so we can reduce the complexity of the key equation solver to a great extent. The EDCME algorithm needs 2t-1 clock cycles to slove the key equation.This time is far less than 3t+37 of the ME algorithm, so the delay of the decoder is shorter and the decoding speed is faster.Among the three stages of pipeline in the RS decoder,the processing delay of the first and the third pipeline is N clock cycles. The processing delay of the second pipeline is 2t-1,which is far less than N.When decoding continuously,the second pipeline is idle most of the time,thus the circuits can not be fully used.In this paper,we proposed a new method to minimize the circuits to solve the key equation.This method can reduce resources,and will not reduce the throughput of the decoder.In practice,we need shortened and punctured RS codes.The algorithm to decode the shortened RS code is the same as the commonly used RS decoder. In this paper, we modified the EDCME algorithm, so it can also be used to decode the punctured RS code.Finally, we realized three types of RS decoder on the FPGA, the commonly used RS decoder, RS decoder for the shortened RS code and RS decoder for the punctured RS code. We tested them in software environment and hardware environment.In the end, we analysed the performance of the RS decoders.In testing, we found that the EDCME algorithm does not consider the situation when the leading coefficient of the syndrome polynomial is zero, so we modified it.