| This thesis introduces and implements a Reed-Solomon (RS) code simulator to study a wide range of RS codes. The simulator first encodes the user's message into a codeword. The user can choose the symbol length m from 3 bits up to 8 bits or the block length N from 7 symbols up to 255 symbols, and the error correcting capability T of up to 16 random errored symbols. Then the user enters an error pattern of arbitrary weight which the simulator adds to the generated codeword. The resulting received word is then decoded. Only the Chien search is used as a root search technique for the error locator polynomial. This simulator does not handle erasures.Commonly, Chien search is used to find out all the possible roots of the error locator polynomial. It is found that for the double error correcting case (T = 2) these roots are not randomly distributed but they follow certain patterns. Based on these patterns, the periodicity algorithm is introduced and its validity is verified by exhaustive computer simulations.It is concluded that the periodicity algorithm is the optimal solution for both decoding time and memory space. This algorithm is found to be very suitable for use in microprocessor based decoders. (Abstract shortened by UMI.)... |
