A recursive method for calculating error probabilities for a Reed-Solomon codeword

A single Reed-Solomon (RS) codeword is transmitted in a channel where each transmitted symbol may experience a different interference level. Each received symbol is decoded using a hard decision mechanism, and the entire codeword is decoded using a bounded-distance (BD) decoder. Due to complexity and speed concerns, it is common practice to assume the probability of incorrect codeword decoding is negligible, and assume the decoder either correctly decodes the received codeword or fails the decoding process. However, we develop an efficient, recursive, mechanism for generating the approximation probabilities of correct decode, incorrect decode, and decoder failure. In the case where each symbol experiences the same fading level our approximation is a tight, and in the case where each symbol is faded differently we show a fast mechanism which gives a lower bound and upper bound