A recursive method for calculating error probabilities for a Reed-Solomon codeword with bounded distance errors and erasures decoding

This paper is the second in a series of two papers dealing with methods for recursively calculating codeword error and erasure probabilities for Reed-Solomon (RS) codewords. As with the previous paper, a single RS codeword is transmitted in a channel where each transmitted symbol experiences independent identically distributed (IID) noise or a channel where each symbol experiences independent differently distributed (IDD) noise. Each received symbol is decoded using a mechanism where a symbol or an erasure is produced, and the entire codeword is decoded using a bounded-distance (BD) decoder. Specifically, this paper deals with an errors and erasures (EE) decoder, while the previous paper addressed errors only (EO) decoding. 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 exact probabilities (correct decode, incorrect decode, and decoder failure) in the IID case and bounds on the probability of incorrect decode for the IDD case.