New results on the performance of linear block codes with Type-I hybrid ARQ protocol

Formulas for the total number of decodable and undecodable vectors are derived for a general (n, k) q-ary block code. These formulas are used to find the probabilities of decoder error and decoder failure. The resulting analytical expressions are computationally efficient and allow accurate calculation of very small values of the probability of decoding failure. A bounded-distance errors-and-erasures decoding scheme is presented that utilizes two effective diameters for decoding. The performance of this decoding scheme is also investigated in conjunction with Type-I hybrid ARQ protocols, and it is shown to significantly improve performance over schemes based on a single effective diameter