Abstract
In this letter, formulas for the total number of decodable and undecodable vectors are derived for a general (n,k) q-ary linear block code. These formulas are used to find the probabilities of decoder error and decoder failure for Reed-Solomon codes under errors-and-erasures decoding. The resulting analytical expressions are computationally efficient and allow accurate calculation of very small values of decoder failure probabilities. The formulas are used to analyze the performance of type-I hybrid automatic-repeat-request (HARQ) protocols with two decoding diameters.
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