Probability of undetected error of hybrid ARQ over the Gilbert-Elliott channel

The authors present a method for computing the probability of undetected error for hybrid ARQ over the Gilbert-Elliott channel (Gilbert, E.N., Bell Syst. Tech. J., vol.39, p.1253-65, 1960; Elliott, E.O., Bell Syst. Tech. J., vol.42, p.1977-97, 1963). The method described by Elliott is extended to the case where the code is used for error detection and error correction simultaneously (hybrid ARQ, type-I). This analytical approach to the evaluation of the probability of undetected error allows the throughput to be calculated as a function of the code rate and length, and systems to be designed that maximize the throughput, given the channel parameters and the desired undetected error probability.