Pairwise error probability on the Gilbert-Elliott channel with application to turbo codes

The Gilbert-Elliott (GE) channel is one of the simplest and practical models for a channel with memory. In this paper, the performance of a binary linear code in a slowly varying Rayleigh fading channel modeled by the GE channel model is considered. An analytical expression for the pairwise error probability of maximum likelihood decoding of a binary linear code on the GE channel model is derived. This expression is obtained as a function of the channel parameters and can be used to obtain the union bound on the bit error probability of any binary linear code on the GE channel if the weight distribution or average weight distribution of the codewords is known. Comparisons between the results obtained by this analytical expression and results obtained through computer simulations in the case of turbo codes show that the analytical results are accurate in establishing the decoder performance in the range where obtaining sufficient data from simulation is impractical