This paper deals with the performance improvement of soft iterative decoders in impulsive interference modeled by additive noise. In case of $alpha$-stable noise, the inputs of the belief propagation decoder are too complex to compute. We propose to use an approximation of the log likelihood ratio in an impulsive environment. Even with this simplification, we show that the performance stays close to the one obtained using the true probability density function. Moreover, the robustness of our solution against the parameter estimation is investigated.