It is confirmed by theoretical analysis and simulation results that, whether the Rayleigh fading channel is perfectly estimated or not, the Max-Log-MAP algorithm is independent of the channel signal-to-noise ratio (SNR).In addition, the Max-Log-MAP algorithm does not depend on any other channel parameter. By scaling the soft output, the Max-Log-MAP decoder performs nearly as well as the Log-MAP decoder, while this gain is achieved without any complexity increase. As no channel parameter estimator is needed, from a practical point of view, decoding turbo codes on the Rayleigh fading channels with the Scaled Max-Log-MAP algorithm is a good compromise among the performance, the complexity and the system robustness.