In this paper, we investigate the signal-to-noise ratio (SNR) sensitivity of the Log-MAP turbo decoder over Rayleigh fading channels. It is shown that the use of the channel reliability factor proposed by Frenger is equivalent to an SNR underestimation when the channel estimate is not perfect. In addition, we propose s simplified method to compute the channel reliability factor, which leads to reduction of the computing complexity while causes no performance degradation.