To evaluate the coding performance of a multilevel coding scheme for Rayleigh fading channel, a virtual automatic gain control and interleaving are applied to the scheme. The automatic gain control is assumed only for the theoretical evaluation of the performance. It is noted that the bit error-rate performance of the scheme for phase shift keying does not change whether the control is assumed or not. By the effect of the virtual automatic gain control and the interleaving, a fading channel with Gaussian noise is theoretically converted into an equivalent time-invariant channel with non-Gaussian noise. The probability density function of the converted non-Gaussian noise is derived. Then, the function is applied to a formula of the bit error-rate of the scheme for non-Gaussian noise. The formula is derived for phase shift keying by modifying that for pulse amplitude modulation. The coding performance for the non-Gaussian noise channel is evaluated by the formula, and the suitable coding with ideal interleaving is searched. As a result, the coding gain of 28 dB is obtained at the bit error-rate of 10-6 by using BCH code of length 31. This result is confirmed by a simulation for the fading channel. Then, the effectiveness of the formula for finite interleaving is evaluated. Finally, the usefulness of the formula, where the noise power is doubled, is shown for a case of a differential detection.