The purpose of this paper is to propose an improvement method of BER for coded 16QAM over Rayleigh fading channel. To overcome the BER degradation due to the fading under mobile communication, we apply trellis coded modulation technique which is efficient to get a coding gain without the expansion of bandwidth. Especially, to minimize the burst error which are the main factor of the BER degradation for mobile communication systems, we apply interleaving/deinterleaving method to the studying system. Also we apply asymmetric signal mapping methods to this TCM scheme. From the computer simulation, BER performance of asymmetric case has achieved about 1 dB improvement of about $10^{-4}$, compared to the traditional symmetric case.