In this paper, the transmission channels of L-band and Ka-band multi-media satellite communication systems for the land mobile satellite(LMS) communication service are modeled. Trellis coded(TC) 8PSK is proposed as a power and bandwidth efficient digital transmission scheme for the LMS system, and its error probability performance is analyzed. Block interleaving and deinterleaving are applied to the transmitter and receiver of LMS system respectively in order to compensate for the BER performance degradation of TC-8PSK caused by multipath fading. Viterbi equalizer is also employed in the receiver for channel equalization, and the corresponding BER performance improvement is analyzed.