In this thesis, in order to apply a punctured convolutional codes to the trellis coded modulation(TCM), an efficient punctured trellis coded modulation(PTCM) based on the decomposition of the metric into orthogonal components is presented. Also, a simulation is performed in an additive white Gaussian noise(AWGN) and a rician fading channel modeling the mobile satellite channel. The PTCM combines punctured convolutional coding with MPSK modulation to provide a large coding gain in a power-limited or bandwidth-limited channel. However, in general the use of the punctured convolutional code structure in the decoder results in a performance loss in comparison to trellis codes, due to difficulties in assigning metrics. But, the study shows no loss in performance for punctured trellis coded MPSK in comparison to TCM, and what is more, the punctured convolutional codes results in some savings in the complexity of Viterbi decoders, compared to TCM of the same rate. Also, the results shows that the punctured trellis coded .pi./8 shift 8PSK is an attractive scheme for power-limited and band-limited systems and especially, the Viterbi decoder with first and Lth phase difference metrics improves BER performance by the mobile satellite channel.