In this paper, in order to apply the idea MDPSK to TCM, we use signal set expansion and set partition by phase differences. Through this we propose the trellis-coded MDPSK. And the Viterbi decoder containing branch metrics of the squared Euclidean distance of the Lth order phase difference as well as the first order phase difference is introduced in order to improve the bit error rate(BER) in the differential detection of the trellis-coded MDPSK. The proposed Viterbi decoder is conceptually same to the sliding multiple symbol dection method which uses the branch metric with the first and Lth order phase differences. We investigate the performance of the uncoded DQPSK and the trallis-coded D8PSK in additive white Gaussian noise (AWGN) through the Monte Carlo simulation under the two cases of using and not using the Lth order phase difference metric. The study shows that trellis-coded 8DPSK is an attractive scheme for power and bandlimited systems while also improving the BER performance when the Viterbi decoder is employed to the Lth order phase order difference metric. This performance improvement has been obtained without sacrificing the bandwidth or the power efficiency.