In this paper, in order to apply the $pi/4$ shift QPSK to TCM, we propose the $pi/8$ shift 8PSK modulation technique and the trellis-coded $pi/8$ shift 8PSK performing signal set expansion and partition by phase difference. In addition, the Viterbi decoder with branch metrics of the squared Euclidean distance of the first phase difference as well as the Lth phase different is introduced in order to improve the bit error rate(BER) performance in differential detection of the trellis-coded $pi/8$ shift 8PSK. The proposed Viterbi decoder is conceptually the same as the sliding multiple detection by using the branch metric with first and Lth order phase difference. We investigate the performance of the uncoded $pi/4$ shift QPSK and the trellis-coded $pi/8$ shift 8PSK with or without the Lth phase difference metric in an additive white Gaussian noise (AWGN) using the Monte Carlo simulation. The study shows that the $pi/4$ shift QPSK with the Trellis-code i.e. the trellis-coded $pi/8$ shift 8PSK is an attractive scheme for power and bandlimited systems and especially, the Viterbi decoder with first and Lth phase difference metrics improves BER performance. Also, the nest proposed algorithm can be used in the TC $pi/8$ shift 8PSK as well as TCMDPSK.