Recently, a new differential encoder was proposed by a look-up table instead of a rule, and the new differential encoding was extended to differential space-time modulation (DSTM). In this thesis, we propose new examples of DSTM using a look-up table. The proposed examples have satisfactory error performance without constellation expansion. In addition, we try multiple-block differential encoding by a look-up table. To further enhance the error performance, we also propose differential space-time trellis code (DSTTC) and construct codes as well as use computers to search good codes. However, the obtained codes of DSTTC are unsatisfactory because their minimum noncoherent distances are small.