對於籬柵編碼調變加相差編碼以及相差籬柵編碼調變兩者，我們提出增加距離量和使用集合分割。此外，本論文將會分析集合分割、設計或搜尋到的籬柵碼以及它們的最小距離。在碼率為每一符號為2位元的情況下，我們皆找到對於籬柵編碼調變加相差編碼以及相差籬柵編碼調變兩者，比原始碼更好的新碼，其也具有較好的錯誤率。另外在碼率為每一符號為3位元的情況下，相差籬柵編碼調變使用十六位元振幅相位偏移調變會比十六位元相位偏移調變的相差籬柵編碼調變以及籬柵編碼調變加相差編碼兩者皆有更大的最小距離和更好的錯誤率。 ;Differential encoding (DE) is a classical technique at the transmitter that allows simple noncoherent detection at the receiver. On the other hand, Trellis-coded modulation (TCM) is a bandwidth efficient technique which offers reliable data transmission. In this paper, we consider TCM with DE for channel phase coherence over N = 2 symbols. Besides the well-known TCM followed by DE (called TCM-DE) for MPSK signals, we propose a new trellis coding extension of DE, called differential trellis coded modulation (DTCM). DTCM is TCM with DE defined in states where distinct states may have distinct DE functions. We propose design methods of DE functions for noncoherently non-catastrophic DTCM.
For both TCM-DE using MPSK signals and DTCM, we propose additive distance measures and set partitioning. Based on the proposed set partitioning, trellis codes are designed or searched and their minimum distances are analyzed. For data rate 2 bits/symbol, the obtained new codes outperform the original codes for both TCM-DE and DTCM, and the new codes of TCM-DE and DTCM have similar bit error rate. For data rate 3 bits/symbol, DTCM using 16APSK (amplitude phase-shift keying) has better minimum distance and BER than both TCM-DE and DTCM using 16PSK.