TCM With Differential Encoding: Set Partitioning, Trellis Designs, and Distance Analysis

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 aim to find the best concatenation order of TCM and DE for channel phase coherence over N=2 symbols. Besides the well-known TCM followed by DE (called TCM-DE) , we propose a new trellis coding extension of DE which extends our earlier work, 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 and DTCM, we propose additive distance measures and set partitioning. Based on the proposed set partitioning, trellis codes are designed or searched for both TCM-DE and DTCM. Both minimum distances and simulation results show that TCM-DE outperforms DTCM and the obtained new codes are better than the original codes.