  A decode and forward protocol based Trellis Coded Modulation (TCM) scheme for
the half-duplex relay channel, in a Rayleigh fading environment, is presented.
The proposed scheme can achieve any spectral efficiency greater than or equal
to one bit per channel use (bpcu). A near-ML decoder for the suggested TCM
scheme is proposed. It is shown that the high SNR performance of this near-ML
decoder approaches the performance of the optimal ML decoder. The high SNR
performance of this near-ML decoder is independent of the strength of the
Source-Relay link and approaches the performance of the optimal ML decoder with
an ideal Source-Relay link. Based on the derived Pair-wise Error Probability
(PEP) bounds, design criteria to maximize the diversity and coding gains are
obtained. Simulation results show a large gain in SNR for the proposed TCM
scheme over uncoded communication as well as the direct transmission without
the relay. Also, it is shown that even for the uncoded transmission scheme, the
choice of the labelling scheme (mapping from bits to complex symbols) used at
the source and the relay significantly impacts the BER vs SNR performance. We
provide a good labelling scheme for $2^l$-PSK signal set, where $l\geq 2$ is an
integer.
