We design parallel concatenated trellis coded modulation (PC-TCM) schemes at 1 bit/sec/Hz for 8-PSK and 8-QAM over the following discrete two-dimensional (2D) channels: (a) a slow-fading Rayleigh channel with discrete carrier tracking by a phase locked loop (PLL), where the PLL signal-to-noise ratio (SNR) is proportional to the fading amplitude squared; (b) an additive white Gaussian noise (AWGN) channel with a PLL; and (c) a fast-fading Rician channel with carrier phase estimation for the line-of-sight (LOS) path only. The fading gain and phase error are assumed independent over successive symbols. The codes for channels (a) and (b) perform within 1 dB of constellation-constrained capacity at bit error rates of 10/sup -6/, while those for channel (c) perform within 1.2 dB of constellation-constrained capacity for LOS-to-diffuse power ratios of 3 dB.