Effects of improving phase transparency on the distance spectrum of trellis codes

In assessing the performance of a TCM scheme, it is necessary to consider the first few lines of its distance spectrum. The distance spectra and performance bounds for 4 and 8-state 32 AMPM trellis codes due to Ungerboeck (1982) and Wei (1984) are computed. It is seen that not all mappings by set partitioning yield equivalent distance spectra although they have the same minimum distance. Results on the distance spectra and performance bounds are also obtained for some multidimensional trellis codes constructed through the idea of multilevel block coding, utilizing 2D signal constellations (e.g. M PSK, M=4, 8, 16 and 16 QAM). It is shown for the 2×16 PSK code that there is an additional 0.2 dB performance loss if the first five spectral lines are considered, as compared to the performance results given by Pietrobon et al. (1990) who consider only the first spectral line