Six-dimensional trellis-coding with QAM signal sets

A family of 6-D trellis-coded modulation (TCM) schemes which involve a 2-step partitioning of the constituent QAM signal alphabet is presented. With infinite constellations without shaping, the asymptotic coding gain is 3 dB for the 2-state code, 4 dB for the 4- and 8-state codes, and 5 dB for the 16- and 32-state codes which involve a smaller alphabet expansion. The authors also describe a rotationally invariant 16-state code that achieves the same asymptotic gain as its linear counterpart. Practical signal constellations are described for 6-D TCM with the spectral efficiency of uncoded 64-QAM, and the performance of these schemes is studied by means of computer simulations. It was found that they achieve an additional coding gain of 0.2-0.3 dB over infinite hypercube-type constellations. The performance of the presented schemes at practical signal-to-noise ratio values is evaluated using transfer function techniques