Uniform distance and error probability properties of TCM schemes

The class of uniform trellis-coded modulation (TCM) techniques is defined, and simple explicit conditions for uniformity are derived. Uniformity is shown to depend on the metric properties of the two subconstellations resulting from the first step in set partitioning, as well as on the assignment of binary labels to channel symbols. The uniform distance property and uniform error property, which are both derived from uniformity but are not equivalent, are discussed. The derived concepts are extended to encompass transmission over a (not necessarily Gaussian) memoryless channel in which the metric used for detection may not be maximum likelihood. An appropriate distance measure is defined that generalizes the Euclidean distance. It is proved that uniformity of a TCM scheme can also be defined under this new distance. The results obtained are shown to hold for channels with phase offset or independent, amplitude-only fading. Examples are included to illustrate the applicability of the results