On the performance of trellis-coded modulation over groups

The performance of a trellis group code has a close relationship with the order of elements of the output group. In this article, I describe the kind of influence the order of group elements exerts on the performance of the code. First, I introduce a wide-sense homomorphic trellis encoder in this article. Next, I explain that there exist some trellis paths that consist of only prime-order elements and the unit element. As a result, if every signal point labeled by prime-order elements has a large Euclidean distance (weight), then there is a possibility of obtaining good group codes. But if one of the Euclidean distances of the points labeled by prime-order elements is small, then we cannot make a good code for a wide-sense homomorphic encoder. We attempt to apply this idea to multilevel codes using a semi-direct product group, and to multidimensional star-16QAM codes, and show some conditions in which the idea is efficient. (C) 1999 Scripta Technica.