Symbolic dynamic techniques for trellis group codes

In this paper, we use symbolic dynamics to describe and analyze the class of geometrically uniform trellis codes. We introduce the notion of group systems and image systems, which establish the connection between symbolic dynamics and trellis coding. We define several properties of general symbolic dynamic systems, and provide a complete classification of group systems and image systems under this framework. We also provide a complete description of all group systems based on the cyclic group and dihedral group, and point out its implications for rotationally invariant trellis group codes based on MPSK signal constellations