Graph-based metrics over QAM constellations

In order to propose a new metric over QAM constellations, diagonal Gaussian graphs defined over quotients of the Gaussian integers are introduced in this paper. Distance properties of the constellations are detailed by means of the vertex-to-vertex distribution of this family of graphs. Moreover, perfect codes for this metric are considered. Finally, notable subgraphs of diagonal Gaussian graphs are studied which leads to relate the proposed metric to other well-known graph-based metrics such as the Lee distance.