On Single Cross Error Correcting Integer Codes with Minimum-Energy Signal Constellations
01 January 2007
Integer codes, defined over integer rings, allow the correction of single cross errors with distance 1 in a signal point constellation on a two-dimensional lattice. Several construction methods support the construction of integer codes that give constellations that have a variety of shapes. In this paper, we characterize all constellations that can be obtained from a particular integer code. In particular, we determine those that minimize the average symbol energy. In addition, we evaluate the symbol error probability when using an integer code for coded QAM constellations.