Optimum asymmetric constellation design for trellis-coded modulation over gaussian channels

This letter studies the optimization of asymmetric constellations for trellis-coded modulation (TCM). Unlike the conventional criterion of maximizing the free Euclidean distance, the criterion here is to minimize the bit error rate (BER) of TCM systems. The letter presents an easy way to derive the BER upper bound for any TCM codes, and proposes the method for designing optimum asymmetric constellations by minimizing the bound. The given method can be applied to TCM systems with arbitrary state numbers. Numerical results verify that all the codes designed by the proposed method achieve better BER performance than symmetric ones.