Optimum TCM Codes Design for Gaussian Channels by Considering Both Euclidean and Hamming Distances

Trellis-coded modulation (TCM) is an attractive coded modulation technique which yields significant coding gain without bandwidth expansion. So far, researches concerning the optimization of TCM codes under Gaussian channels have concentrated on minimizing the error-event probability (EEP). The criterion is to maximize the free Euclidean distance of TCM coded sequences. However, for bitwise communication systems, minimizing the bit error rate (BER) is particularly important. This paper illustrates that the conventional TCM coding criterion is not sufficient in terms of minimizing BER. The reason is that the BER depends on not only Euclidean but also Hamming distances. We then propose a new criterion for TCM codes design, which considers both Euclidean and Hamming distances. Based on the proposed criterion, a general design method is given. A number of optimum TCM codes are designed by using this method. Simulation results verify that, compared with the conventional best-performed TCM codes, our codes not only yield the minimum EEP but also achieve better BER performance.