## Trellis Coded Modulation (TCM)

In 1976, G. Ungerboeck and I. Csajka published a very famous paper on this exact topic (see Ungerboeck and Csajka (1976)), where they showed that in fact the potential coding gain could indeed out-weigh the Eb/N0 penalty of increased symbol states, by 3–4 dB! In a later paper (see Ungerboeck (1982)) examples of M-ary PSK and M-ary QAM schemes with coding gains in excess of 6 dB were presented. The efficient implementation of these coding schemes often makes use of the convolutional encoding and the trellis-based Viterbi decoding algorithms mentioned earlier. For this reason, this type of coding is often referred to as Trellis Coded Modulation (TCM).