Six-dimensional trellis-coded modulation

A family of trellis-coded modulation (TCM) schemes is presented which is based on two-step partitioning of six-dimensional (6D) signal constellations. Maximum-likelihood detection of these schemes based on the Viterbi algorithm is described. The asymptotic gain is 3.01 dB for the two-state code, and 4.33 dB for the four- and eight-state codes which involve a smaller expansion of the uncoded signal alphabet. A comparison is made between proposed schemes and the conventional 2D TCM in terms of tradeoff between performance and detection complexity. It is shown that some of the proposed schemes have a significant advantage over 2D TCM. In particular, the eight-state 6D trellis code involves only half of the complexity of the eight-state 2D code while providing an additional gain of 0.15 dB