The exponential bound parameter is numerically evaluated for 16-zone quantized 8-PSK for signal vectors bisecting decision regions and for signal vectors lying on decision boundaries. For decision regions of equal span, signal vectors lying on decision boundaries are superior, confirming the result of Parsons and Wilson (1990). Signal vectors bisecting decision regions are superior if span of decision regions not containing signal vectors is optimized. Using the partial derivative, it is shown that the optimal configuration depends on SNR. Furthermore, the optimal configuration is not necessarily one in which the decision boundaries are straight lines.>

TCM, combining modulation and coding, achieves coding gains over conventional uncoded multilevel modulation without the attendant bandwidth expansion. Since TCM was proposed Ungerboeck (1982, 1987) substantial work has done in this area. A large portion of the TCM work has been in the area of high-speed data transmission over voice grade modems using quadrature amplitude modulation, QAM. QAM, not having a constant envelope, is unattractive for employing a TWT with its nonlinear behavior as the power stage. Additional work has been done in utilizing M-ary PSK with TCM. Simulations by Taylor and Chan (1981) utilizing a 4-state convolutional code demonstrated the coding gain of a rate 2/3 coded 8-PSK modulation scheme. Wilson et. al. (1984) obtained results for 16-PSK TCM using codes with 4 to 32 states and achieved coding gains of 3.5 to 4.8 dB respectively, over 8-PSK and demonstrated that small memory codes achieved good gains with simple design procedures.>