Channel coding with quadrature-quadrature phase shift-keying (Q2PSK) signals

Channel coding due to trellis modulation has been proved to be useful for bandlimited channels. However, these modulations, mostly designed with n-use of 2D signals, are primarily aimed at coding gain only. It is pointed out that utilization of all available signal dimensions, which is limited by the time-bandwidth product, may improve the bandwidth efficiency and simultaneously bring an additional coding gain. Trellis coding with a spectrally efficient 4D signal set based on Q²PSK is addressed. Without any expansion of the Q ²PSK signal set, a simple hand-designed 16-state trellis code provides a coding gain of 6.02 dB. With the same number of states in G. Ungergoeck´s (1982) 8-PSK trellis, the gain is 4.1 dB. In low intersymbol interference situations, the bandwidth efficiency of this coded Q²PSK is twice that of coded 8-PSK; if both operate at 2 b/s Hz and P_b(E)=10^-5, the coded Q²PSK provides a saving of about 4 dB over the coded 8-PSK. Some fully connected trellises with an expanded signal due to 2-use of Q²PSK signals are also presented. Two such codes ar rate-7/8 achieve a gain of 5.45 dB with only eight states