CHANNEL CODING WITH QUADRATURE QUADRATURE PHASE SHIFT-KEYING (Q2PSK) SIGNALS

Channel coding due to trellis modulation has been proven to be useful for band-limited channels. However, these modulations, mostly designed with n-use of 2-1) signals, are primarily aimed at coding gain only. This paper attempts to point out that utilization of all available signal space 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 4-D signal set due to newly developed Q2PSK is addressed. Without any expansion of the Q2PSK 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 Ungerboeck's 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 Pb(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 set due to 2-use of Q2PSK signals are also presented. Two such codes at rate-7/8 achieve a gain of 5.45 dB with only eight states; these codes are proven to be optimum in the light of some performance bounds presented. © 1990 IEEE