0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 q Channel capacity (bits) near−optimal discrete input Gaussian signaling over a deterministic schedule mixture input SNR=10dB SNR=0dB Fig. 2. Achievable rates under duty cycle constraint for 0 dB and 10 dB SNRs. probability matrix P$_{X}$$_{2}$$_{|}$$_{X}$$_{1}$ and stationary probability P$_{X}$ for q = 0 . 5 , c = 1 . 0 and SNR = 8 dB. The symmetry of the transition probability matrix is evident, as conditioned on that two consecutive symbols are nonzero, they are independent. Fig. 3 shows the stationary (marginal) distribution for suboptimal Markov input. In order to compensate the transition cost, additional fraction of zero symbol should be transmitted, P$_{X}$ (0) > q . As the SNR increases, more and more weights are put on distant constellation points, where less and less weights are put on the zero letter. In Fig. 4, the rates achieved by various optimized input distributions are plotted against the SNR. The rate achieved by the optimized Markov input is larger than that of suboptimal i.i.d. input calculated by 31