−4 −2 0 2 4 6 8 10 12 14 16 18 20 0 5 10 15 20 25 30 0.10 0.81 0.10 0.81 0.10 0.81 0.10 0.80 0.10 0.01 0.79 0.09 0.02 0.77 0.09 0.03 0.75 0.08 0.04 0.02 0.73 0.07 0.05 0.03 0.01 0.70 0.06 0.05 0.03 0.02 0.67 0.05 0.05 0.04 0.03 0.02 0.65 0.05 0.04 0.04 0.03 0.02 0.01 0.62 0.04 0.04 0.03 0.03 0.03 0.02 0.01 0.60 SNR(dB) Probability mass points Fig. 3. The marginal distribution of the stationary Markov input. Duty cycle ≤ 0 . 5 , transition cost c = 1 . 0 . formula (93) with duty cycle constraint ( q, c ) . The lower bound L ( µ ) is quite tight and can be regarded as a good approximation of mutual information of first-order Markov inputs. Figs. 5 and 6 demonstrate the sensitivity of the achievable rates to the duty cycle parameter q and the transition cost c , respectively. The performance of Markov inputs is superior to i.i.d. inputs as well as Gaussian signaling with deterministic schedule. Fig 5 shows that the performance of i.i.d. input is similar to the deterministic schedule, which implies that different from the case under the idealized duty cycle constraint, i.i.d. input is not a good choice under the realistic duty cycle constraint. 32