Bounds on the information rate of intertransition-time-restricted binary signaling over an AWGN channel

Upper and lower bounds on the capacity of a continuous-time additive white Gaussian noise (AWGN) channel with bilevel (±√P) input signals subjected to a minimum inter-transition time (T_min) constraint are derived. The channel model and input constraints reflect basic features of certain magnetic recording systems. The upper bounds are based on Duncan´s relation between the average mutual information in an AWGN regime and the mean-square error (MSE) of an optimal causal estimator. Evaluation or upper-bounding the MSE of suboptimal causal estimators yields the desired upper bounds. The lower bound is found by invoking the extended “Mrs. Gerber´s” lemma and asymptotic properties of the entropy of max-entropic bipolar (d, k) codes. Asymptotic results indicate that at low SNR=PT_min/N₀, with N₀ designating the noise one-sided power spectral density, the capacity tends to P/N ₀ nats per second (nats/s), i.e., it equals the capacity in the simplest average power limited case. At high SNR, the capacity in the simplest average power limited case. At high SNR, the capacity behaves asymptotically as T_min^-1ln(SNR/ln(SNR)) (nats/s), demonstrating the degradation relatively to T_avg ^-1 lnSNR, which is the asymptotic known behavior of the capacity with a bilevel average intertransition-time (T_avg) restricted channel input. Additional lower bounds are obtained by considering specific signaling formats such as pulsewidth modulation. The effect of mild channel filtering on the lower bounds on capacity is also addressed, and novel techniques to lower-bound the capacity in this case are introduced