On information transfer by envelope-constrained signals over the AWGN channel

Using T.E. Duncan´s theorem (1970) on the relation between mutual information and the mean-square error of the optimum causal estimator of a random signal in additive white Gaussian noise (AWGN), the maximum achievable information transfer over the AWGN channel is derived with the random telegraph wave input. The information transfer is bounded and symptotically determined for the Wiener phase-modulated process input at large signal-to-noise ratio (SNR). Both results are compared to the information transfer for the capacity-achieving Gauss-Markov input process. For both the Wiener phase-modulated and the Gauss-Markov processes the information transfer increases asymptotically as the square root of SNR, but for the random telegraph wave it increases only as its logarithm