Bounds on the capacity of a binary input AWGN channel with intertransition duration restrictions

A binary waveform, taking on the values ±√P=±1, with an intertransition time restricted to be above some T_min is a continuous time counterpart of the discrete time run-length-limited codes extensively used in magnetic recording and other channels. Upper bounds on the capacity of an additive white Gaussian noise channel with such a restriction are derived through the use of Duncan´s theorem, relating average mutual information with causal optimal estimation. Lower bounds, based on evaluation of specific signaling schemes, are discussed and compared with the upper bounds. At low signal to noise ratio (SNR) the capacity equals that of average power limited and otherwise unrestricted input waveforms. At high SNR the capacity behaves logarithmically, similarly to the mutual information corresponding to a random telegraph channel input waveform