Codes for zero spectral density at zero frequency (Corresp.)

In pulse-amplitude modulation (PAM) digital transmission systems line encoding is used for shaping the spectrum of the encoded symbol sequence to suit the frequency characteristics of the transmission channel. In particular, it is often required that the encoded symbol sequence have a zero mean and spectral density vanishing at zero frequency. We show that the finite running digital sum condition is a necessary and sufficient condition for this to occur. The result holds in particular for alphabetic codes, which are the most widely used line codes.