We consider the problem of transmission of analog data over a noisy channel. It is assumed
that the channel input is of the form\surd S f (t, X), where X is an n-dimensional source
vector, and S is the allowable transmitted power. The performance of any given modulation
scheme f (t,\cdot) as a function of the transmitted power S is studied. Lower bounds on the
average distortion produced by noise for a class of distortion functions are derived. These
bounds relate the" smoothness" of modulation techniques to the minimum error that can be …