  Minimum power required to achieve a distortion-noise profile, i.e., a
function indicating the maximum allowed distortion value for each noise level,
is studied for the transmission of Gaussian sources over Gaussian channels
under a regime of bandwidth approaching zero. A simple but instrumental lower
bound to the minimum required power for a given profile is presented. For an
upper bound, a dirty-paper based coding scheme is proposed and its
power-distortion tradeoff is analyzed. Finally, upper and lower bounds to the
minimum power is analyzed and compared for specific distortion-noise profiles,
namely rational profiles with order one and two.
