Source coding and transmission of signals over time-varying channels with side information

We look at the problem of transmitting information over time-varying channels with side information, where for time-varying channels the statistics of the channel change with time and by channel side information we mean the current state of the channel. We show that when this side information is available at both the transmitter and the receiver, then for the power-constrained channel, the power allocation policy that achieves minimum end-to-end distortion is not necessarily the same as the one required for maximum transmission rate