  The capacity of time-varying channels with periodic feedback at the
transmitter is evaluated. It is assumed that the channel state information is
perfectly known at the receiver and is fed back to the transmitter at the
regular time-intervals. The system capacity is investigated in two cases: i)
finite state Markov channel, and ii) additive white Gaussian noise channel with
time-correlated fading. In the first case, it is shown that the capacity is
achievable by multiplexing multiple codebooks across the channel. In the second
case, the channel capacity and the optimal adaptive coding is obtained. It is
shown that the optimal adaptation can be achieved by a single Gaussian
codebook, while adaptively allocating the total power based on the side
information at the transmitter.
