  In this work, we obtain lower and upper bounds on the maximal transmission
rate at a given codeword length $n$, average probability of error $\epsilon$
and power constraint $\bar{P}$, over a finite valued, block fading additive
white Gaussian noise (AWGN) channel with channel state information (CSI) at the
transmitter and the receiver. These bounds characterize deviation of the finite
blocklength coding rates from the channel capacity which is in turn achieved by
the water filling power allocation across time. The bounds obtained also
characterize the rate enhancement possible due to the CSI at the transmitter in
the finite blocklength regime. The results are further elucidated via numerical
examples.
