  We consider a block fading additive white Gaussian noise (AWGN) channel with
perfect channel state information (CSI) at the transmitter and the receiver.
First, for a given codeword length and non-vanishing average probability of
error, we obtain lower and upper bounds on the maximum transmission rate. We
derive bounds for three kinds of power constraints inherent to a wireless
transmitter. These include the canonical peak power constraint and average
power constraint. In addition, we consider a time varying peak power constraint
imposed by an \emph{energy harvesting device}-a mechanism that powers many
modern-day wireless transmitters. The bounds characterize \emph{second order}
deviation of finite blocklength coding rates from the channel capacity, which
is in turn achieved by \textit{water-filling} power allocation across time. The
bounds obtained also indicate the rate enhancement possible due to CSI at the
transmitter in the finite blocklength regime. Next, we provide bounds on the
optimal exponent with which error probability drops to zero when channel coding
rate is simultaneously allowed to approach capacity \emph{at a certain rate},
as the codeword length increases. These bounds identify what is known as the
moderate deviation regime of the block fading channel. We compare the bounds
numerically to bring out the efficacy of our results.
