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

Second Order and Moderate Deviation Analysis of a Block Fading Channel with Deterministic and Energy Harvesting Power Constraints