  This paper investigates the information-theoretic limits of energy-harvesting
(EH) channels in the finite blocklength regime. The EH process is characterized
by a sequence of i.i.d. random variables with finite variances. We use the
save-and-transmit strategy proposed by Ozel and Ulukus (2012) together with
Shannon's non-asymptotic achievability bound to obtain lower bounds on the
achievable rates for both additive white Gaussian noise channels and discrete
memoryless channels under EH constraints. The first-order terms of the lower
bounds of the achievable rates are equal to $C$ and the second-order (backoff
from capacity) terms are proportional to $-\sqrt{ \frac{\log n}{n}}$, where $n$
denotes the blocklength and $C$ denotes the capacity of the EH channel, which
is the same as the capacity without the EH constraints. The constant of
proportionality of the backoff term is found and qualitative interpretations
are provided.
