  We consider an energy-harvesting communication system where a transmitter
powered by an exogenous energy arrival process and equipped with a finite
battery of size $B_{max}$ communicates over a discrete-time AWGN channel. We
first concentrate on a simple Bernoulli energy arrival process where at each
time step, either an energy packet of size $E$ is harvested with probability
$p$, or no energy is harvested at all, independent of the other time steps. We
provide a near optimal energy control policy and a simple approximation to the
information-theoretic capacity of this channel. Our approximations for both
problems are universal in all the system parameters involved ($p$, $E$ and
$B_{max}$), i.e. we bound the approximation gaps by a constant independent of
the parameter values. Our results suggest that a battery size $B_{max}\geq E$
is (approximately) sufficient to extract the infinite battery capacity of this
channel. We then extend our results to general i.i.d. energy arrival processes.
Our approximate capacity characterizations provide important insights for the
optimal design of energy harvesting communication systems in the regime where
both the battery size and the average energy arrival rate are large.
