  This paper investigates the achievable rates of an additive white Gaussian
noise (AWGN) energy-harvesting (EH) channel with an infinite battery. The EH
process is characterized by a sequence of blocks of harvested energy, which is
known causally at the source. The harvested energy remains constant within a
block while the harvested energy across different blocks is characterized by a
sequence of independent and identically distributed (i.i.d.) random variables.
The blocks have length $L$, which can be interpreted as the coherence time of
the energy arrival process. If $L$ is a constant or grows sublinearly in the
blocklength $n$, we fully characterize the first-order term in the asymptotic
expansion of the maximum transmission rate subject to a fixed tolerable error
probability $\varepsilon$. The first-order term is known as the
$\varepsilon$-capacity. In addition, we obtain lower and upper bounds on the
second-order term in the asymptotic expansion, which reveal that the second
order term scales as $\sqrt{\frac{L}{n}}$ for any $\varepsilon$ less than
$1/2$. The lower bound is obtained through analyzing the save-and-transmit
strategy. If $L$ grows linearly in $n$, we obtain lower and upper bounds on the
$\varepsilon$-capacity, which coincide whenever the cumulative distribution
function (cdf) of the EH random variable is continuous and strictly increasing.
In order to achieve the lower bound, we have proposed a novel adaptive
save-and-transmit strategy, which chooses different save-and-transmit codes
across different blocks according to the energy variation across the blocks.
