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An additive white Gaussian noise energy-harvesting channel with aninfinite-sized battery is considered. The energy arrival process is modeled asa sequence of independent and identically distributed random variables. Thechannel capacity $\frac{1}{2}\log(1+P)$ is achievable by the so-calledbest-effort and save-and-transmit schemes where $P$ denotes the batteryrecharge rate. This paper analyzes the save-and-transmit scheme whose transmitpower is strictly less than $P$ and the best-effort scheme as a special case ofsave-and-transmit without a saving phase. In the finite blocklength regime, weobtain new non-asymptotic achievable rates for these schemes that approach thecapacity with gaps vanishing at rates proportional to $1/\sqrt{n}$ and$\sqrt{(\log n)/n}$ respectively where~$n$ denotes the blocklength. The prooftechnique involves analyzing the escape probability of a Markov process. When$P$ is sufficiently large, we show that allowing the transmit power to back offfrom $P$ can improve the performance for save-and-transmit. The results areextended to a block energy arrival model where the length of each energy block$L$ grows sublinearly in $n$. We show that the save-and-transmit andbest-effort schemes achieve coding rates that approach the capacity with gapsvanishing at rates proportional to $\sqrt{L/n}$ and $\sqrt{\max\{\log n,L\}/n}$ respectively.

Non-Asymptotic Achievable Rates for Gaussian Energy-Harvesting Channels: Best-Effort and Save-and-Transmit