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

An additive white Gaussian noise energy-harvesting channel with an infinite-sized battery is considered. The energy arrival process is modeled as a sequence of independent and identically distributed random variables. The channel capacity $\frac {1}{2}\log (1+P)$ is achievable by the so-called best-effort and save-and-transmit schemes where $P$ denotes the battery recharge rate. This paper analyzes the save-and-transmit scheme whose transmit power is strictly less than $P$ and the best-effort scheme as a special case of save-and-transmit without a saving phase. In the finite blocklength regime, we obtain new non-asymptotic achievable rates for these schemes that approach the capacity with gaps vanishing at rates proportional to /\sqrt {n}$ and $({(\log n)/n})^{1/2}$ respectively where $n$ denotes the blocklength. The proof technique involves analyzing the escape probability of a Markov process. When $P$ is sufficiently large, we show that allowing the transmit power to back off from $P$ can improve the performance for save-and-transmit. The results are extended 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 and best-effort schemes achieve coding rates that approach the capacity with gaps vanishing at rates proportional to $\sqrt {L/n}$ and $({\max \{\log n, L\}/n})^{1/2}$ , respectively.