  Wirelessly powered communications will entail short packets due to naturally
small payloads, low-latency requirements and/or insufficient energy resources
to support longer transmissions. In this paper, a wirelessly powered
communication system is investigated where an energy harvesting transmitter,
charged by one or more power beacons via wireless energy transfer, attempts to
communicate with a receiver over a noisy channel. Under a save-then-transmit
protocol, the system performance is characterized using metrics such as the
energy supply probability at the transmitter, and the achievable rate at the
receiver for the case of short packets. Leveraging the framework of
finite-length information theory, tractable analytical expressions are derived
for the considered metrics in terms of system parameters such as the harvest
blocklength, the transmit blocklength, the harvested power and the transmit
power. The analysis provides several useful design guidelines. Though using a
small transmit power or a small transmit blocklength helps avoid energy
outages, the consequently smaller signal-to-noise ratio or the fewer coding
opportunities may cause an information outage. Scaling laws are derived to
capture this inherent trade-off between the harvest and transmit blocklengths.
Moreover, the asymptotically optimal transmit power is derived in closed-form.
Numerical results reveal that power control is essential for improving the
achievable rate of the system in the finite blocklength regime. The
asymptotically optimal transmit power yields nearly optimal performance in the
finite blocklength regime.
