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We consider a two-phase Wireless-Powered Communication Network under Nakagami-m fading, where a wireless energy transfer process first powers a sensor node that then uses such energy to transmit its data in the wireless information transmission phase. We explore a fixed transmit rate scheme designed to cope with the reliability and delay constraints of the system while attaining closed-form approximations for the optimum wireless energy transfer and wireless information transmission blocklength. Then, a more-elaborate rate control strategy exploiting the readily available battery charge information is proposed and the results evidence its outstanding performance when compared with the fixed transmit rate, for which no battery charge information is available. It even reaches an average rate performance close to that of an ideal scheme requiring full Channel State Information at transmitter side. Numerical results show the positive impact of a greater number of antennas at the destination, and evidence that the greater the reliability constraints, the smaller the message sizes on average, and the smaller the optimum information blocklengths. Finally, we corroborate the appropriateness of using the asymptotic blocklength formulation as an approximation of the non-asymptotic finite blocklength results., Comment: 14 pages, 8 figures, accepted for publication in IEEE TWC