  In this paper, we consider a class of wireless powered communication devices
using hybrid automatic repeat request (HARQ) protocol to ensure reliable
communications. In particular, we analyze the trade-off between accumulating
mutual information and harvesting RF energy at the receiver of a point-to-point
link over a time-varying independent and identically distributed (i.i.d.)
channel. The transmitter is assumed to have a constant energy source while the
receiver relies, solely, on the RF energy harvested from the received signal.
At each time slot, the incoming RF signal is split between information
accumulation and energy accumulation with the objective of minimizing the
expected number of re-transmissions. A major finding of this work is that the
optimal policy minimizing the expected number of re-transmissions utilizes the
incoming RF signal to either exclusively harvest energy or to accumulate mutual
information. This finding enables achieving an optimal solution in feasible
time by converting a two dimensional uncountable state Markov decision process
(MDP) with continuous action space into a countable state MDP with binary
decision space.
