  We consider a monitoring application where sensors periodically report data
to a common receiver in a time division multiplex fashion. The sensors are
constrained by the limited and unpredictable energy availability provided by
Energy Harvesting (EH), and by the channel impairments. To maximize the quality
of the reported data, the packets transmitted contain newly generated data
blocks together with up to $r - 1$ previously unsuccessfully delivered ones,
where $r$ is a design parameter; such blocks are compressed, concatenated and
encoded with a channel code. The scheme applies lossy compression, such that
the fidelity of the individual blocks is traded with the reliability provided
by the channel code. We show that the proposed strategy outperforms the one in
which retransmissions are not allowed. We also investigate the tradeoff between
the value of $r$, the compression and coding rates, under the constraints of
the energy availability, and, once $r$ has been decided, use a Markov Decision
Process (MDP) to optimize the compression/coding rates. Finally, we implement a
reinforcement learning algorithm, through which devices can learn the optimal
transmission policy without knowing a priori the statistics of the EH process,
and show that it indeed reaches the performance obtained via MDP.
