  We consider online scheduling for an energy harvesting communication system
where a sensor node collects samples from a Gaussian source and sends them to a
destination node over a Gaussian channel. The sensor is equipped with a
finite-sized battery that is recharged by an independent and identically
distributed (i.i.d.) energy harvesting process over time. The goal is to
minimize the long term average distortion of the source samples received at the
destination. We study two problems: the first is when sampling is cost-free,
and the second is when there is a sampling cost incurred whenever samples are
collected. We show that fixed fraction policies [Shaviv-Ozgur], in which a
fixed fraction of the battery state is consumed in each time slot, are
near-optimal in the sense that they achieve a long term average distortion that
lies within a constant additive gap from the optimal solution for all energy
arrivals and battery sizes. For the problem with sampling costs, the
transmission policy is bursty; the sensor can collect samples and transmit for
only a portion of the time.
