  Source-channel coding for an energy limited wireless sensor node is
investigated. The sensor node observes independent Gaussian source samples with
variances changing over time slots and transmits to a destination over a flat
fading channel. The fading is constant during each time slot. The compressed
samples are stored in a finite size data buffer and need to be delivered in at
most $d$ time slots. The objective is to design optimal transmission policies,
namely, optimal power and distortion allocation, over the time slots such that
the average distortion at destination is minimized. In particular, optimal
transmission policies with various energy constraints are studied. First, a
battery operated system in which sensor node has a finite amount of energy at
the beginning of transmission is investigated. Then, the impact of energy
harvesting, energy cost of processing and sampling are considered. For each
energy constraint, a convex optimization problem is formulated, and the
properties of optimal transmission policies are identified. For the strict
delay case, $d=1$, $2D$ waterfilling interpretation is provided. Numerical
results are presented to illustrate the structure of the optimal transmission
policy, to analyze the effect of delay constraints, data buffer size, energy
harvesting, processing and sampling costs.
