  The problem of real-time remote tracking and reconstruction of a two-state
Markov process is considered here. A transmitter sends samples from an observed
information source to a remote monitor over an unreliable wireless channel. The
receiver, in turn, performs an action according to the state of the
reconstructed source. We propose a state-aware randomized stationary sampling
and transmission policy which accounts for the importance of different states
of the information source, and their impact on the goal of the communication
process. We then analyze the performance of the proposed policy, and compare it
with existing goal-oriented joint sampling and transmission policies, with
respect to a set of performance metrics. Specifically, we study the real-time
reconstruction error, the cost of actuation error, the consecutive error, and a
new metric, coined importance-aware consecutive error. In addition, we
formulate and solve a constrained optimization problem that aims to obtain the
optimal sampling probabilities that minimize the average cost of actuation
error. Our results show that in the scenario of constrained sampling
generation, the optimal state-aware randomized stationary policy outperforms
all other sampling policies for fast evolving sources, and, under certain
conditions, for slowly varying sources. Otherwise, a semantics-aware policy
performs better only when the source is slowly varying.
