  We consider the problem of real-time remote monitoring of a two-state Markov
process, where a sensor observes the state of the source and makes a decision
on whether to transmit the status updates over an unreliable channel or not. We
introduce a modified randomized stationary sampling and transmission policy
where the decision to perform sampling occurs probabilistically depending on
the current state of the source and whether the system was in a sync state
during the previous time slot or not. We then propose two new performance
metrics, coined the Version Innovation Age (VIA) and the Age of Incorrect
Version (AoIV) and analyze their performance under the modified randomized
stationary and other state-of-the-art sampling and transmission policies.
Specifically, we derive closed-form expressions for the distribution and the
average of VIA, AoIV, and Age of Incorrect Information (AoII) under these
policies. Furthermore, we formulate and solve three constrained optimization
problems. The first optimization problem aims to minimize the average VIA
subject to constraints on the time-averaged sampling cost and time-averaged
reconstruction error. In the second and third problems, the objective is to
minimize the average AoIV and AoII, respectively, while considering a
constraint on the time-averaged sampling cost. Finally, we compare the
performance of various sampling and transmission policies and identify the
conditions under which each policy outperforms the others in optimizing the
proposed metrics.
