  We consider a source monitoring a stochastic process with a transmitter to
transmit timely information through a wireless ON/OFF channel to a destination.
We assume that once the source samples the data, the sampled data has to be
processed to identify the state of the stochastic process. The processing can
take place either at the source before transmission or after transmission at
the destination. The objective is to minimize the distortion while keeping the
age of information (AoI) that measures the timeliness of information under a
certain threshold. We use a stationary randomized policy (SRP) framework to
solve the formulated problem. We show that the two-dimensional discrete-time
Markov chain considering the AoI and instantaneous distortion as the state is
lumpable and we obtain the expression for the expected AoI under the SRP.
