  An information source generates independent and identically distributed
status update messages from an observed random phenomenon which takes $n$
distinct values based on a given pmf. These update packets are encoded at the
transmitter node to be sent to a receiver node which wants to track the
observed random variable with as little age as possible. The transmitter node
implements a selective $k$ encoding policy such that rather than encoding all
possible $n$ realizations, the transmitter node encodes the most probable $k$
realizations. We consider three different policies regarding the remaining
$n-k$ less probable realizations: $highest$ $k$ $selective$ $encoding$ which
disregards whenever a realization from the remaining $n-k$ values occurs;
$randomized$ $selective$ $encoding$ which encodes and sends the remaining $n-k$
realizations with a certain probability to further inform the receiver node at
the expense of longer codewords for the selected $k$ realizations; and
$highest$ $k$ $selective$ $encoding$ $with$ $an$ $empty$ $symbol$ which sends a
designated empty symbol when one of the remaining $n-k$ realizations occurs.
For all of these three encoding schemes, we find the average age and determine
the age-optimal real codeword lengths, including the codeword length for the
empty symbol in the case of the latter scheme, such that the average age at the
receiver node is minimized. Through numerical evaluations for arbitrary pmfs,
we show that these selective encoding policies result in a lower average age
than encoding every realization, and find the corresponding age-optimal $k$
values.
