  Previous works on age of information and erasure channels have dealt with
specific models and computed the average age or average peak age for certain
settings. In this paper, given a source that produces a letter every $T_s$
seconds and an erasure channel that can be used every $T_c$ seconds, we ask
what is the coding strategy that minimizes the time-average age of information
that an observer of the channel output incurs. We first analyze the case where
the source alphabet and the channel-input alphabet have the same size. We show
that a trivial coding strategy is optimal and a closed form expression for the
age can be derived. We then analyze the case where the alphabets have different
sizes. We use a random coding argument to bound the average age and show that
the average age achieved using random codes converges to the optimal average
age of linear block codes as the source alphabet becomes large.
