  A status updating communication system is examined, in which a transmitter
communicates with a receiver over a noisy channel. The goal is to realize
timely delivery of fresh data over time, which is assessed by an
age-of-information (AoI) metric. Channel coding is used to combat the channel
errors, and feedback is sent to acknowledge updates' reception. In case
decoding is unsuccessful, a hybrid ARQ protocol is employed, in which
incremental redundancy (IR) bits are transmitted to enhance the decoding
ability. This continues for some amount of time in case decoding remains
unsuccessful, after which a new (fresh) status update is transmitted instead.
In case decoding is successful, the transmitter has the option to idly wait for
a certain amount of time before sending a new update. A general problem is
formulated that optimizes the codeword and IR lengths for each update, and the
waiting times, such that the long term average AoI is minimized. Stationary
deterministic policies are investigated, in which the codeword and IR lengths
are fixed for each update, and the waiting time is a deterministic function of
the AoI. The optimal waiting policy is then derived, and is shown to have a
threshold structure, in which the transmitter sends a new update only if the
AoI grows above a certain threshold that is a function of the codeword and IR
lengths. Choosing the codeword and IR lengths is discussed in the context of
binary symmetric channels.
