On the Age of Information in Erasure Channels with Feedback

We consider a status updating system where having timely knowledge about the information source at the destination (monitor) is of utmost importance. By utilizing the age of information (AoI) metric, the freshness of status update over an erasure channel is investigated. Due to the erasure nature of the update transmission, an error-free feedback channel from the monitor to the source is necessary for reducing AoI. Each status update contains $K$ packets which can be sent through the channel one at a time. At each channel use, one status update is available from the information source. Depending on how many packets have been received successfully out of the $K$ packets, we need to decide whether to continue sending the current update or terminate it and start sending the newly generated update. In this paper, we find the optimal failure tolerance when the erasure probability ($\epsilon$) is in the regime $\epsilon \to 0$ and also provide a lower and an upper bound for the average AoI for all erasure probabilities. Moreover, for all $\epsilon$, we provide a lower bound for failure tolerance to minimize peak AoI.