Timely Updates over an Erasure Channel

Using an age of information (AoI) metric, we examine the transmission of coded updates through a binary erasure channel to a monitor/receiver. %Coded redundancy is employed to ensure the timely delivery of codupdate packets. We start by deriving the average status update age of an infinite incremental redundancy (IIR) system in which the transmission of a $k$-symbol update continues until $k$ symbols are received. This system is then compared to a fixed redundancy (FR) system in which each update is transmitted as an $n$ symbol packet and the packet is successfully received if and only if at least $k$ symbols are received. If fewer than $k$ symbols are received, the update is discarded. Unlike the IIR system, the FR system requires no feedback from the receiver. For a single monitor system, we show that tuning the redundancy to the symbol erasure rate enables the FR system to perform as well as the IIR system. As the number of monitors is increased, the FR system outperforms the IIR system that guarantees delivery of all updates to all monitors.