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.

Given a source that produces a letter every Tsseconds and an erasure channel that can be used every Tcseconds, we ask what is the coding strategy that minimizes the time-average "age of information" that an observer of the channel output incurs. We will see that one has to distinguish the cases when the source and channel-input alphabets have equal or different size. In the first case, we show that a trivial coding strategy is optimal and a closed form expression for the age may be derived. In the second, we use random coding argument to bound the average age and show that the average age achieved using random codes converges to the optimal average age as the source alphabet becomes large.

Consider a stream of status updates generated by a source, where each update is of one of two types: priority or ordinary; these updates are to be transmitted through a network to a monitor. We analyze a transmission policy that treats updates depending on their content: ordinary updates are served in a first-come first-served fashion, whereas the priority updates receive preferential treatment. An arriving priority update discards and replaces any currently-in-service priority update, and preempts (with eventual resume) any ordinary update. We model the arrival processes of the two kinds of updates as independent Poisson processes and the service times as two (possibly different rate) exponentials. We find the arrival and service rates under which the system is stable and give closed-form expressions for average peak age and a lower bound on the average age of the ordinary stream. We give numerical results on the average age of both streams and observe the effect of each stream on the age of the other.

We consider a system where randomly generated updates are to be transmitted to a monitor, but only a single update can be in the system at a time. Therefore, the source has to prioritize between the two possible transmission policies: preempting the current update or discarding the new one. We consider Poisson arrivals and general service time, and refer to this system as the M/G/1/1 queue. We start by studying the average status update age and the optimal update arrival rate for these two schemes under general service time distribution. We then apply these results on two practical scenarios in which updates are sent through an erasure channel using (a) an infinite incremental redundancy (IIR) HARQ system and (b) a fixed redundancy (FR) HARQ system. We show that in both schemes the best strategy would be not to preempt. Moreover, we also prove that, from an age point of view, IIR is better than FR.

Using an age of information (AoI) metric, we examine the transmission of coded updates through a binary erasure channel to a monitor/receiver. 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.

We consider a scenario where a monitor is interested in being up to date with respect to the status of some system which is not directly accessible to this monitor. However, we assume a source node has access to the status and can send status updates as packets to the monitor through a communication system. We also assume that the status updates are generated randomly as a Poisson process. The source node can manage the packet transmission to minimize the age of information at the destination node, which is defined as the time elapsed since the last successfully transmitted update was generated at the source. We use queuing theory to model the source-destination link and we assume that the time to successfully transmit a packet is a gamma distributed service time. We consider two packet management schemes: LCFS (Last Come First Served) with preemption and LCFS without preemption. We compute and analyze the average age and the average peak age of information under these assumptions. Moreover, we extend these results to the case where the service time is deterministic.