AI summaryⓘ
The authors study a system where updates about a physical process are sent to a receiver using different fixed transmission options that vary in blocklength (data size) and error probability. They focus on creating fixed schedules without feedback to keep the information as fresh as possible, measured by average Age of Information (AoI) and exponential AoI. They find that using a single fixed blocklength for all transmissions is usually not the best approach, especially when considering the exponential AoI metric. The authors use mathematical tools to determine when using one blocklength is optimal and when mixing blocklengths in a schedule is better, providing formulas and conditions for these cases. Their work includes examples with practical codebooks, suggesting their findings can help design better update systems in real communications.
Age of Information (AoI)Exponential Age of InformationBlocklengthError ProbabilityDeterministic SchedulesMarkov Decision ProcessDinkelbach's AlgorithmTransmission SchemeLDPC CodebookStationary Randomized Policies
Abstract
In this paper, we consider a general status update system, consisting of a source at which a physical process is monitored and a receiver. For transmission of status updates, a discrete set of blocklength error probability tuples is available. A typical example is a communication system with a fixed set of modulation and coding schemes. We assume that no feedback channel for acknowledgments exists and thus investigate the problem of constructing deterministic schedules for the status updating system. The average Age of Information (AoI) and average exponential AoI are appropriate performance metrics to capture the freshness of information. Interestingly, a static blocklength is shown to be suboptimal in general. While for the average AoI the gains that can be achieved by using a non-trivial periodic schedule are relatively small, they are significant for the average exponential AoI. Motivated by this, we prove conditions for single-blocklength optimality when two blocklengths are available. To achieve this, we use a Dinkelbach-like approach to reformulate the problem as an infinite-state transient average-cost Markov Decision Process and apply careful bounding techniques to derive the optimality conditions. As a converse, we analyze stationary randomized policies to certify the parameter regions where a non-trivial deterministic schedule outperforms the best constant schedule. Extensions to the case with more than two transmission lengths are provided. Numerical results show that the derived conditions cover a large portion of the parameter space and suggest that the optimality conditions for a constant schedule with the shorter blocklength, while sufficient, may also be necessary. As an example, we apply the results to the problem of age-optimal transmission with a small LDPC codebook, which illustrates the practical applicability.