Quantization Rate and AoI-Induced Distortion Trade-off Analysis with Application to Remote Agents

In this paper, we consider a communication system where an agent is receiving update information from a source/controller through a wireless channel. In particular, we investigate the problem of optimal quantization considering a unified distortion measure caused by the quantization and the age of information (AoI). To this end, we propose an upperbound for the quantization distortion given an arbitrarily distributed stochastic process. We then provide a specific example of the above problem where the question is whether to send the commands (actions) or the command generator (action distribution) to the agent. We show that a command generator which is a probability distribution function (PDF) can be a more efficient policy when the cost of communication is of interest. We analyze the existing tradeoff between the rate of change of the update and the channel use. We show that since the faster the process varies, the larger the distortion becomes, it requires a higher quantization rate to meet the same level of distortion.