Distortion Minimization with Age of Information and Cost Constraints

TL;DR

This paper addresses the challenge of minimizing distortion in real-time source monitoring over wireless channels by balancing age of information and processing costs, using a Markov chain approach.

Contribution

It introduces a stationary randomized policy framework for joint AoI and distortion optimization, demonstrating lumpability of the Markov chain for analytical tractability.

Findings

Derived an expression for expected AoI under the proposed policy.

Proved the lumpability of the Markov chain considering AoI and distortion.

Provided insights into the trade-offs between distortion, AoI, and processing costs.

Abstract

We consider a source monitoring a stochastic process with a transmitter to transmit timely information through a wireless ON/OFF channel to a destination. We assume that once the source samples the data, the sampled data has to be processed to identify the state of the stochastic process. The processing can take place either at the source before transmission or after transmission at the destination. The objective is to minimize the distortion while keeping the age of information (AoI) that measures the timeliness of information under a certain threshold. We use a stationary randomized policy (SRP) framework to solve the formulated problem. We show that the two-dimensional discrete-time Markov chain considering the AoI and instantaneous distortion as the state is lumpable and we obtain the expression for the expected AoI under the SRP.