Balancing Data Freshness and Distortion in Real-time Status Updating with Lossy Compression

Real-time status updating plays a pivotal role in automated control, situational awareness, and networked monitoring. However, how to balance data freshness and its distortion due to lossy compression remains open. In this paper, we are interested in the optimal cross-layer policy that minimizes the Age-of-Information (AoI) and distortion simultaneously over an ON/OFF channel. Specifically, we formulate a hierarchical framework to jointly schedule the lossy compression in the application layer and the packet scheduling in the physical layer. In the application layer, we characterize the compression loss using age or forgetting factor weighted distortion. The optimal tradeoff between the age reduction and compression loss is then revealed via convex optimizations. It allows us to further determine how many packets to send in the physical layer based on a probabilistic scheduling policy. To this end, a Constrained Markov Decision Process (CMDP) problem is formulated and solved by Linear Programming (LP), which gives the optimal tradeoff between the data freshness and distortion, as well as, the optimal cross-layer strategy to strike the AoI-distortion tradeoff.