Predictive Semantic Updating for Low-Power IoT over Erasure Channels

Abstract

In low-power IoT systems, a sensing device must convey task-relevant state to a remote receiver under a severe energy budget, so every transmission spent on a refresh competes directly with downstream task accuracy. We study this trade-off in a goal-oriented setting where device and receiver share a lightweight Markov predictor of the semantic dynamics: between updates the receiver acts on the predicted state, and the device decides when to spend energy on a refresh over an unreliable low-power uplink, modeled as an erasure channel with reliable acknowledgment feedback. The performance criterion is the long-run average of the tasklevel Bayes risk plus a per-attempt energy cost. For a binary symmetric semantic source under 0-1 task loss, the joint beliefage state collapses to a scalar prediction age, and we prove that the optimal stationary policy is an age-threshold policy. We derive a closed-form cycle-average cost accounting for retransmissions, together with a discrete optimality condition: refresh when the instantaneous Bayes risk, corrected for the expected penalty of an erased attempt, first exceeds the longrun average cost per slot. Numerical results show the task-losscoupled threshold substantially outperforms periodic and ageonly baselines, tolerates uncertainty in the erasure probability, and stays near-optimal near the true source persistence.