Version AoI Optimization under Power and General Distortion Constraints in Uplink NOMA

Abstract: The Version Age of Information (VAoI) quantifies information freshness by measuring the number of versions the receiver lags behind. This paper studies VAoI minimization in an $M$-user uplink non-orthogonal multiple access (NOMA) system where users maintain single-packet buffers and transmissions are constrained by average power and information-quality constraints, modeled by a general distortion function. A fundamental trade-off arises: transmitting more bits per update improves information quality but increases power consumption, reducing transmission opportunities and increasing VAoI, while transmitting fewer bits has the opposite effect. We formulate a weighted-sum VAoI minimization problem as a convex optimization problem. However, users' power allocations are coupled through multiple-access capacity constraints per channel state, leading to exponential complexity. To address this, we develop a VAoI-agnostic stationary randomized policy that jointly optimizes scheduling, bit allocation, and power control without tracking instantaneous VAoI, and achieves a provable 2-approximation to the globally optimal average VAoI. Leveraging Lagrangian dual decomposition, we derive closed-form expressions for the scheduling probabilities and power allocations, and efficiently determine the optimal successive interference cancellation decoding order, avoiding exhaustive search Numerical results show that NOMA significantly outperforms time-division multiple access (TDMA): at high power budgets, NOMA achieves near-zero VAoI, whereas TDMA saturates at a non-zero value, consistent with the analysis. The proposed general distortion framework accommodates diverse bit-priority structures by assigning unequal importance to different bits within an update.