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

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.