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.

翻译：版本信息年龄（VAoI）通过衡量接收端滞后的版本数量来量化信息新鲜度。本文研究$M$用户上行非正交多址接入（NOMA）系统中VAoI的最小化问题，其中用户维护单数据包缓冲区，传输受平均功率和信息质量约束（由一般失真函数建模）。存在一个基本权衡：每次更新传输更多比特可提升信息质量，但会增加功耗，减少传输机会并增加VAoI；而传输更少比特则产生相反效果。我们将加权和VAoI最小化问题建模为凸优化问题。然而，用户的功率分配通过每信道状态的多址接入容量约束耦合，导致指数级复杂度。为解决此问题，我们提出一种与VAoI无关的平稳随机策略，该策略无需追踪瞬时VAoI即可联合优化调度、比特分配和功率控制，并实现全局最优平均VAoI的可证明2倍近似。利用拉格朗日对偶分解，我们推导出调度概率和功率分配的闭式表达式，并高效确定最优串行干扰消除解码顺序，避免穷举搜索。数值结果表明，NOMA显著优于时分多址（TDMA）：在高功率预算下，NOMA可实现接近零的VAoI，而TDMA饱和于非零值，这与理论分析一致。所提出的通用失真框架通过赋予更新内不同比特不相等重要性，可适应多种比特优先级结构。