We consider a joint sampling and compression system for timely status updates. Samples are taken, quantized and encoded into binary sequences, which are sent to the destination. We formulate an optimization problem to jointly design sampler, quantizer and encoder, minimizing the age of information (AoI) on the basis of satisfying a mean-squared error (MSE) distortion constraint of the samples. We prove that the zero-wait sampling, the uniform quantization, and the real-valued AoI-optimal coding policies together provide an asymptotically optimal solution to this problem, i.e., as the average distortion approaches zero, the combination achieves the minimum AoI asymptotically. Furthermore, we prove that the AoI of this solution is asymptotically linear with respect to the log MSE distortion with a slope of $-\frac{3}{4}$. We also show that the real-valued Shannon coding policy suffices to achieve the optimal performance asymptotically. Numerical simulations corroborate the analysis.

翻译：我们考虑面向及时状态更新的联合采样与压缩系统。样本经采集、量化和编码为二进制序列后发送至目的地。我们构建了一个联合设计采样器、量化器和编码器的优化问题，在满足样本均方误差（MSE）失真约束的基础上最小化信息年龄（AoI）。我们证明零等待采样、均匀量化和实数值AoI最优编码策略的组合能够渐近最优地解决该问题，即当平均失真趋近于零时，该组合渐近地达到最小AoI。进一步地，我们证明该解法的AoI与对数MSE失真呈渐近线性关系，斜率为$-\frac{3}{4}$。我们还表明实数值香农编码策略足以渐近地实现最优性能。数值仿真验证了理论分析。