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：我们研究了一种用于定时状态更新的联合采样与压缩系统。样本经采集、量化和编码后形成二进制序列，并传输至目的地。我们提出了一个优化问题，用于联合设计采样器、量化器和编码器，在满足样本均方误差(MSE)失真约束的前提下最小化信息年龄(AoI)。我们证明了零等待采样、均匀量化和实值AoI最优编码策略共同为该问题提供渐近最优解，即当平均失真趋近零时，该组合可渐近实现最小AoI。进一步地，我们证明了该解的AoI与对数MSE失真呈渐近线性关系，斜率为$-\frac{3}{4}$。我们还证明了实值香农编码策略足以渐近达到最优性能。数值仿真结果验证了理论分析。