面向及时状态更新的采样器与压缩器联合设计：年龄-失真折中
Joint Design of Sampler and Compressor for Timely Status Updates: Age-Distortion Tradeoff
AI总结：
本文研究及时状态更新的联合采样与压缩系统，提出联合设计采样器、量化器和编码器以在满足MSE失真约束下最小化AoI，并证明零等待采样、均匀量化与实值AoI最优编码策略的组合渐近最优，且AoI与对数MSE失真呈斜率为-3/4的渐近线性关系。
摘要：
我们考虑一个用于及时状态更新的联合采样与压缩系统。样本被采集、量化并编码为二进制序列，发送至目的地。我们构建了一个优化问题，以联合设计采样器、量化器和编码器，在满足样本的均方误差（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、均匀量化和实值AoI最优编码策略共同为该问题提供了渐近最优解，即随着平均失真趋近于零，该组合渐近地实现最小AoI。此外，我们证明该解的AoI相对于对数MSE失真呈渐近线性关系，斜率为$-\ rac{3}{4}$。我们还表明，实值Shannon编码策略足以渐近地实现最优性能。数值仿真验证了该分析。
英文摘要：
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.
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