论文标题
与因果解码器相反的矢量价值威特森豪森反例的功率估计权衡取舍
Power-Estimation Trade-off of Vector-valued Witsenhausen Counterexample with Causal Decoder
论文作者
论文摘要
研究了著名的Witsenhausen反例设置的矢量值扩展，其中编码器（即第一个决策者）非案例制造商知道并编码I.I.D.状态序列和解码器，即第二个决策者，因果估计临时状态。编码方案是从有限字母的协调问题转移到的，事实证明它是最佳的。高斯设置的扩展是基于非标准弱典型性方法，并且需要仔细的平均估计误差分析，因为临时状态是由解码器估算的。我们提供了一个单书的表达，该表达式表征了维森豪斯电力成本和估计成本之间的最佳权衡。在执行通道输入的双重作用的同时，两个辅助随机变量改善了与解码器的通信，这也控制了系统的状态。有趣的是，我们表明，一对离散和连续的辅助随机变量优于Witsenhausen Two -Twip Taigh Strategy和最佳仿射政策。随机变量的最佳选择仍然未知。
The vector-valued extension of the famous Witsenhausen counterexample setup is studied where the encoder, i.e. the first decision maker, non-causally knows and encodes the i.i.d. state sequence and the decoder, i.e. the second decision maker, causally estimates the interim state. The coding scheme is transferred from the finite alphabet coordination problem for which it is proved to be optimal. The extension to the Gaussian setup is based on a non-standard weak typicality approach and requires a careful average estimation error analysis since the interim state is estimated by the decoder. We provide a single-letter expression that characterizes the optimal trade-off between the Witsenhausen power cost and estimation cost. The two auxiliary random variables improve the communication with the decoder, while performing the dual role of the channel input, which also controls the state of the system. Interestingly, we show that a pair of discrete and continuous auxiliary random variables, outperforms both Witsenhausen two point strategy and the best affine policies. The optimal choice of random variables remains unknown.
