具有非因果状态估计器的向量值Witsenhausen反例的最优高斯策略
Optimal Gaussian Strategies for Vector-valued Witsenhausen Counterexample with Non-causal State Estimator
AI总结：
研究向量值Witsenhausen模型，刻画第一决策者功率成本与第二决策者估计成本的最优权衡，发现时分仿射策略为最佳线性方案，但非因果块编码方案性能更优。
摘要：
在本研究中，我们研究了一个向量值Witsenhausen模型，其中第二个决策者（DM）在获取观测向量后选择估计向量。第一个DM因果地行动，而第二个DM非因果地估计。当向量长度增长时，我们通过单字母表达式刻画了第一个DM的功率成本与第二个DM的估计成本之间的最优权衡。本文表明，最佳线性方案是通过在两个仿射策略之间使用时分方法实现的，这与Witsenhausen在1968年的解的凸包络相一致。此外，Witsenhausen的两点策略以及Grover和Sahai在2010年提出的两个设备均非因果操作的方案，优于我们的最佳线性方案。因此，使用块编码方案获得的增益仅在所有DM非因果操作时才可实现。
英文摘要：
In this study, we investigate a vector-valued Witsenhausen model where the second decision maker (DM) acquires a vector of observations before selecting a vector of estimations. Here, the first DM acts causally whereas the second DM estimates non-causally. When the vector length grows, we characterize, via a single-letter expression, the optimal trade-off between the power cost at the first DM and the estimation cost at the second DM. In this paper, we show that the best linear scheme is achieved by using the time-sharing method between two affine strategies, which coincides with the convex envelope of the solution of Witsenhausen in 1968. Here also, Witsenhausen's two-point strategy and the scheme of Grover and Sahai in 2010 where both devices operate non-causally, outperform our best linear scheme. Therefore, gains obtained with block-coding schemes are only attainable if all DMs operate non-causally.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
