带反馈的因果向量值 Witsenhausen 反例
Causal Vector-valued Witsenhausen Counterexamples with Feedback
AI总结：
本文利用经验协调编码研究连续向量值 Witsenhausen 反例，刻画三类因果/非因果编解码场景下的可实现代价区域，并证明信道反馈仅在非因果解码时提升性能。
摘要：
我们通过经验协调编码的视角研究连续向量值 Witsenhausen 反例。我们刻画了三种场景下可实现代价对的区域：（i）因果编码与因果解码，（ii）带信道反馈的因果编码与因果解码，以及（iii）带信道反馈的因果编码与非因果解码。在这些向量值版本的问题中，最优编码方案必须依赖分时策略，因为在标量版本问题中，可实现代价对的区域可能不是凸的。我们考察了当编码器为因果、解码器为因果或非因果时信道反馈的作用，并证明仅当解码器为非因果时，反馈才能提升性能。
英文摘要：
We study the continuous vector-valued Witsenhausen counterexample through the lens of empirical coordination coding. We characterize the region of achievable pairs of costs in three scenarios: (i) causal encoding and causal decoding, (ii) causal encoding and causal decoding with channel feedback, and (iii) causal encoding and noncausal decoding with channel feedback. In these vector-valued versions of the problem, the optimal coding schemes must rely on a time-sharing strategy, since the region of achievable pairs of costs might not be convex in the scalar version of the problem. We examine the role of the channel feedback when the encoder is causal and the decoder is either causal or non-causal, and we show that feedback improves the performance, only when the decoder is non-causal.
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