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arXiv · 2501.18308

Zero Estimation Cost Strategy for Witsenhausen Counterexample with Causal Encoder

Mengyuan Zhao·Tobias J. Oechtering·Maël Le Treust
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Abstract

We propose a zero estimation cost (ZEC) scheme for causal-encoding noncausal-decoding vector-valued Witsenhausen counterexample based on the coordination coding result. In contrast to source coding, our goal is to communicate a controlled system state. The introduced ZEC scheme is a joint control-communication approach that transforms the system state into a sequence that can be efficiently communicated using block coding. Numerical results show that our approach significantly reduces the power required for achieving zero-estimation-cost state reconstruction at the decoder. In the second part, we introduce a more general non-zero estimation cost (Non-ZEC) scheme. We observe numerically that the Non-ZEC scheme operates as a time-sharing mechanism between the two-point strategy and the ZEC scheme. Overall, by leveraging block-coding gain, our proposed methods substantially improve the power-estimation trade-off for Witsenhausen counterexample.

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Mengyuan Zhao, Tobias J. Oechtering, Maël Le Treust. 2025-01-30. Zero Estimation Cost Strategy for Witsenhausen Counterexample with Causal Encoder. https://arxiv.org/abs/2501.18308

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