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 controlcommunication approach that transforms the system state into a sequence that can be efficiently communicated using block coding. The noncausal decoder receives sufficient information for reconstructing the system state perfectly, enabling the achievable estimation cost to be zero. Numerical results show that our approach significantly reduces the power budget 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 Witsenhausen's original 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.
Part of ISBN 9798331543990
QC 20251202