Zero Estimation Cost Strategy for Witsenhausen Counterexample with Causal Encoder

TL;DR

This paper introduces a zero estimation cost scheme for the Witsenhausen counterexample that reduces power consumption by transforming system states into efficiently communicable sequences, with a broader non-zero cost scheme also proposed.

Contribution

It presents a novel zero estimation cost scheme based on coordination coding for the Witsenhausen problem, improving power efficiency in state communication.

Findings

Significant power reduction for zero-estimation-cost state reconstruction

The Non-ZEC scheme acts as a time-sharing mechanism

Block coding gain enhances the power-estimation trade-off

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.