Zero Estimation Cost Strategy for Witsenhausen Counterexample with Causal Encoder

2025-01-30

AI Summary

This paper addresses the joint optimization of state reconstruction power consumption and estimation accuracy for the vector Witsenhausen counterexample under causal encoding and noncausal decoding. Method: We propose a novel Zero Estimation Cost (ZEC) strategy, achieving zero-estimation-error state reconstruction at the decoder for the first time; theoretically establish that conventional nonzero-cost schemes are time-sharing combinations of ZEC and two-point strategies; and develop a unified control–communication framework grounded in coordinated coding theory and block-coding gain, validated via numerical optimization and simulation. Contribution/Results: ZEC substantially lowers the power–estimation trade-off frontier: across multiple parameter configurations, it significantly reduces transmitter power relative to baseline schemes while strictly guaranteeing zero estimation error—establishing a provably optimal paradigm for low-power, high-accuracy state sensing.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Learning to Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Large-scale security measurements

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.

Problem

• Complex Systems
• Energy Efficiency
• Information Precision

Innovation

• Zero Estimation Cost (ZEC) scheme
• Energy-efficient coding and decoding
• Trade-off between energy consumption and information accuracy