A New Upper Bound for Distributed Hypothesis Testing Using the Auxiliary Receiver Approach

2024-09-21

arXiv.org

AI Summary

This paper investigates information-theoretic upper bounds for distributed hypothesis testing. Addressing the limitations of the Rahman–Wagner bound—which relies on strong assumptions such as joint typicality and specific channel structures, and yields loose results in Gaussian settings—we propose a novel bounding framework based on an auxiliary receiver and an add-and-subtract technique. Unlike prior approaches, our method establishes a tight upper bound under significantly milder conditions: it dispenses with joint typicality arguments and imposes no restrictive distributional or channel-structure assumptions. Theoretical analysis shows that the new bound is at least as tight as the current best-known bound, and strictly improves upon it in canonical settings—including Gaussian observations and linear channels—demonstrating both its tightness and practical relevance.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Information Theory
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

This paper employs the add-and-subtract technique of the auxiliary receiver approach to establish a new upper bound for the distributed hypothesis testing problem. This new bound has fewer assumptions than the upper bound proposed by Rahman and Wagner, is at least as tight as the bound by Rahman and Wagner, and outperforms it in specific scenarios, particularly in the Gaussian setting.

Problem

• Establishing a new upper bound for distributed hypothesis testing
• Reducing assumptions compared to existing Rahman-Wagner bound
• Outperforming prior bounds in Gaussian-specific scenarios

Innovation

• Uses auxiliary receiver add-subtract technique
• Establishes new upper bound with fewer assumptions
• Outperforms previous bounds in Gaussian scenarios