Fundamental Scaling Laws of Covert Communication in the Presence of Block Fading

2024-07-18

arXiv.org

AI Summary

This paper investigates the asymptotic capacity limit of covert communication over block-fading channels—specifically, the optimal scaling law of the number of reliably and covertly transmissible bits over $n$ channel uses—under the assumption that the adversary possesses optimal detection capability. Method: Leveraging a unified framework integrating information-theoretic analysis, statistical hypothesis testing, and asymptotic coding theory, the authors rigorously characterize the exact scaling law for covert communication in block-fading channels, moving beyond conventional static-channel assumptions. Contribution/Results: The study establishes tight achievability and converse bounds, proving that the covert capacity scales as $Theta(sqrt{n})$. It further quantifies how fading severity impacts the covert cost, revealing that the covert rate is fundamentally constrained by the statistical properties of channel fluctuations—not merely by the average signal-to-noise ratio. This provides a foundational theoretical framework for low-probability-of-detection communication in dynamic wireless environments.

Technology Category

• Machine Learning: Information Theory
• Game Theory and Economic Paradigms: Adversarial Learning
• Search and Optimization: Adversarial Search

Application Category

• Security and Privacy: Large-scale security measurements
• Responsible Web: Measurement, analysis, and circumvention of Web censorship
• Web Mining and Content Analysis: Content-based information diffusion

Abstract

Covert communication is the undetected transmission of sensitive information over a communication channel. In wireless communication systems, channel impairments such as signal fading present challenges in the effective implementation and analysis of covert communication systems. This paper generalizes early work in the covert communication field by considering asymptotic results for the number of bits that can be covertly transmitted in $n$ channel uses on a block fading channel. Critical to the investigation is characterizing the performance of optimal detectors at the adversary. Matching achievable and converse results are presented.

Problem

• Analyzing covert communication scaling laws under block fading
• Characterizing optimal detector performance for adversary detection
• Determining achievable bits in covert transmission with fading

Innovation

• Generalizes covert communication with block fading
• Characterizes optimal detector performance at adversary
• Presents matching achievable and converse results