Covert Communication in the Presence of an Uninformed Jammer (1608.00698v3)

Abstract: Recent work has established that when transmitter Alice wishes to communicate reliably to recipient Bob without detection by warden Willie, with additive white Gaussian noise (AWGN) channels between all parties, communication is limited to $\mathcal{O}(\sqrt{n})$ bits in $n$ channel uses. However, this assumes Willie has an accurate statistical characterization of the channel. When Willie has uncertainty about such and his receiver is limited to a threshold test on the received power, Alice can transmit covertly with a power that does not decrease with $n$, thus conveying $\mathcal{O}(n)$ bits covertly and reliably in $n$ uses of an AWGN channel. Here, we consider covert communication of $\mathcal{O}(n)$ bits in $n$ channel uses while generalizing the environment and removing any restrictions on Willie's receiver. We assume an uninformed "jammer" is present to help Alice, and we consider AWGN and block fading channels. In some scenarios, Willie's optimal detector is a threshold test on the received power. When the channel between the jammer and Willie has multiple fading blocks per codeword, a threshold test on the received power is not optimal. However, we establish that Alice can remain covert with a transmit power that does not decrease with $n$ even when Willie employs an optimal detector.

• The paper demonstrates that leveraging an uninformed jammer allows covert transmission to scale to O(n) bits by effectively masking signals.
• It establishes that, even with fading channels, a simple power detector remains optimal for the adversary, ensuring robust performance.
• The study extends covert communication theory beyond the square root law, paving the way for resilient real-world communication systems.

Covert Communication in the Presence of an Uninformed Jammer: An Overview

The paper "Covert Communication in the Presence of an Uninformed Jammer" explores the feasibility and mechanisms of covert communication between two parties, Alice and Bob, in the presence of an adversarial warden, Willie, and assisted by an uninformed jammer. Covert communication, unlike traditional secure communication that focuses on encrypting message content, emphasizes concealing the existence of communication itself from external detection. This requirement is particularly salient in situations involving oppressive surveillance, military operations, or any environment where revealing the mere occurrence of communication can have severe consequences.

The foundational concept underpinning covert communication is the square root law (SRL), asserting that when communicating over additive white Gaussian noise (AWGN) channels, the number of bits that can be transmitted covertly scales as $\mathcal{O}(\sqrt{n})$ for $n$ uses of the channel. This constraint is predominately due to Willie having an accurate statistical model of his observations, limiting Alice's ability to remain undetected. However, this work shifts focus onto scenarios where Willie faces uncertainty regarding his channel model, particularly the noise levels, due to the unpredictable interference from an uninformed jammer.

The notion explored in this paper is the utilization of a jammer, which, while being uninformed of the exact communication occurrence between Alice and Bob, emits noise that masks the covert signals to Willie. A notable distinction from previous studies is that, contrary to the case where Willie's receiver is restricted to a threshold test for detection, the jammer's presence allows Alice to operate under a higher transmit power regime that does not diminish with increasing channel uses, thereby enabling the transmission of $\mathcal{O}(n)$ bits covertly.

Key Contributions

1. Uninformed Jammer Interaction: The paper introduces the concept of using an uninformed jammer that remains oblivious to instances of Alice's transmissions but effectively masks these communications to Willie. This eliminates the necessity for the jammer to be synchronized or coordinated with Alice, thus simplifying practical implementations.
2. Optimal Detection at Willie: A significant theoretical result from the paper is establishing the optimal detection strategy for Willie under various channel conditions. For AWGN channels and when the jammer-to-Willie channel is fading, the optimality of a power detector is retained even when the jammer's interference levels vary, adding robustness to Alice's transmission strategy.
3. Positive Rate Covert Communication: Demonstrating conditions under which Alice can covertly transmit $\mathcal{O}(n)$ bits, the paper significantly enhances the capabilities over the conventional SRL restrictions. This positive rate of information transfer is possible when Willie cannot accurately model the noise statistics he encounters, which the jammer effectively introduces.
4. Extension to Fading Channels: The analysis extends beyond simple AWGN and incorporates block fading models, reflecting more realistic and complex wireless environments. Under the single fading block per slot scenario, where the jammer's signal introduces irreversible distortions to Willie's received signal model, the results generalize but still support the increased covert throughput.

Implications and Future Directions

This research advances the understanding of the interplay between jamming and covert communication, suggesting that strategic interference can safeguard against detection while maintaining reliable message delivery. Practically, this insight finds use in mobile communication, tactical military networks, and civilian applications in regions with high censorship.

Future directions may involve exploring more sophisticated jammer behaviors, dynamic channels, and quantifying performance metrics considering finite-length keys shared between communicating parties. Additionally, transitioning these theoretical findings into real-world systems necessitates tackling the challenges posed by synchronization issues and environmental unpredictability.

In summary, the paper delineates a pathway towards enhancing covert communication by capitalizing on jamming uncertainty, laying the foundation for constructing resilient communication protocols in adversarial scenarios.