[Paper Review] Adding Common Randomness Can Remove the Secrecy Constraints in Communication Networks

Fan Li, Jinyuan Chen|arXiv (Cornell University)|Jul 10, 2019

Wireless Communication Security Techniques29 references4 citations

TL;DR

This paper demonstrates that adding common randomness at transmitters can completely eliminate the generalized degrees-of-freedom (GDoF) penalty imposed by secrecy constraints in three fundamental wireless networks: the two-user symmetric Gaussian interference channel with confidential messages, the symmetric Gaussian wiretap channel with a helper, and the two-user symmetric Gaussian multiple access wiretap channel. By using a novel Markov chain-based interference neutralization scheme, common randomness effectively jams eavesdroppers without degrading legitimate receivers, achieving the same GDoF as the non-secrecy counterpart.

ABSTRACT

In communication networks secrecy constraints usually incur an extra limit in capacity or generalized degrees-of-freedom (GDoF), in the sense that a penalty in capacity or GDoF is incurred due to the secrecy constraints. Over the past decades a significant amount of effort has been made by the researchers to understand the limits of secrecy constraints in communication networks. In this work, we focus on how to remove the secrecy constraints in communication networks, i.e., how to remove the GDoF penalty due to secrecy constraints. We begin with three basic settings: a two-user symmetric Gaussian interference channel with confidential messages, a symmetric Gaussian wiretap channel with a helper, and a two-user symmetric Gaussian multiple access wiretap channel. Interestingly, in this work we show that adding common randomness at the transmitters can totally remove the penalty in GDoF or GDoF region of the three settings considered here. The results reveal that adding common randomness at the transmitters is a powerful way to remove the secrecy constraints in communication networks in terms of GDoF performance. Common randomness can be generated offline. The role of the common randomness is to jam the information signal at the eavesdroppers, without causing too much interference at the legitimate receivers. To accomplish this role, a new method of Markov chain-based interference neutralization is proposed in the achievability schemes utilizing common randomness. From the practical point of view, we hope to use less common randomness to remove secrecy constraints in terms of GDoF performance. With this motivation, for most of the cases we characterize the minimal GDoF of common randomness to remove secrecy constraints, based on our derived converses and achievability.

Motivation & Objective

• To address the fundamental problem of secrecy constraints that reduce capacity and GDoF in wireless networks.
• To investigate whether and how common randomness can remove the GDoF penalty caused by secrecy constraints.
• To characterize the minimal amount of common randomness required to achieve this removal in terms of GDoF performance.
• To develop a practical and efficient signaling scheme that leverages common randomness to neutralize eavesdropper interference without harming legitimate receivers.

Proposed method

• Proposes a Markov chain-based interference neutralization technique where each interference signal is canceled by a subsequent signal generated from the same common randomness.
• Designs transmit signals using common randomness to create directional jamming at eavesdroppers while ensuring residual interference at legitimate receivers is below noise floor.
• Employs a structured signaling framework where common randomness generates sequences of signals with controlled amplitudes and phases to achieve interference cancellation in a chain-like manner.
• Uses lattice-based signal design and quantization to enable reliable decoding of common randomness symbols at receivers, ensuring minimal error probability as power increases.
• Applies converse arguments and minimum distance analysis to bound estimation error and establish reliability of signal recovery.
• Derives bounds on the required GDoF of common randomness through probabilistic analysis of channel coefficient outage sets, ensuring robustness for almost all channel realizations.

Experimental results

Research questions

• RQ1 Can common randomness at transmitters eliminate the GDoF penalty caused by secrecy constraints in interference and wiretap channels?
• RQ2 What is the minimal GDoF of common randomness required to achieve full secrecy constraint removal in these networks?
• RQ3 How can interference be effectively neutralized at eavesdroppers without degrading legitimate receiver performance?
• RQ4 Can a structured signaling scheme based on Markov chains and lattice coding achieve reliable communication and jamming under secrecy constraints?
• RQ5 How does the performance of the proposed scheme scale with transmit power, and what is the outage probability for reliable decoding?

Key findings

• Adding common randomness at transmitters completely removes the GDoF penalty in the two-user symmetric Gaussian interference channel with confidential messages, restoring the original 'W'-shaped GDoF region.
• For the symmetric Gaussian wiretap channel with a helper, common randomness enables secure communication at the same GDoF as the non-secrecy case.
• In the two-user symmetric Gaussian multiple access wiretap channel, the proposed scheme achieves the same sum GDoF as the non-secrecy baseline, proving full removal of the secrecy penalty.
• The minimum distance between decoded signal combinations is bounded below by $ \kappa P^{\epsilon/2} $ for almost all channel coefficients, ensuring reliable detection as $ P \to \infty $.
• The Lebesgue measure of the outage set where this bound fails is at most $ 1792\kappa \cdot P^{-\epsilon/2} $, proving near-universal reliability.
• The error probability for decoding common randomness symbols and confidential messages vanishes as power increases, confirming asymptotic reliability of the scheme.