[Paper Review] Secure Transmission on the Two-hop Relay Channel with Scaled Compute-and-Forward

Zhijie Ren, Jasper Goseling+2 more|arXiv (Cornell University)|Sep 14, 2015

Wireless Communication Security Techniques12 references3 citations

TL;DR

This paper proposes two novel secure transmission schemes for a two-hop relay channel with an untrusted relay using scaled compute-and-forward, leveraging random binning and lattice chain codes to achieve secrecy. In high SNR or low relay power regimes, both schemes achieve the secrecy rate upper bound, approaching within 0.5 bits/channel use of the capacity without secrecy constraints.

ABSTRACT

In this paper, we consider communication on a two-hop channel, in which a source wants to send information reliably and securely to the destination via a relay. We consider both the untrusted relay case and the external eavesdropper case. In the untrusted relay case, the relay behaves as an eavesdropper and there is a cooperative node which sends a jamming signal to confuse the relay when the it is receiving from the source. We propose two secure transmission schemes using the scaled compute-and-forward technique. One of the schemes is based on a random binning code and the other one is based on a lattice chain code. It is proved that in either the high Signal-to-Noise-Ratio (SNR) scenario and/or the restricted relay power scenario, if the destination is used as the jammer, both schemes outperform all existing schemes and achieve the upper bound. In particular, if the SNR is large and the source, the relay, and the cooperative jammer have identical power and channels, both schemes achieve the upper bound for secrecy rate, which is merely $1/2$ bit per channel use lower than the channel capacity without secrecy constraints. We also prove that one of our schemes achieves a positive secrecy rate in the external eavesdropper case in which the relay is trusted and there exists an external eavesdropper.

Motivation & Objective

• Address the challenge of secure communication in a two-hop relay channel where the relay is untrusted and may eavesdrop on the source's transmission.
• Overcome the limitations of prior schemes that fail to achieve positive secrecy rates under certain channel conditions.
• Design new transmission schemes that exploit the compute-and-forward framework with scaling to enable reliable and secure communication.
• Achieve the secrecy rate upper bound in high SNR and restricted relay power scenarios, outperforming existing methods.
• Extend the framework to handle external eavesdroppers when the relay is trusted, ensuring positive secrecy rates.

Proposed method

• Introduce a modified compute-and-forward technique called 'scaled compute-and-forward' to enable reliable decoding of linear combinations at the relay.
• Use random binning code at the source to generate artificial noise, enhancing secrecy against the untrusted relay.
• Implement a lattice chain code at the source to create structured randomness, improving reliability and security.
• Employ a cooperative jammer (the destination) to transmit a jamming signal that confuses the untrusted relay but is known to the destination.
• Apply modulo operations at the relay using lattice structures to preserve the desired signal while suppressing eavesdropping.
• Ensure long-term transmission efficiency by adapting the transmission rate based on relay power constraints, using block-fading models with large K.

Experimental results

Research questions

• RQ1 Can a secure transmission scheme be designed for a two-hop relay channel with an untrusted relay that achieves the secrecy rate upper bound?
• RQ2 How does the performance of the proposed schemes compare to existing cooperative jamming and compute-and-forward schemes in high SNR and low relay power regimes?
• RQ3 What is the achievable secrecy rate when the relay is trusted but an external eavesdropper exists?
• RQ4 Can the proposed schemes maintain positive secrecy rates under asymmetric channel conditions and limited relay power?
• RQ5 What role does the choice of code structure (random binning vs. lattice chain) play in achieving optimal secrecy rates?

Key findings

• In the high SNR regime and under identical power and channel conditions for source, relay, and destination, both schemes achieve a secrecy rate of $ \frac{1}{2}\log_2(1 + \text{SNR}) - \frac{1}{2} $, which is within 0.5 bits/channel use of the compute-and-forward capacity.
• The proposed schemes achieve the secrecy rate upper bound in high SNR and restricted relay power scenarios, outperforming all existing schemes.
• The random binning-based scheme achieves a positive secrecy rate in the external eavesdropper case, where the relay is trusted but an external eavesdropper exists.
• The lattice chain-based scheme achieves the same upper bound in symmetric scenarios, demonstrating robustness and optimality under ideal conditions.
• Both schemes significantly improve secrecy rates across a wide range of channel configurations, especially in high SNR regimes.
• The schemes are scalable to low-power relays by using long-term transmission blocks, ensuring reliable communication even when $ P_R < P_A $.