[Paper Review] Secrecy in Cooperative Relay Broadcast Channels

Ersen Ekrem, Şennur Ulukuş|ArXiv.org|Nov 9, 2008

Wireless Communication Security Techniques19 references4 citations

TL;DR

This paper investigates secrecy in cooperative relay broadcast channels, proposing a novel coding scheme that combines Marton's broadcast channel coding with Cover and El Gamal's compress-and-forward relaying to enhance individual secrecy rates. The key contribution is demonstrating that user cooperation enables both users to achieve positive secrecy rates in Gaussian channels—unlike scalar Gaussian broadcast channels without cooperation, where only one user can have positive secrecy rate.

ABSTRACT

We investigate the effects of user cooperation on the secrecy of broadcast channels by considering a cooperative relay broadcast channel. We show that user cooperation can increase the achievable secrecy region. We propose an achievable scheme that combines Marton's coding scheme for broadcast channels and Cover and El Gamal's compress-and-forward scheme for relay channels. We derive outer bounds for the rate-equivocation region using auxiliary random variables for single-letterization. Finally, we consider a Gaussian channel and show that both users can have positive secrecy rates, which is not possible for scalar Gaussian broadcast channels without cooperation.

Motivation & Objective

• To study the impact of user cooperation on secrecy in broadcast channels, where each user must keep its message confidential from the other.
• To develop an achievable secrecy rate region for a cooperative relay broadcast channel (CRBC) with a single-sided cooperation link.
• To extend prior work on secrecy in broadcast and relay channels by integrating cooperation into the secrecy framework.
• To derive outer bounds on the rate-equivocation region using auxiliary random variables for single-letterization.
• To analyze the Gaussian CRBC case and demonstrate that cooperation enables both users to achieve positive secrecy rates.

Proposed method

• Proposes a hybrid coding scheme combining Marton's dirty-paper coding for broadcast channels and compress-and-forward relaying for relay channels.
• Introduces auxiliary random variables (e.g., $U_1, U_2, V_1, V_2, ilde{Y}_1, ilde{Y}_2$) to model cooperation and compression at the relay users.
• Uses joint typicality decoding at receivers, with user 1 decoding user 2’s message via compressed channel output $\hat{Y}_2$.
• Applies Fano’s lemma and typicality arguments to bound equivocation rates and ensure secrecy.
• Derives outer bounds on the rate-equivocation region using auxiliary random variables to enable single-letter characterization.
• Analyzes the Gaussian CRBC case by evaluating mutual information terms involving $Y_1, Y_2, \hat{Y}_1, \hat{Y}_2$ under Gaussian input assumptions.

Experimental results

Research questions

• RQ1 Can user cooperation in a broadcast channel improve the secrecy rates of both users simultaneously?
• RQ2 How does cooperation affect the equivocation rate at each receiver in a two-user cooperative relay broadcast channel?
• RQ3 What is the achievable secrecy rate region for a CRBC with a single-sided cooperation link?
• RQ4 Can both users achieve positive secrecy rates in a Gaussian CRBC, and if so, how is this enabled by cooperation?
• RQ5 What are the outer bounds on the rate-equivocation region for this channel model?

Key findings

• User cooperation increases the achievable secrecy region in cooperative relay broadcast channels compared to non-cooperative models.
• The proposed scheme achieves positive secrecy rates for both users in a Gaussian CRBC, which is impossible in scalar Gaussian broadcast channels without cooperation.
• The scheme enables user 1 to act as a relay for user 2 by using compress-and-forward relaying, improving user 2’s secrecy rate.
• Outer bounds on the rate-equivocation region are derived using auxiliary random variables, enabling a single-letter characterization.
• For user 1, the equivocation rate is bounded below by $nI(V_1;Y_1,\hat{Y}_2|X_1,U_2) - nI(V_1;Y_2,\hat{Y}_1|X_2,V_2,U_1) - nI(V_1;V_2) - n\epsilon_n$, ensuring secrecy.
• When user 1’s rate is low, the equivocation rate is bounded below by $nR_1 - n\epsilon_n$, confirming secrecy under low-rate transmission.