[Paper Review] Topological Interference Management with Confidential Messages

Jean de Dieu Mutangana, Ravi Tandon|arXiv (Cornell University)|Oct 27, 2020

Coding theory and cryptography4 citations

TL;DR

This paper introduces the Topological Interference Management with Confidential Messages (TIM-CM) framework, where transmitters operate without channel state information but know only the network topology, aiming to achieve reliable and confidential communication. It proposes two schemes—secure partitioning and secure independent sets—and establishes necessary and sufficient conditions for positive symmetric secure degrees of freedom (SDoF), fully characterizing optimal SDoF for all 2- and 3-user topologies with tight outer bounds.

ABSTRACT

The topological interference management (TIM) problem refers to the study of the K-user partially connected interference networks with no channel state information at the transmitters (CSIT), except for the knowledge of network topology. In this paper, we study the TIM problem with confidential messages (TIM-CM), where message confidentiality must be satisfied in addition to reliability constraints. In particular, each transmitted message must be decodable at its intended receiver and remain confidential at the remaining (K-1) receivers. Our main contribution is to present a comprehensive set of results for the TIM-CM problem by studying the symmetric secure degrees of freedom (SDoF). To this end, we first characterize necessary and sufficient conditions for feasibility of positive symmetric SDoF for any arbitrary topology. We next present two achievable schemes for the TIM-CM problem: For the first scheme, we use the concept of secure partition and, for the second one, we use the concept of secure independent sets. We also present outer bounds on symmetric SDoF for any arbitrary network topology. Using these bounds, we characterize the optimal symmetric SDoF of all K=2-user and K=3-user network topologies.

Motivation & Objective

• To address the challenge of achieving reliable and confidential communication in partially connected K-user interference networks with no channel state information at transmitters (CSIT).
• To extend the topological interference management (TIM) framework to incorporate message confidentiality constraints.
• To characterize the symmetric secure degrees of freedom (SDoF) for arbitrary network topologies under secrecy and reliability constraints.
• To develop achievable schemes that ensure intended receivers decode messages while all other receivers remain ignorant.

Proposed method

• Introduces the TIM-CM problem by combining topological interference management with physical layer security, where transmitters know only the network topology and must satisfy both reliability and confidentiality.
• Proposes a secure partitioning scheme that partitions interfering signals to ensure secrecy, leveraging structured signal alignment under topology constraints.
• Develops a secure independent set scheme based on graph-theoretic concepts, where transmitters align signals in a way that preserves secrecy across unintended receivers.
• Derives outer bounds on symmetric SDoF using entropy and mutual information inequalities, particularly leveraging the Markov chain and conditioning properties.
• Uses a permutation-based signal generator condition to analyze interference alignment and secrecy, ensuring that messages remain confidential under decodability constraints.
• Applies a recursive entropy decomposition technique to bound the uncertainty at unintended receivers, proving the feasibility of positive SDoF under specific topological conditions.

Experimental results

Research questions

• RQ1 Under what topological conditions can positive symmetric secure degrees of freedom be achieved in a K-user partially connected interference network with no CSIT?
• RQ2 How can interference be managed securely when transmitters lack instantaneous or even statistical channel state information?
• RQ3 What are the fundamental limits of secure degrees of freedom in TIM-CM, and how do they depend on network topology?
• RQ4 Can secure communication be achieved via structured signal alignment without relying on channel state information?
• RQ5 How do the proposed schemes—secure partitioning and secure independent sets—compare in terms of achievable SDoF across different topologies?

Key findings

• The paper establishes necessary and sufficient conditions for the feasibility of positive symmetric SDoF in any arbitrary K-user TIM-CM network topology.
• For all 2-user and 3-user network topologies, the optimal symmetric secure degrees of freedom are fully characterized using derived outer bounds and achievable schemes.
• The secure partitioning scheme achieves positive symmetric SDoF by strategically grouping interfering signals to limit information leakage at unintended receivers.
• The secure independent set scheme achieves positive SDoF by exploiting graph-theoretic independence structures in the interference topology.
• Outer bounds on symmetric SDoF are derived using entropy inequalities and Markov chain arguments, proving tightness for 2- and 3-user cases.
• The results show that even without CSIT, secure degrees of freedom can be achieved when network topology provides sufficient structural asymmetry to enable secure interference alignment.