Key Agreement over an Interference Channel with Noiseless Feedback: Achievable Region & Distributed Allocation

TL;DR

This paper explores secret key agreement in a wireless interference channel with noiseless feedback, proposing achievable regions, analyzing power allocation schemes, and highlighting the potential for cooperative strategies to improve key rates.

Contribution

It introduces an information-theoretic framework for secret key establishment over interference channels with feedback, including a game-theoretic analysis of power allocation impacts.

Findings

Achievable secret key rate regions are characterized for discrete memoryless interference channels.

Performance of different power allocation schemes is analyzed in Gaussian interference channels.

Nash equilibrium outcomes are shown to be inefficient, suggesting benefits of cooperation.

Abstract

Secret key establishment leveraging the physical layer as a source of common randomness has been investigated in a range of settings. We investigate the problem of establishing, in an information-theoretic sense, a secret key between a user and a base-station (BS) (more generally, part of a wireless infrastructure), but for two such user-BS pairs attempting the key establishment simultaneously. The challenge in this novel setting lies in that a user can eavesdrop another BS-user communications. It is thus paramount to ensure the two keys are established with no leakage to the other user, in spite the interference across neighboring cells. We model the system with BS-user communication through an interference channel and user-BS communication through a public channel. We find the region including achievable secret key rates for the general case that the interference channel (IC) is discrete and memoryless. Our results are examined for a Gaussian IC. In this setup, we investigate the performance of different transmission schemes for power allocation. The chosen transmission scheme by each BS essentially affects the secret key rate of the other BS-user. Assuming base stations are trustworthy but that they seek to maximize the corresponding secret key rate, a game-theoretic setting arises to analyze the interaction between the base stations.We model our key agreement scenario in normal form for different power allocation schemes to understand performance without cooperation. Numerical simulations illustrate the inefficiency of the Nash equilibrium outcome and motivate further research on cooperative or coordinated schemes.