[Paper Review] Secrecy Outage Capacity of Fading Channels

Onur Güngör, Jian Tan+3 more|arXiv (Cornell University)|Dec 13, 2011

Wireless Communication Security Techniques12 references4 citations

TL;DR

This paper introduces the concept of secrecy outage capacity for fading channels, characterizing the fundamental limits of secure communication under delay constraints. It proposes a key-buffering scheme using opportunistic key exchange and power control to achieve non-zero secrecy rates even when the eavesdropper's channel is stronger on average, with sharp capacity bounds derived for both full and partial channel state information at the transmitter.

ABSTRACT

This paper considers point to point secure communication over flat fading channels under an outage constraint. More specifically, we extend the definition of outage capacity to account for the secrecy constraint and obtain sharp characterizations of the corresponding fundamental limits under two different assumptions on the transmitter CSI (Channel state information). First, we find the outage secrecy capacity assuming that the transmitter has perfect knowledge of the legitimate and eavesdropper channel gains. In this scenario, the capacity achieving scheme relies on opportunistically exchanging private keys between the legitimate nodes. These keys are stored in a key buffer and later used to secure delay sensitive data using the Vernam's one time pad technique. We then extend our results to the more practical scenario where the transmitter is assumed to know only the legitimate channel gain. Here, our achievability arguments rely on privacy amplification techniques to generate secret key bits. In the two cases, we also characterize the optimal power control policies which, interestingly, turn out to be a judicious combination of channel inversion and the optimal ergodic strategy. Finally, we analyze the effect of key buffer overflow on the overall outage probability.

Motivation & Objective

• Address the fundamental limits of secure communication for delay-sensitive traffic over fading channels with secrecy constraints.
• Overcome the limitation of zero ergodic secrecy capacity when the eavesdropper's channel is on average stronger than the legitimate channel.
• Characterize the secrecy outage capacity under two scenarios: perfect CSI at the transmitter (legitimate and eavesdropper channels known) and partial CSI (only legitimate channel known).
• Derive optimal power control policies that combine channel inversion and ergodic strategies to maximize secrecy rate under outage constraints.
• Analyze the impact of key buffer overflow on secrecy outage probability, providing bounds on loss probability due to finite buffer size.

Proposed method

• Propose a secrecy outage capacity framework that extends traditional outage capacity to incorporate secrecy constraints.
• Use a key buffer at both transmitter and receiver to store secret key bits generated during favorable channel states (when main channel outperforms eavesdropper channel).
• Apply the one-time pad (Vernam’s cipher) to encrypt delay-sensitive data using stored key bits, avoiding secrecy outages during poor eavesdropper conditions.
• For the full CSI case, derive the optimal power control policy that maximizes secrecy rate under outage constraints using a combination of channel inversion and ergodic power allocation.
• For the partial CSI case, employ privacy amplification techniques to generate secret key bits without eavesdropper CSI, relying only on main channel feedback.
• Model the key queue dynamics and derive asymptotic tail bounds on the key buffer overflow probability using heavy-traffic queueing theory and Loynes' stability results.

Experimental results

Research questions

• RQ1 What is the fundamental limit of secure communication for delay-sensitive traffic over fading channels under a secrecy outage constraint?
• RQ2 How does the secrecy outage capacity change when the transmitter has perfect knowledge of both legitimate and eavesdropper channel gains?
• RQ3 What is the optimal power control policy that maximizes secrecy rate under secrecy outage constraints when only the legitimate channel state is known?
• RQ4 How does key buffer overflow affect the overall secrecy outage probability in a practical system with finite buffer size?
• RQ5 Can non-zero secrecy rates be achieved for delay-limited traffic even when the eavesdropper’s channel is on average stronger than the legitimate channel?

Key findings

• The secrecy outage capacity is strictly positive even when the eavesdropper’s channel is stronger on average, provided that the transmitter can opportunistically exchange keys during favorable channel states.
• For the full CSI case, the optimal power control policy is a hybrid of channel inversion and ergodic power allocation, achieving the highest possible secrecy rate under outage constraints.
• In the partial CSI scenario, privacy amplification enables secret key generation without eavesdropper CSI, and the resulting secrecy outage capacity is characterized via a finite buffer model.
• The key buffer overflow probability is bounded using heavy-traffic queueing theory, showing that the loss ratio decays exponentially with buffer size under optimal power control.
• The asymptotic tail distribution of the key queue converges to an exponential distribution under heavy-traffic conditions, with the decay rate depending on the excess rate above the secrecy capacity.
• The derived secrecy outage capacity and power control policies are tight and generalize prior results on delay-limited secrecy capacity, providing sharp fundamental limits for practical systems.