Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Symposium on Communications, Control and Signal Processing

Secrecy capacity of the 2-2-1 gaussian MIMO wire-tap channel

Shabnam Shafiee, Nan Liu, Şennur Ulukuş

Published Mar 1, 2008• 12 citations
Publisher

Abstract

We find the secrecy capacity of the 2-2-1 Gaussian MIMO wire-tap channel, which consists of a transmitter and a receiver with two antennas each, and an eavesdropper with a single antenna. We determine the secrecy capacity of this channel by proposing an achievable scheme and then developing a tight upper bound that meets the proposed achievable secrecy rate. We show that, for this channel, Gaussian signalling in the form of beam-forming is optimal, and no pre-processing of information is necessary.

DOI
10.1109/isccsp.2008.4537221

Related papers

Towards the Secrecy Capacity of the Gaussian MIMO Wire-Tap Channel: The 2-2-1 Channel

Shabnam Shafiee, Nan Liu, Sennur Ulukus

We find the secrecy capacity of the 2-2-1 Gaussian MIMO wiretap channel, which consists of a transmitter and a receiver with two antennas each, and an eavesdropper with a single antenna. We determine the secrecy capacity of this channel by proposing an achievable scheme and then developing a tight upper bound that meets the proposed achievable secrecy rate. We show that, for this channel, Gaussian signalling in the form of beam-forming is optimal, and no pre-processing of information is necessary.

arXiv:0709.3541•IEEE Transactions on Information Theory•Aug 24, 2009•234 citations

Towards the secrecy capacity of the Gaussian MIMO wire-tap channel: The 2-2-1 channel

Shabnam Shafiee, Nan Liu, Şennur Ulukuş

Abstract—We find the secrecy capacity of the 2-2-1 Gaussian MIMO wiretap channel, which consists of a transmitter and a receiver with two antennas each, and an eavesdropper with a single antenna. We determine the secrecy capacity of this channel by proposing an achievable scheme and then developing a tight upper bound that meets the proposed achievable secrecy rate. We show that, for this channel, Gaussian signalling in the form of beam-forming is optimal, and no pre-processing of information is necessary. Index Terms—Information-theoretic security, multiple-input multiple-output (MIMO), multiple antennas, secrecy capacity,

•Jan 1, 2007•267 citations

Precoding Schemes for the Gaussian Wire-Tap Channels

Jun H. Cheng

This paper presents an investigation of channel capacity for the MIMO wire-tap channel. Instantaneous channel state information of the intended receiver and the eavesdropper are assumed to be available at the transmitter. We consider that the eavesdropper employs optimum combining, and investigate the two cases the intended receiver employs. We derive analytical expressions of the average secrecy capacities for these two cases in the high-SNR regime. We compare the performance of the proposed antenna selection scheme to a precoding scheme based on generalized singular value decomposition. Our investigations show that the average secrecy capacities increase with the number of antennas when the eavesdropper is at high SNR.

International Conference on Cyber-Enabled Distributed Computing and Knowledge Discovery (CyberC)•Sep 1, 2015•0 citations

On the Optimal Precoding for MIMO Gaussian Wire-Tap Channels

Arash Khabbazibasmenj, Maksym A. Girnyk, Sergiy A. Vorobyov +2 more

We consider the problem of finding secrecy rate of a multiple-input multiple-output (MIMO) wire-tap channel. A transmitter, a legitimate receiver, and an eavesdropper are all equipped with multiple antennas. The channel states from the transmitter to the legitimate user and to the eavesdropper are assumed to be known at the transmitter. In this contribution, we address the problem of finding the optimal precoder/transmit covariance matrix maximizing the secrecy rate of the given wiretap channel. The problem formulation is shown to be equivalent to a difference of convex functions programming problem and an efficient algorithm for addressing this problem is developed.

arXiv:1411.0103•Nov 1, 2014•8 citations

On the optimal precoding for MIMO Gaussian wire-tap channels

We consider the problem of finding secrecy rate of a multiple-input multiple-output (MIMO) wire-tap channel. A transmitter, a legitimate receiver, and an eavesdropper are all equipped with multiple antennas. The channel states from the transmitter to the legitimate user and to the eavesdropper are assumed to be known at the transmitter. In this contribution, we address the problem of finding the optimal precoder/transmit covariance matrix maximizing the secrecy rate of the given wiretap channel. The problem formulation is shown to be equivalent to a difference of convex functions programming problem and an efficient algorithm for addressing this problem is developed.

•Jan 1, 2013•0 citations

Asymptotic analysis of large MIMO wire-tap channel via replica method

H.S. Wang, G.H. Zeng

Security has been one of the most significant problems surrounding wireless communications, in large part due to the openness of wireless medium where eavesdropping can be easily accomplished. In this work, the prior results on secrecy capacity is extended to the Gaussian MIMO wire-tap channel, where the transmitter, the receiver and illegal wire-tapper all employ multiple antenna technique. A reasonable security criterion is firstly defined for the MIMO wire-tap channel in this paper. Next the secrecy capacity and the achievable rate-equivocation (R, d) region in this multiple antenna scenario are derived. Finally, the analyzed results are validated by the numerical simulations.

IEEE International Symposium on Signal Processing and Information Technology (ISSPIT)•Dec 1, 2007•0 citations
We find the secrecy capacity of the 2-2-1 Gaussian MIMO wire-tap channel, which consists of a transmitter and a receiver with two antennas each, and an eavesdropper with a single antenna. We determine the secrecy capacity of this channel by proposing an achievable scheme and then developing a tight upper bound that meets the proposed achievable secrecy rate. We show that, for this channel, Gaussian signalling in the form of beam-forming is optimal, and no pre-processing of information is necessary.
We find the secrecy capacity of the 2-2-1 Gaussian MIMO wiretap channel, which consists of a transmitter and a receiver with two antennas each, and an eavesdropper with a single antenna. We determine the secrecy capacity of this channel by proposing an achievable scheme and then developing a tight upper bound that meets the proposed achievable secrecy rate. We show that, for this channel, Gaussian signalling in the form of beam-forming is optimal, and no pre-processing of information is necessary.
Abstract—We find the secrecy capacity of the 2-2-1 Gaussian MIMO wiretap channel, which consists of a transmitter and a receiver with two antennas each, and an eavesdropper with a single antenna. We determine the secrecy capacity of this channel by proposing an achievable scheme and then developing a tight upper bound that meets the proposed achievable secrecy rate. We show that, for this channel, Gaussian signalling in the form of beam-forming is optimal, and no pre-processing of information is necessary. Index Terms—Information-theoretic security, multiple-input multiple-output (MIMO), multiple antennas, secrecy capacity,
This paper presents an investigation of channel capacity for the MIMO wire-tap channel. Instantaneous channel state information of the intended receiver and the eavesdropper are assumed to be available at the transmitter. We consider that the eavesdropper employs optimum combining, and investigate the two cases the intended receiver employs. We derive analytical expressions of the average secrecy capacities for these two cases in the high-SNR regime. We compare the performance of the proposed antenna selection scheme to a precoding scheme based on generalized singular value decomposition. Our investigations show that the average secrecy capacities increase with the number of antennas when the eavesdropper is at high SNR.
We consider the problem of finding secrecy rate of a multiple-input multiple-output (MIMO) wire-tap channel. A transmitter, a legitimate receiver, and an eavesdropper are all equipped with multiple antennas. The channel states from the transmitter to the legitimate user and to the eavesdropper are assumed to be known at the transmitter. In this contribution, we address the problem of finding the optimal precoder/transmit covariance matrix maximizing the secrecy rate of the given wiretap channel. The problem formulation is shown to be equivalent to a difference of convex functions programming problem and an efficient algorithm for addressing this problem is developed.
We consider the problem of finding secrecy rate of a multiple-input multiple-output (MIMO) wire-tap channel. A transmitter, a legitimate receiver, and an eavesdropper are all equipped with multiple antennas. The channel states from the transmitter to the legitimate user and to the eavesdropper are assumed to be known at the transmitter. In this contribution, we address the problem of finding the optimal precoder/transmit covariance matrix maximizing the secrecy rate of the given wiretap channel. The problem formulation is shown to be equivalent to a difference of convex functions programming problem and an efficient algorithm for addressing this problem is developed.
Security has been one of the most significant problems surrounding wireless communications, in large part due to the openness of wireless medium where eavesdropping can be easily accomplished. In this work, the prior results on secrecy capacity is extended to the Gaussian MIMO wire-tap channel, where the transmitter, the receiver and illegal wire-tapper all employ multiple antenna technique. A reasonable security criterion is firstly defined for the MIMO wire-tap channel in this paper. Next the secrecy capacity and the achievable rate-equivocation (R, d) region in this multiple antenna scenario are derived. Finally, the analyzed results are validated by the numerical simulations.