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

IEEE Transactions on Information Theory

Providing Secrecy With Structured Codes: Two-User Gaussian Channels

Xiang He, Aylin Yener

Published Jan 30, 2014• 68 citations
Publisher

Abstract

Recent results have shown that structured codes can be used to construct good channel codes, source codes, and physical layer network codes for Gaussian channels. For Gaussian channels with secrecy constraints, however, efforts to date rely on Gaussian random codes. In this paper, we advocate that structure in random code generation is useful for providing secrecy as well. In particular, a Gaussian wiretap channel in the presence of a cooperative jammer is studied. Previously, the achievable secrecy rate for this channel was derived using Gaussian signaling, which saturated at high signal-to-noise ratio (SNR), owing to the fact that the cooperative jammer simultaneously helps by interfering with the eavesdropper, and hurts by interfering with the intended receiver. In this paper, a new achievable rate is derived through imposing a lattice structure on the signals transmitted by both the source and the cooperative jammer, which are aligned at the eavesdropper but remain separable at the intended receiver. We prove that the achieved secrecy rate does not saturate at high SNR for all values of channel gains except when the channel is degraded.

DOI
10.1109/tit.2014.2298132

Related papers

On Secrecy Capacity of Gaussian Wiretap Channel Aided by A Cooperative Jammer

Lingxiang Li, Zhi Chen, Jun Fang

We study the secrecy capacity of Gaussian wiretap channel aided by an external jammer/helper. Both the transmitter and the intended receiver are equipped with a single antenna, while the eavesdropper and the jammer are equipped with$M$and$N$antennas, respectively. Generally, an analytical form of the secrecy capacity in this scenario is difficult to obtain. Instead, we consider a null-space jamming scheme which totally nulls out the jamming signal at the legitimate receiver, and derive lower and upper bounds on its maximal achievable secrecy rate${R_N}$. The relationship between the average secrecy capacity${\bar C_N}$of Gaussian wiretap channel and the average secrecy rate${\bar R_N}$achieved by the null-space jamming scheme is investigated, and we prove that${\bar R_N} \leq {\bar C_N} \leq {\bar R_{N + 1}}$. Based on this inequality and the derived lower and upper bounds on${R_N}$, the upper and lower bounds on the average secrecy capacity of Gaussian wiretap channel aided by an external jammer can be obtained, where our result shows that when$N > M$, the average secrecy capacity increases linearly with the total transmit power; while when$N \leq M - 1$, there exists a performance ceiling on it.

IEEE Signal Processing Letters•Jul 9, 2014•24 citations

The gaussian two-way relay channel with wiretapper

Sung‐Soo Kim, Won-Yong Shin, Koji Ishibashi

Secrecy capacity is analyzed in a Gaussian two-way relay wiretap channel (TRWC), where two legitimate source nodes wish to exchange their messages through a relay in the presence of an eavesdropper. We assume that all intended nodes operate in full-duplex mode and there is no direct path between two sources. In the Gaussian TRWC, we propose an achievable coding scheme composed of superposed lattice codes with both structured and random codebooks. A jamming strategy is further introduced at the two sources as well as at the relay to maximize the achievable secrecy rate regions, where each node allocates part of its power to jam the eavesdropper. Our result indicates that positive achievable secrecy rates are maintained even for the reversely degraded scenario. In addition, assuming two sources with equal power constraint, it is shown that the scheme asymptotically achieves within 1/2 bit from the cut-set bound based on the channel with no secrecy constraints, as the downlink phase is in the high signal-to-noise ratio regime.

Asilomar Conference on Signals, Systems and Computers (ACSSC)•Nov 1, 2011•3 citations

Solutions for the MIMO Gaussian Wiretap Channel With a Cooperative Jammer

S. Ali. A. Fakoorian, Arnold Lee Swindlehurst

We study the Gaussian MIMO wiretap channel with a transmitter, a legitimate receiver, an eavesdropper and an external helper, each equipped with multiple antennas. The transmitter sends confidential messages to its intended receiver, while the helper transmits jamming signals independent of the source message to confuse the eavesdropper. The jamming signal is assumed to be treated as noise at both the intended receiver and the eavesdropper. We obtain a closed-form expression for the structure of the artificial noise covariance matrix that guarantees a secrecy rate larger or at least equal to the secrecy capacity of the wiretap channel with no jamming signal. We also describe how to find specific realizations of this covariance matrix expression that provide good secrecy rate performance, even when there is no nontrivial null space between the helper and the intended receiver. Unlike prior work, our approach considers the general MIMO case, and is not restricted to SISO or MISO scenarios.

arXiv:1101.4435•IEEE Transactions on Signal Processing•Jul 7, 2011•131 citations

The General Gaussian Multiple-Access and Two-Way Wiretap Channels: Achievable Rates and Cooperative Jamming

Ender Tekin, Aylin Yener

The general Gaussian multiple-access wiretap channel (GGMAC-WT) and the Gaussian two-way wiretap channel (GTW-WT) are considered. In the GGMAC-WT, multiple users communicate with an intended receiver in the presence of an eavesdropper who receives their signals through another GMAC. In the GTW-WT, two users communicate with each other over a common Gaussian channel, with an eavesdropper listening through a GMAC. A secrecy measure that is suitable for this multiterminal environment is defined, and achievable secrecy rate regions are found for both channels. For both cases, the power allocations maximizing the achievable secrecy sum rate are determined. It is seen that the optimum policy may prevent some terminals from transmission in order to preserve the secrecy of the system. Inspired by this construct, a new scheme cooperative jamming is proposed, where users who are prevented from transmitting according to the secrecy sum rate maximizing power allocation policy ldquojamrdquo the eavesdropper, thereby helping the remaining users. This scheme is shown to increase the achievable secrecy sum rate. Overall, our results show that in multiple-access scenarios, users can help each other to collectively achieve positive secrecy rates. In other words, cooperation among users can be invaluable for achieving secrecy for the system.

arXiv:cs/0702112•IEEE Transactions on Information Theory•May 29, 2008•841 citations

Secure Degrees of Freedom for Gaussian Channels with Interference: Structured Codes Outperform Gaussian Signaling

Xiang He, Aylin Yener

In this work, we prove that a positive secure degree of freedom is achievable for a large class of real Gaussian channels as long as the channel is not degraded and the channel is fully connected. This class includes the MAC wiretap channel, the 2-user interference channel with confidential messages, the 2-user interference channel with an external eavesdropper. Best known achievable schemes to date for these channels use Gaussian signaling. In this work, we show that structured codes outperform Gaussian random codes at high SNR when channel gains are real numbers.

arXiv:0905.2638•Globecom•Nov 1, 2009•25 citations

Secure Degrees of Freedom for Gaussian Channels with Interference: Structured Codes Outperform Gaussian Signaling

Xiang He, Aylin Yener

Abstract—In this work, we prove that a positive secure degree of freedom is achievable for a large class of real Gaussian channels as long as the channel is not degraded and the channel is fully connected. This class includes the MAC wiretap channel, the 2-user interference channel with confidential messages, the 2-user interference channel with an external eavesdropper. Best known achievable schemes to date for these channels use Gaussian signaling. In this work, we show that structured codes outperform Gaussian random codes at high SNR when channel gains are real numbers. I.

•Mar 16, 2011•29 citations
Recent results have shown that structured codes can be used to construct good channel codes, source codes, and physical layer network codes for Gaussian channels. For Gaussian channels with secrecy constraints, however, efforts to date rely on Gaussian random codes. In this paper, we advocate that structure in random code generation is useful for providing secrecy as well. In particular, a Gaussian wiretap channel in the presence of a cooperative jammer is studied. Previously, the achievable secrecy rate for this channel was derived using Gaussian signaling, which saturated at high signal-to-noise ratio (SNR), owing to the fact that the cooperative jammer simultaneously helps by interfering with the eavesdropper, and hurts by interfering with the intended receiver. In this paper, a new achievable rate is derived through imposing a lattice structure on the signals transmitted by both the source and the cooperative jammer, which are aligned at the eavesdropper but remain separable at the intended receiver. We prove that the achieved secrecy rate does not saturate at high SNR for all values of channel gains except when the channel is degraded.
We study the secrecy capacity of Gaussian wiretap channel aided by an external jammer/helper. Both the transmitter and the intended receiver are equipped with a single antenna, while the eavesdropper and the jammer are equipped withMMMandNNNantennas, respectively. Generally, an analytical form of the secrecy capacity in this scenario is difficult to obtain. Instead, we consider a null-space jamming scheme which totally nulls out the jamming signal at the legitimate receiver, and derive lower and upper bounds on its maximal achievable secrecy rateRN{R_N}RN​. The relationship between the average secrecy capacityCˉN{\bar C_N}CˉN​of Gaussian wiretap channel and the average secrecy rateRˉN{\bar R_N}RˉN​achieved by the null-space jamming scheme is investigated, and we prove thatRˉN≤CˉN≤RˉN+1{\bar R_N} \leq {\bar C_N} \leq {\bar R_{N + 1}}RˉN​≤CˉN​≤RˉN+1​. Based on this inequality and the derived lower and upper bounds onRN{R_N}RN​, the upper and lower bounds on the average secrecy capacity of Gaussian wiretap channel aided by an external jammer can be obtained, where our result shows that whenN>MN > MN>M, the average secrecy capacity increases linearly with the total transmit power; while whenN≤M−1N \leq M - 1N≤M−1, there exists a performance ceiling on it.
Secrecy capacity is analyzed in a Gaussian two-way relay wiretap channel (TRWC), where two legitimate source nodes wish to exchange their messages through a relay in the presence of an eavesdropper. We assume that all intended nodes operate in full-duplex mode and there is no direct path between two sources. In the Gaussian TRWC, we propose an achievable coding scheme composed of superposed lattice codes with both structured and random codebooks. A jamming strategy is further introduced at the two sources as well as at the relay to maximize the achievable secrecy rate regions, where each node allocates part of its power to jam the eavesdropper. Our result indicates that positive achievable secrecy rates are maintained even for the reversely degraded scenario. In addition, assuming two sources with equal power constraint, it is shown that the scheme asymptotically achieves within 1/2 bit from the cut-set bound based on the channel with no secrecy constraints, as the downlink phase is in the high signal-to-noise ratio regime.
We study the Gaussian MIMO wiretap channel with a transmitter, a legitimate receiver, an eavesdropper and an external helper, each equipped with multiple antennas. The transmitter sends confidential messages to its intended receiver, while the helper transmits jamming signals independent of the source message to confuse the eavesdropper. The jamming signal is assumed to be treated as noise at both the intended receiver and the eavesdropper. We obtain a closed-form expression for the structure of the artificial noise covariance matrix that guarantees a secrecy rate larger or at least equal to the secrecy capacity of the wiretap channel with no jamming signal. We also describe how to find specific realizations of this covariance matrix expression that provide good secrecy rate performance, even when there is no nontrivial null space between the helper and the intended receiver. Unlike prior work, our approach considers the general MIMO case, and is not restricted to SISO or MISO scenarios.
The general Gaussian multiple-access wiretap channel (GGMAC-WT) and the Gaussian two-way wiretap channel (GTW-WT) are considered. In the GGMAC-WT, multiple users communicate with an intended receiver in the presence of an eavesdropper who receives their signals through another GMAC. In the GTW-WT, two users communicate with each other over a common Gaussian channel, with an eavesdropper listening through a GMAC. A secrecy measure that is suitable for this multiterminal environment is defined, and achievable secrecy rate regions are found for both channels. For both cases, the power allocations maximizing the achievable secrecy sum rate are determined. It is seen that the optimum policy may prevent some terminals from transmission in order to preserve the secrecy of the system. Inspired by this construct, a new scheme cooperative jamming is proposed, where users who are prevented from transmitting according to the secrecy sum rate maximizing power allocation policy ldquojamrdquo the eavesdropper, thereby helping the remaining users. This scheme is shown to increase the achievable secrecy sum rate. Overall, our results show that in multiple-access scenarios, users can help each other to collectively achieve positive secrecy rates. In other words, cooperation among users can be invaluable for achieving secrecy for the system.
In this work, we prove that a positive secure degree of freedom is achievable for a large class of real Gaussian channels as long as the channel is not degraded and the channel is fully connected. This class includes the MAC wiretap channel, the 2-user interference channel with confidential messages, the 2-user interference channel with an external eavesdropper. Best known achievable schemes to date for these channels use Gaussian signaling. In this work, we show that structured codes outperform Gaussian random codes at high SNR when channel gains are real numbers.
Abstract—In this work, we prove that a positive secure degree of freedom is achievable for a large class of real Gaussian channels as long as the channel is not degraded and the channel is fully connected. This class includes the MAC wiretap channel, the 2-user interference channel with confidential messages, the 2-user interference channel with an external eavesdropper. Best known achievable schemes to date for these channels use Gaussian signaling. In this work, we show that structured codes outperform Gaussian random codes at high SNR when channel gains are real numbers. I.