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16
Interference alignment for the multiantenna compound wiretap channel
 IEEE Trans. Inform. Theory
, 2011
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Cited by 27 (3 self)
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All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.
Secure Degrees of Freedom of the Gaussian Wiretap Channel with Helpers
"... Abstract — The secrecy capacity of the canonical Gaussian wiretap channel does not scale with the transmit power, and hence, the secure d.o.f. of the Gaussian wiretap channel with no helpers is zero. It has been known that a strictly positive secure d.o.f. can be obtained in the Gaussian wiretap cha ..."
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Cited by 22 (16 self)
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Abstract — The secrecy capacity of the canonical Gaussian wiretap channel does not scale with the transmit power, and hence, the secure d.o.f. of the Gaussian wiretap channel with no helpers is zero. It has been known that a strictly positive secure d.o.f. can be obtained in the Gaussian wiretap channel by using a helper which sends structured cooperative signals. We show that the exact secure d.o.f. of the Gaussian wiretap channel with a helper is 1. Our achievable scheme is based on 2 real interference alignment and cooperative jamming, which renders the message signal and the cooperative jamming signal separable at the legitimate receiver, but aligns them perfectly at the eavesdropper preventing any reliable decoding of the message signal. Our converse is based on two key lemmas. The first lemma quantifies the secrecy penalty by showing that the net effect of an eavesdropper on the system is that it eliminates one of the independent channel inputs. The second lemma quantifies the role of a helper by developing a direct relationship between the cooperative jamming signal of a helper and the message rate. We extend this result to the case of M helpers, and show that the exact secure d.o.f. in this case is M
Ergodic Secret Alignment
, 2012
"... In this paper, we introduce two new achievable schemes for the fading multiple access wiretap channel (MACWT). In the model that we consider, we assume that perfect knowledge of the state of all channels is available at all the nodes in a causal fashion. Our schemes use this knowledge together wit ..."
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Cited by 21 (17 self)
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In this paper, we introduce two new achievable schemes for the fading multiple access wiretap channel (MACWT). In the model that we consider, we assume that perfect knowledge of the state of all channels is available at all the nodes in a causal fashion. Our schemes use this knowledge together with the timevarying nature of the channel model to align the interference from different users at the eavesdropper perfectly in a onedimensional space while creating a higher dimensionality space for the interfering signals at the legitimate receiver, hence allowing for better chance of recovery. While we achieve this alignment through signal scaling at the transmitters in our first scheme (scalingbased alignment), we let nature provide this alignment through the ergodicity of the channel coefficients in the second scheme [ergodic secret alignment (ESA)] [1], [2]. For each scheme, we obtain the resulting achievable secrecy rate region. We show that the secrecy rates achieved by both schemes in the twouser fading MACWT scale with signaltonoise ratio (SNR) as 1 2 log(SNR). Hence, we show the suboptimality of the independent identically distributed (i.i.d.) Gaussian signalingbased schemes with and without cooperative jamming by showing that the secrecy rates achieved using i.i.d. Gaussian signaling with cooperative jamming do not scale with SNR. In addition, we introduce an improved version of our ESA scheme where we incorporate cooperative jamming to achieve higher secrecy rates. Moreover, we derive the necessary optimality conditions for the power control policy that maximizes the secrecy sum rate achievable by our ESA scheme when used solely and with cooperative jamming. Finally, we discuss the extension of the proposed schemes to the case where there are more than two users and show that, for theuser fading MACWT, each of the two schemes achieves secrecy sum rate that scales with SNR as 1 log(SNR).
Secure Degrees of Freedom of Onehop Wireless Networks
, 2012
"... We study the secure degrees of freedom (d.o.f.) of onehop wireless networks by considering four fundamental wireless network structures: Gaussian wiretap channel, Gaussian broadcast channel with confidential messages, Gaussian interference channel with confidential messages, and Gaussian multiple a ..."
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Cited by 19 (12 self)
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We study the secure degrees of freedom (d.o.f.) of onehop wireless networks by considering four fundamental wireless network structures: Gaussian wiretap channel, Gaussian broadcast channel with confidential messages, Gaussian interference channel with confidential messages, and Gaussian multiple access wiretap channel. The secrecy capacity of the canonical Gaussian wiretap channel does not scale with the transmit power, and hence, the secure d.o.f. of the Gaussian wiretap channel with no helpers is zero. It has been known that a strictly positive secure d.o.f. can be obtained in the Gaussian wiretap channel by using a helper which sends structured cooperative signals. We show that the exact secure d.o.f. of the Gaussian wiretap channel with a helper is 1 2. Our achievable scheme is based on real interference alignment and cooperative jamming, which renders the message signal and the cooperative jamming signal separable at the legitimate receiver, but aligns them perfectly at the eavesdropper preventing any reliable decoding of the message signal. Our converse is based on two key lemmas. The first lemma quantifies the secrecy penalty by showing that the net effect of an eavesdropper on the system is that it eliminates one of the independent channel inputs. The second lemma quantifies the role of a helper by developing a direct relationship between the cooperative jamming signal of a helper and the message rate. We extend this result to the case of M helpers, and show that the exact secure d.o.f. in this case is M M+1. We then generalize this approach to more general network structures with multiple messages. We show that the sum secure d.o.f. of the Gaussian broadcast channel with confidential messages and M helpers is 1, the sum secure d.o.f. of the twouser interference channel with confidential messages is 2 3, the sum secure d.o.f. of the twouser interference channel with confidential messages and M helpers is 1, and the sum secure d.o.f. of the Kuser multiple access wiretap channel is
Real interference alignment for the Kuser Gaussian interference compound wiretap channel
 In 48th Annual Allerton Conference on Communication, Control and Computing
, 2010
"... Abstract — We study the Kuser Gaussian interference wiretap channel with N external eavesdroppers. All the transmitters, receivers and eavesdroppers have a single antenna each. We propose an achievable scheme to lower bound the secure degrees of freedom (d.o.f.) for each transmitterreceiver pair. ..."
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Cited by 11 (10 self)
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Abstract — We study the Kuser Gaussian interference wiretap channel with N external eavesdroppers. All the transmitters, receivers and eavesdroppers have a single antenna each. We propose an achievable scheme to lower bound the secure degrees of freedom (d.o.f.) for each transmitterreceiver pair. Our approach is based on the (real) interference alignment technique. Our achievable scheme not only aligns the interference at each receiver to prevent the d.o.f. from vanishing, but also aligns the signals observed by the eavesdroppers to reduce the secrecy penalty. The achievable secure d.o.f. of each transmitterreceiver pair is shown to be 1 2 channel gains.
1 SecretKey Generation using Correlated Sources and Channels
, 906
"... We study the problem of generating a shared secret key between two terminals in a joint sourcechannel setup — the sender communicates to the receiver over a discrete memoryless wiretap channel and additionally the terminals have access to correlated discrete memoryless source sequences. We establish ..."
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We study the problem of generating a shared secret key between two terminals in a joint sourcechannel setup — the sender communicates to the receiver over a discrete memoryless wiretap channel and additionally the terminals have access to correlated discrete memoryless source sequences. We establish lower and upper bounds on the secretkey capacity. These bounds coincide, establishing the capacity, when the underlying channel consists of independent, parallel and reversely degraded wiretap channels. In the lower bound, the equivocation terms of the source and channel components are functionally additive. The secretkey rate is maximized by optimally balancing the the source and channel contributions. This tradeoff is illustrated in detail for the Gaussian case where it is also shown that Gaussian codebooks achieve the capacity. When the eavesdropper also observes a source sequence, the secretkey capacity is established when the sources and channels of the eavesdropper are a degraded version of the legitimate receiver. Finally the case when the terminals also have access to a public discussion channel is studied. We propose generating separate keys from the source and channel components and establish the optimality of this approach when the when the channel outputs of the receiver and the eavesdropper are conditionally independent given the input. I.
On the Sum Secure Degrees of Freedom of TwoUnicast Layered Wireless Networks
"... Abstract—In this paper, we study the sum secure degrees of freedom (d.o.f.) of twounicast layered wireless networks. Without a secrecy constraint, the sum d.o.f. of this class of networks was studied by [1] and shown to take only one of three possible values: 1, 3/2 and 2, for all network configura ..."
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Cited by 7 (4 self)
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Abstract—In this paper, we study the sum secure degrees of freedom (d.o.f.) of twounicast layered wireless networks. Without a secrecy constraint, the sum d.o.f. of this class of networks was studied by [1] and shown to take only one of three possible values: 1, 3/2 and 2, for all network configurations. We consider the setting where the message of each sourcedestination pair must be kept informationtheoretically secure from the unintended receiver. We show that the sum secure d.o.f. can take 0, 1, 3/2, 2 and at most countably many other positive values, which we enumerate. s1 u1 u2 u3 t1 t2 s2 w1 w2 w3
Ergodic secret alignment for the fading multiple access wiretap channel
 in IEEE Int. Conf. Commun., Cape Town, South Africa
, 2010
"... Abstract—In this paper, we provide a new achievable ergodic secrecy rate region for the multiple access wiretap channel in fading. Our achievable scheme is based on repeating each symbol at two fading instances, as in the original ergodic interference alignment technique of Nazer et. al. We choose t ..."
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Abstract—In this paper, we provide a new achievable ergodic secrecy rate region for the multiple access wiretap channel in fading. Our achievable scheme is based on repeating each symbol at two fading instances, as in the original ergodic interference alignment technique of Nazer et. al. We choose the channel states where the symbols are repeated in such a way that the received signals are aligned favorably at the legitimate receiver, while they are aligned unfavorably at the eavesdropper. We show that our new scheme outperforms plain Gaussian signaling and Gaussian signaling with Gaussian channel prefixing, i.e., cooperative jamming, in high signaltonoise ratios (SNR). In particular, we show that, while Gaussian signaling with or without channel prefixing yields zero secure degrees of freedom, our new achievable scheme provides a total of 1/2 secure degrees of freedom in a twouser multiple access channel in fading. I.
Interference Channels with Strong Secrecy
, 2009
"... Abstract—It is known that given the real sum of two independent uniformly distributed lattice points from the same nested lattice codebook, the eavesdropper can obtain at most 1 bit of information per channel regarding the value of one of the lattice points. In this work, we study the effect of this ..."
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Cited by 3 (1 self)
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Abstract—It is known that given the real sum of two independent uniformly distributed lattice points from the same nested lattice codebook, the eavesdropper can obtain at most 1 bit of information per channel regarding the value of one of the lattice points. In this work, we study the effect of this 1 bit information on the equivocation expressed in three commonly used information theoretic measures, i.e., the Shannon entropy, the Rényi entropy and the min entropy. We then demonstrate its applications in an interference channel with a confidential message. In our previous work, we showed that nested lattice codes can outperform Gaussian codes for this channel when the achieved rate is measured with the weak secrecy notion. Here, with the Rényi entropy and the min entropy measure, we prove that the same secure degree of freedom is achievable with the strong secrecy notion as well. A major benefit of the new coding scheme is that the strong secrecy is generated from a single lattice point instead of a sequence of lattice points. Hence the mutual information between the confidential message and the observation of the eavesdropper decreases much faster with the number of channel uses than previously known strong secrecy coding methods for nested lattice codes. I.
A new achievable ergodic secrecy rate region for the fading multiple access wiretap channel
 ALLERTON CONF. COMMUN., CONTROL COMPUT
, 2009
"... We give a new achievable ergodic secrecy rate region for the twouser fading multiple access wiretap channel. Our scheme creates a vector channel between the two transmitters and the intended receiver that has fullrank and creates another vector channel between the two transmitters and the eavesdr ..."
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We give a new achievable ergodic secrecy rate region for the twouser fading multiple access wiretap channel. Our scheme creates a vector channel between the two transmitters and the intended receiver that has fullrank and creates another vector channel between the two transmitters and the eavesdropper whose rank is 1. In this sense, our scheme removes interference from the main receiver multiple access channel by introducing an extra dimension in this channel, while sustaining the interference in the eavesdropper multiple access channel by keeping the rank of this channel equal to one. We show that the secrecy sum rate achieved by our scheme scales with SNR. In particular, we show that a total number of 1/2 secure degrees of freedom is achievable for the two users. Moreover, we compare our scheme with the Gaussian signaling scheme with cooperative jamming which improves significantly over the plain Gaussian signaling scheme. Our proposed scheme outperforms Gaussian signaling schemes (with or without cooperative jamming) at high signaltonoise ratios (SNR). In particular, we show that Gaussian signaling schemes with or without cooperative jamming achieve zero secure degrees of freedom, while our proposed scheme achieves 1/2 total secure degrees of freedom.