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Providing Secrecy With Structured Codes: Tools and Applications to TwoUser Gaussian Channels
, 2009
"... 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 random codes. In this work, we advocate that structured c ..."
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Cited by 45 (17 self)
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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 random codes. In this work, we advocate that structured codes are useful for providing secrecy, and show how to compute the secrecy rate when structured codes are used. In particular, we solve the problem of bounding equivocation rates with one important class of structured codes, i.e., nested lattice codes. Having established this result, we next demonstrate the use of structured codes for secrecy in twouser Gaussian channels. In particular, with structured codes, we prove that a positive secure degree of freedom is achievable for a large class of fully connected Gaussian channels as long as the channel is not degraded. By way of this, for these channels, we establish that structured codes outperform Gaussian random codes at high SNR. This class of channels include the twouser multiple access wiretap channel, the twouser interference channel with confidential messages and the twouser interference wiretap channel. A notable consequence of this result is that, unlike the case with Gaussian random codes, using structured codes for both transmission and cooperative jamming, it is possible to achieve an arbitrary large secrecy rate given enough power.
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
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
A New Outer Bound for the Gaussian Interference Channel with Confidential Messages
"... Abstract—In this work, we derive new outer bounds for the twouser interference channel with confidential messages. An upper bound is found for the sum rate. When the interfering link of the first user is greater than 1, a new upper bound on 2R1 + R2 is obtained by studying a special form of the thr ..."
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Cited by 18 (6 self)
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Abstract—In this work, we derive new outer bounds for the twouser interference channel with confidential messages. An upper bound is found for the sum rate. When the interfering link of the first user is greater than 1, a new upper bound on 2R1 + R2 is obtained by studying a special form of the threeuser interference channel. The bounds are then compared with known bounds for the symmetric interference channel under strong interference regime. In particular, examples are presented to showcase for channel parameters where positive secrecy rates are known to be achievable, the new bounds improve upon the known outer bounds on the secrecy capacity region. It is shown that, in some cases, the 2R1+R2 bound also improves the bound on the sum rate. I.
Secure Broadcasting: The Secrecy Rate Region
"... In this paper, we consider a scenario where a source node wishes to broadcast two confidential messages for two respective receivers, while a wiretapper also receives the transmitted signal. This model is motivated by wireless communications, where individual secure messages are broadcast over open ..."
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Cited by 18 (3 self)
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In this paper, we consider a scenario where a source node wishes to broadcast two confidential messages for two respective receivers, while a wiretapper also receives the transmitted signal. This model is motivated by wireless communications, where individual secure messages are broadcast over open media and can be received by any illegitimate receiver. The secrecy level is measured by the equivocation rate at the eavesdropper. We first study the general (nondegraded) broadcast channel with confidential messages. We present an inner bound on the secrecy capacity region for this model. The inner bound coding scheme is based on a combination of random binning, and the GelfandPinsker bining. This scheme matches Marton’s inner bound on the broadcast channel without confidentiality constraint. We further study the situation in which the channels are degraded. For the degraded broadcast channel with confidential messages, we present the secrecy capacity region. Our achievable coding scheme is based on Cover’s superposition scheme and random binning. We refer to this scheme as Secret Superposition Scheme. In this scheme, we show that randomization in the first layer increases the secrecy rate of the second layer. This capacity region matches the capacity region of the degraded broadcast channel without security constraint. It also matches the secrecy capacity for the conventional wiretap channel. Our converse proof is based on a combination of the converse proof of the conventional degraded broadcast channel and Csiszar Lemma. We then assume that the channels are Additive White Gaussian Noise (AWGN) and show that secret superposition scheme with Gaussian codebook is optimal. The converse proof is based on the generalized entropy power inequality. Finally, we use a broadcast strategy for the slowly fading wiretap channel when only the eavesdropper’s channel is fixed and known at the transmitter. We derive the optimum power allocation for the layers which maximizes the total average rate.
Secure Degrees of Freedom for Gaussian Channels with Interference: Structured Codes Outperform Gaussian Signaling
"... 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 2user interference channel with confidential ..."
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Cited by 17 (2 self)
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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 2user interference channel with confidential messages, the 2user 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.
A Secure Communication Game with a Relay Helping the Eavesdropper
"... Abstract—In this work a four terminal Gaussian network composed of a source, a destination, an eavesdropper and a jammer relay is studied. The jammer relay does not hear the source transmission. It assists the eavesdropper and aims to decrease the achievable secrecy rates. The source, on the other h ..."
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Cited by 15 (2 self)
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Abstract—In this work a four terminal Gaussian network composed of a source, a destination, an eavesdropper and a jammer relay is studied. The jammer relay does not hear the source transmission. It assists the eavesdropper and aims to decrease the achievable secrecy rates. The source, on the other hand, aims to increase the achievable secrecy rates. Assuming Gaussian strategies at the source and the jammer relay, this problem is formulated as a twoplayer zerosum continuous game, where the payoff is the achieved secrecy rate. For this game the Nash Equilibrium is generally achieved with mixed strategies. The optimal cumulative distribution functions for the source and the jammer relay that achieve the value of the game, which is the equilibrium secrecy rate, are found. I.
Gamal, “On the Secrecy Rate Region for the Interference Channel
 in Proc. 2008 IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’08
, 2008
"... Abstract — This paper studies interference channels with security constraints. The existence of an external eavesdropper in a twouser interference channel is assumed, where the network users would like to secure their messages from the external eavesdropper. The cooperative binning and channel pref ..."
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Cited by 10 (5 self)
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Abstract — This paper studies interference channels with security constraints. The existence of an external eavesdropper in a twouser interference channel is assumed, where the network users would like to secure their messages from the external eavesdropper. The cooperative binning and channel prefixing scheme is proposed for this system model which allows users to cooperatively add randomness to the channel in order to degrade the observations of the external eavesdropper. This scheme allows users to add randomness to the channel in two ways: 1) Users cooperate in their design of the binning codebooks, and 2) Users cooperatively exploit the channel prefixing technique. As an example, the channel prefixing technique is exploited in the Gaussian case to transmit a superposition signal consisting of binning codewords and independently generated noise samples. Gains obtained form the cooperative binning and channel prefixing scheme compared to the single user scenario reveals the positive effect of interference in increasing the network security. Remarkably, interference can be exploited to cooperatively add randomness into the network in order to enhance the security. I.
Secure Degrees of Freedom of KUser Gaussian Interference Channels: A Unified View
, 2013
"... We determine the exact sum secure degrees of freedom (d.o.f.) of the Kuser Gaussian interference channel. We consider three different secrecy constraints: 1) Kuser interference channel with one external eavesdropper (ICEE), 2) Kuser interference channel with confidential messages (ICCM), and 3) ..."
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Cited by 5 (4 self)
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We determine the exact sum secure degrees of freedom (d.o.f.) of the Kuser Gaussian interference channel. We consider three different secrecy constraints: 1) Kuser interference channel with one external eavesdropper (ICEE), 2) Kuser interference channel with confidential messages (ICCM), and 3) Kuser interference channel with confidential messages and one external eavesdropper (ICCMEE). We show that for all of these three cases, the exact sum secure d.o.f. is K(K−1) 2K−1. We show converses for ICEE and ICCM, which imply a converse for ICCMEE. We show achievability for ICCMEE, which implies achievability for ICEE and ICCM. We develop the converses by relating the channel inputs of interfering users to the reliable rates of the interfered users, and by quantifying the secrecy penalty in terms of the eavesdroppers’ observations. Our achievability uses structured signaling, structured cooperative jamming, channel prefixing, and asymptotic real interference alignment. While the traditional interference alignment provides some amount of secrecy by mixing unintended signals in a smaller subspace at every receiver, in order to attain the optimum sum secure d.o.f., we incorporate structured cooperative jamming into the achievable scheme, and intricately design the structure of all of the transmitted signals jointly.