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## MIMO Multiple Access Channel with an Arbitrarily Varying Eavesdropper: Secrecy degrees of freedom (2013)

Venue: | IEEE TRANSACTIONS ON INFORMATION THEORY, FEBRUARY |

Citations: | 13 - 5 self |

### Citations

1350 | Information Theory: Coding Theorems for Discrete Memoryless Systems, Akadémiai Kiado - Cśiszar, Körner |

1227 |
Communication theory of secrecy systems
- Shannon
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Citation Context ...ments existing cryptographic techniques. Furthermore the associated techniques do not rely on a computationally bounded adversarial model, but instead provide a rigorous theoretical proof of security =-=[5]-=- making such techniques appealing in certain mission-critical application. Secure communication using multiple antennas has been extensively studied in recent times, see e.g., [6]–[14]. These works in... |

753 |
Broadcast channels with confidential messages
- Csiszár, Körner
- 1978
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Citation Context ...opper with unbounded computational power. Since then, an extensive body of work has been devoted to studying this problem for different network models by deriving fundamental transmission rate limits =-=[2]-=-–[4] and designing lowcomplexity schemes to approach these limits in practice [5], [6]. Secure communication using multiple antennas was extensively studied as well, see e.g., [7]–[18], [30]. These wo... |

240 | Secure transmission with multiple antennas II: The MIMOME wiretap channel,” - Khisti, Wornell - 2010 |

228 |
Introduction to Modern Cryptography,
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- 2007
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Citation Context ...ated with an adversary eavesdropping a carefully selected group of sub-channels. I. INTRODUCTION While prevalent architectures for secure communication are primarily based on cryptographic techniques =-=[1]-=-, they cannot address all the vulnerabilities in complex networked systems. The area of physical layer security [2]–[4] investigates security solutions using resources at the physical layer and compli... |

171 | The secrecy capacity of the MIMO wiretap channel,” - Oggier, Hassibi - 2011 |

167 |
Communication theory of secrecy systems,” Bell Sys
- Shannon
- 1949
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Citation Context ...y varying channel, information theoretic security, MIMO multiple access wiretap channel, secrecy degrees of freedom. I. INTRODUCTION I NFORMATION theoretic security was first introduced by Shannon in =-=[1]-=-, which studied the problem of transmitting confidential information in a communication system in the presence of an eavesdropper with unbounded computational power. Since then, an extensive body of w... |

165 | Guaranteeing secrecy using artificial noise,” - Goel, Negi - 2008 |

130 |
Towards a generalized singular value decomposition.
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- 1981
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Citation Context ...nsformation that reduces the model to the case of parallel independent channels in the previous section while preserving the s.d.o.f. region. As we discuss next, this transformation involves the GSVD =-=[35]-=- and a channel enhancement argument. For an analogous application of GSVD to broadcast channels, see e.g., [21], [36], [37]. We note that channel enhancement techniques are used in many different prob... |

91 | Multiple access channels with confidential messages,”
- Liang, Poor
- 2008
(Show Context)
Citation Context ...he best of our knowledge the s.d.o.f. region remains open when the eavesdropper channel is perfectly known to all terminals. A significant body of literature already exists on this problem. See e.g., =-=[3]-=-, [18]–[20]. If the channel model has real inputs and outputs, Gaussian signaling is in general suboptimal and user cooperating strategies as well as signal alignment techniques are necessary [21]. In... |

89 | The general Gaussian multiple access and two-way wire-tap channels: Achievable rates and cooperative jamming,”
- Tekin, Yener
- 2008
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Citation Context ...thus settling the open problem raised in [20] for the case of two transmitters. The scalar multiple-access channel when the eavesdropper channel is perfectly known, has been studied extensively e.g., =-=[22]-=-–[29]. If the channel model has real inputs and output, Gaussian signaling is in general suboptimal and user cooperating strategies, as well as signal alignment techniques, are necessary [26]. It was ... |

78 | Towards the secrecy capacity of the Gaussian MIMO wire-tap channel: The 2-2-1 channel,” - Shafiee, Liu, et al. - 2009 |

70 | The secrecy capacity region of the Gaussian MIMO multireceiver wiretap channel,” - Ekrem, Ulukus - 2011 |

67 | Compound wiretap channels,”
- Liang, Kramer, et al.
- 2009
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Citation Context ...ate limits [2]–[4] and designing lowcomplexity schemes to approach these limits in practice [5], [6]. Secure communication using multiple antennas was extensively studied as well, see e.g., [7]–[18], =-=[30]-=-. These works investigated efficient signaling mechanisms using the spatial degrees of freedom provided by multiple antennas to limit an eavesdropper’s ability to decode information. The underlying in... |

66 | Multiaccess fading channels. I. Polymatroid structure, optimal resource allocation and throughput capacities - Tse, Hanly - 1998 |

61 |
Physical-Layer Security: From Information Theory to Security Engineering,
- Bloch, Barros
- 2011
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Citation Context ...r with unbounded computational power. Since then, an extensive body of work has been devoted to studying this problem for different network models by deriving fundamental transmission rate limits [2]–=-=[4]-=- and designing lowcomplexity schemes to approach these limits in practice [5], [6]. Secure communication using multiple antennas was extensively studied as well, see e.g., [7]–[18], [30]. These works ... |

59 | Multiple-input multipleoutput Gaussian broadcast channels with confidential messages,” - Liu, Liu, et al. - 2010 |

56 |
A note on the secrecy capacity of the multiple-antenna wiretap channel,”
- Liu, Shamai
- 2009
(Show Context)
Citation Context ...ogous application of GSVD to broadcast channels, see e.g., [21], [36], [37]. We note that channel enhancement techniques are used in many different problems in multiuser information theory; see e.g., =-=[12]-=-. A. GSVD Transformation Theorem 2[35]: Given a pair of matrices and such that the rank of is ,andtherankof is , there exists unitary matrices and nonsingular upper triangular matrix such that for , (... |

55 | Information theoretic security,” Foundations and Trends in Communications and - Liang, Poor, et al. - 2008 |

45 | Providing Secrecy With Structured Codes: Tools and Applications to Two-User Gaussian Channels,” Submitted to
- He, Yener
- 2009
(Show Context)
Citation Context ...ly e.g., [22]–[29]. If the channel model has real inputs and output, Gaussian signaling is in general suboptimal and user cooperating strategies, as well as signal alignment techniques, are necessary =-=[26]-=-. It was shown in [28, Sec. 5.16] that the individual s.d.o.f. of this model could not exceed 2/3. Recently, [29] improves this result and shows that the sum s.d.o.f. of this model cannot exceed 2/3 a... |

40 | On the secrecy of multiple access wiretap channel - Ekrem, Ulukus - 2008 |

30 | Robust beamforming for security in MIMO wiretap channels with imperfect CSI,”
- Mukherjee, Swindlehurst
- 2011
(Show Context)
Citation Context ...sion rate limits [2]–[4] and designing lowcomplexity schemes to approach these limits in practice [5], [6]. Secure communication using multiple antennas was extensively studied as well, see e.g., [7]–=-=[18]-=-, [30]. These works investigated efficient signaling mechanisms using the spatial degrees of freedom provided by multiple antennas to limit an eavesdropper’s ability to decode information. The underly... |

27 | Interference alignment for the multi-antenna compound wiretap channel
- Khisti
- 2011
(Show Context)
Citation Context ..., the first eavesdropper implies the following upper bound on : (10) and the second eavesdropper implies the following upper bound on : (11) Their joint effect can be captured by adding (10) and (11) =-=[33]-=-, which leads to: (12) Since there is only one term, which is ,attherightsideofthe mutual information ,weobservethesum s.d.o.f. cannot exceed 1, thereby justifying that (9) is indeed the largest possi... |

25 | MIMO wiretap channels with arbitrarily varying eavesdropper channel states
- He, Yener
(Show Context)
Citation Context ...simistic but stronger assumption, references [19]–[21] study secrecy capacity when the eavesdropper channel is arbitrarily varying and its channel states are known to the eavesdropper only. Reference =-=[20]-=- studies the single-user Gaussian multi-input-multi-output (MIMO) wiretap channel and characterizes the secrecy degrees of freedom (s.d.o.f.). The same paper extended the single user analysis to the t... |

24 |
Gamal. Cooperation for Secrecy: The Relay-Eavesdropper Channel
- Lai, El
- 2008
(Show Context)
Citation Context ...ectures for secure communication are primarily based on cryptographic techniques [1], they cannot address all the vulnerabilities in complex networked systems. The area of physical layer security [2]–=-=[4]-=- investigates security solutions using resources at the physical layer and compliments existing cryptographic techniques. Furthermore the associated techniques do not rely on a computationally bounded... |

19 | Secure degrees of freedom of one-hop wireless networks
- Xie, Ulukus
(Show Context)
Citation Context ...settling the open problem raised in [20] for the case of two transmitters. The scalar multiple-access channel when the eavesdropper channel is perfectly known, has been studied extensively e.g., [22]–=-=[29]-=-. If the channel model has real inputs and output, Gaussian signaling is in general suboptimal and user cooperating strategies, as well as signal alignment techniques, are necessary [26]. It was shown... |

17 |
On the secure Degrees-ofFreedom of the multiple-access-channel
- Bagherikaram, Motahari, et al.
- 2010
(Show Context)
Citation Context ... [18]–[20]. If the channel model has real inputs and outputs, Gaussian signaling is in general suboptimal and user cooperating strategies as well as signal alignment techniques are necessary [21]. In =-=[22]-=- it is established that s.d.o.f. of 1/2 is achievable using real interference alignment for almost all configurations of channel gains. If the channel model has complex inputs and outputs, it is shown... |

15 | Using antenna array redundancy and channel diversity for secure wireless transmissions,”
- Li, Hwu, et al.
- 2007
(Show Context)
Citation Context ...smission rate limits [2]–[4] and designing lowcomplexity schemes to approach these limits in practice [5], [6]. Secure communication using multiple antennas was extensively studied as well, see e.g., =-=[7]-=-–[18], [30]. These works investigated efficient signaling mechanisms using the spatial degrees of freedom provided by multiple antennas to limit an eavesdropper’s ability to decode information. The un... |

15 | Cooperation and information theoretic security in wireless networks - He - 2010 |

13 | Information theoretic security,” Found - Liang, Poor, et al. - 2008 |

12 | On the compound MIMO broadcast channels with confidential messages - Kobayashi, Liang, et al. - 2009 |

8 |
Secure Communication Over Arbitrarily Varying Wiretap Channels,” Master Thesis, December 2009, available online at http://etd.nd.edu/ETD-db/theses/available/etd-12112009-112419/unrestricted/MolavianJaziE122009.pdf
- Molavianjazi
(Show Context)
Citation Context ...dropper’s channel state information is available either completely or partially, although such an assumption maynot be justified in practice. As a more pessimistic but stronger assumption, references =-=[19]-=-–[21] study secrecy capacity when the eavesdropper channel is arbitrarily varying and its channel states are known to the eavesdropper only. Reference [20] studies the single-user Gaussian multi-input... |

8 | MIMO Broadcast Channel with Arbitrarily Varying Eavesdropper Channel
- He, Khisti, et al.
- 2011
(Show Context)
Citation Context ...reserving the s.d.o.f. region. As we discuss next, this transformation involves the GSVD [35] and a channel enhancement argument. For an analogous application of GSVD to broadcast channels, see e.g., =-=[21]-=-, [36], [37]. We note that channel enhancement techniques are used in many different problems in multiuser information theory; see e.g., [12]. A. GSVD Transformation Theorem 2[35]: Given a pair of mat... |

8 | Shitz), “On the Secrecy Degrees of Freedom of the Multi-Antenna Block Fading Wiretap Channels
- Kobayashi, Piantanida, et al.
- 2011
(Show Context)
Citation Context ...probability is defined as, . (1) (2) We say that the rate-pair is achievable if there exists a sequence of codes with that satisfies the above conditions. The associated s.d.o.f. are defined as [30], =-=[31]-=-: The set of all achievable s.d.o.f. constitutes secrecy degrees of freedom. We note the use of in (5) implies that for any coding scheme one must consider a subsequence of powers that attains the . F... |

5 |
On the application of LDPC codes to a novel wiretap channel inspired by quantum key distribution
- Thangaraj, Dihidar, et al.
- 2005
(Show Context)
Citation Context ...as been devoted to studying this problem for different network models by deriving fundamental transmission rate limits [2]–[4] and designing lowcomplexity schemes to approach these limits in practice =-=[5]-=-, [6]. Secure communication using multiple antennas was extensively studied as well, see e.g., [7]–[18], [30]. These works investigated efficient signaling mechanisms using the spatial degrees of free... |

4 | Polynomial-time, semantically-secure encryption achieving the secrecy capacity,” arXiv preprint arXiv:1201.3160
- Bellare, Tessaro
- 2012
(Show Context)
Citation Context ...en devoted to studying this problem for different network models by deriving fundamental transmission rate limits [2]–[4] and designing lowcomplexity schemes to approach these limits in practice [5], =-=[6]-=-. Secure communication using multiple antennas was extensively studied as well, see e.g., [7]–[18], [30]. These works investigated efficient signaling mechanisms using the spatial degrees of freedom p... |

4 | Distributed Storage Codes Meet Multiple-Access Wiretap Channels,” in - Papailiopoulos, Dimakis - 2010 |

4 |
Secure Broadcast Codes over linear determintic channels
- Khisti, Silva, et al.
- 2010
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Citation Context ...ing the s.d.o.f. region. As we discuss next, this transformation involves the GSVD [35] and a channel enhancement argument. For an analogous application of GSVD to broadcast channels, see e.g., [21], =-=[36]-=-, [37]. We note that channel enhancement techniques are used in many different problems in multiuser information theory; see e.g., [12]. A. GSVD Transformation Theorem 2[35]: Given a pair of matrices ... |

4 |
Gaussian two-way wiretap channel with an arbitrarily varying eavesdropper
- He, Yener
- 2011
(Show Context)
Citation Context ...erent from the case where the eavesdropper channel is fixed and its state is known to all terminals. This is also observed for example in the MIMO broadcast channel [21] and the two-way channel [38], =-=[39]-=-. Finally, we note that the proposed setup allows the eavesdropper terminals to perfectly emulate the legitimate receiver’s channel if sufficiently many antennas are available. Such an assumption may ... |

4 | Transmission with Multiple Antennas-II: The MIMOME Wiretap Channel - “Secure - 2010 |

4 |
Degrees of Freedom Region of the Gaussian
- Ekrem, Ulukus
- 2010
(Show Context)
Citation Context ...s transformation involves the generalized singular value decomposition (GSVD) [28] and a channel enhancement argument. For an analogous application of GSVD to broadcast channels see e.g., [18], [29], =-=[30]-=-. A. GSVD Transformation Theorem 2: [28] Given a pair of matrices H1 and H2 such that the rank of Hi is ri, i = 1, 2, and the rank of [ H1 | H2 ] is r0, there exists unitary matrices U1,U2,W,Q and non... |

3 | Degrees of freedom region of the Gaussian MIMO broadcast channel with common and private messages
- Ekrem, Ulukus
(Show Context)
Citation Context ...e s.d.o.f. region. As we discuss next, this transformation involves the GSVD [35] and a channel enhancement argument. For an analogous application of GSVD to broadcast channels, see e.g., [21], [36], =-=[37]-=-. We note that channel enhancement techniques are used in many different problems in multiuser information theory; see e.g., [12]. A. GSVD Transformation Theorem 2[35]: Given a pair of matrices and su... |

3 | Secrecy When the Eavesdropper Controls its Channel States
- He, Yener
- 2011
(Show Context)
Citation Context ...y different from the case where the eavesdropper channel is fixed and its state is known to all terminals. This is also observed for example in the MIMO broadcast channel [21] and the two-way channel =-=[38]-=-, [39]. Finally, we note that the proposed setup allows the eavesdropper terminals to perfectly emulate the legitimate receiver’s channel if sufficiently many antennas are available. Such an assumptio... |

2 | On the secure dof of the single-antenna mac - Bagherikaram, Motahari, et al. |

1 | Cooperation and Information Theoretic Security - He |

1 |
Two-way Wiretap Channel with an Arbitrarily Varying Eavesdropper
- “Gaussian
- 2011
(Show Context)
Citation Context ...erent from the case where the eavesdropper channel is fixed and its state is known to all terminals. This is also observed for example in the MIMO broadcast channel [18] and the two-way channel [31], =-=[32]-=-. Characterizing secure transmission limits for a broader class of communication models with this assumption is hence important and is left as future work. APPENDIX A PROOF OF LEMMA 1 For Rs,1, from F... |