### Citations

7188 | Convex optimization
- Boyd, Vandenberghe
- 2004
(Show Context)
Citation Context ... from a secrecy perspective. The optimization of each objective function is solved such that it is the solution of the derivative of the Lagrangian and applying the Karush-KuhnTucker (KKT) conditions =-=[21]-=-. In particular, the achievable secrecy rate is maximized subject to fixed total power constraint for each transmitter. The solution of such optimization problem is the optimal power allocation that e... |

1166 |
Gamal, “Capacity theorems for the relay channel
- Cover, El
- 1979
(Show Context)
Citation Context ...ork We can consider that the achievable secrecy rate regions for the model in Figure 1 with two relay devices and one eavesdropper coincide with that of the MAC with one common eavesdropper, see [7], =-=[19]-=-, [20]. Therefore, we can conclude the following theorem. Theorem 1: (Achievability): The achievable secure rate regions for the model in Figure 1 is upper bounded by the 2Notice that the channel gain... |

559 |
The wire-tap channel
- Wyner
- 1975
(Show Context)
Citation Context ...less cloud. Index Terms—Achievable secrecy rate, Cooperation, MAC, Relaying. I. INTRODUCTION The Wiretap channel models scenarios of the data transmission under security attacks on the physical layer =-=[1]-=-. This paper focuses on the physical layer security in a wiretap channel model of interest; including two legitimate transmitters that are relay devices, one legitimate receiver, and one eavesdropper.... |

151 | The relay-eavesdropper channel: Cooperation for secrecy
- Lai, Gamal
(Show Context)
Citation Context ...rent cooperative schemes. In [7], the authors provide upper bounds of the achievable rates of a discrete memoryless MAC channel with confidential messages are to be transmitted in perfect secrecy. In =-=[8]-=-, the authors devise several cooperation strategies and characterize the corresponding achievable rate-equivocation region. They consider a deaf helper phenomenon, where the relay is able to facilitat... |

110 | Secrecy capacity of wireless channels
- Barros, Rodrigues
- 2006
(Show Context)
Citation Context ...r cooperative virtual MIMOs [3] by directly maximizing the mutual information, or via optimizing other design criterion such as, minimizing the mean square error [4], or minimizing the bit error rate =-=[5]-=-. In [6], the authors address secure communications of one source-destination pair with the help of multiple cooperating relays in the presence of one or more eavesdroppers with different cooperative ... |

92 |
Improving wireless physical layer security via cooperating relays
- Dong, Han, et al.
- 2010
(Show Context)
Citation Context ...ative virtual MIMOs [3] by directly maximizing the mutual information, or via optimizing other design criterion such as, minimizing the mean square error [4], or minimizing the bit error rate [5]. In =-=[6]-=-, the authors address secure communications of one source-destination pair with the help of multiple cooperating relays in the presence of one or more eavesdroppers with different cooperative schemes.... |

81 | Relay channels with confidential messages
- Oohama
(Show Context)
Citation Context ...g achievable rate-equivocation region. They consider a deaf helper phenomenon, where the relay is able to facilitate secure communications while being totally ignorant of the transmitted messages. In =-=[9]-=-, the author studied the security of communication for the relay channel under the situation that some of the transmitted messages are confidential to the relay. Moreover, in [10], the authors conside... |

15 |
Wireless Secrecy Regions With Friendly Jamming,” Information Forensics and Security
- Vilela, Bloch, et al.
- 2011
(Show Context)
Citation Context ...vices in a wiretap setup without cooperative scenarios has concluded that there is a distance consideration for which the secrecy can exist, otherwise not, and they call it secrecy coverage distance, =-=[22]-=-. Now for the setup of cooperative devices for the model in Figure 2, the distance between Alice and Eve should be, dae η ≤ Gae Gaj daj η (77) and the distance between John and Eve should be, dje η ≤ ... |

12 | Cooperative jamming for wireless physical layer security
- Dong, Han, et al.
- 2009
(Show Context)
Citation Context ...nsmitted messages. In [9], the author studied the security of communication for the relay channel under the situation that some of the transmitted messages are confidential to the relay. Moreover, in =-=[10]-=-, the authors considered cooperative jamming where a relay equipped with multiple antennas transmits a jamming signal to create interference at the eavesdropper. They proposed design methods to determ... |

10 | Giannakis, “Mutual information jammer-relay games
- Wang, B
- 2008
(Show Context)
Citation Context ...sical layer security relied on game theory. The maximization of reliable information rates with different channel models with cooperative relaying and with the existence of a jammer are considered in =-=[12]-=-. Optimal power allocation strategies were derived for a zero sum game with an unfriendly jammer in [13]. In [14], the authors studied the achievable secrecy rates for a non-cooperative zero sum game ... |

10 | Physical layer security game: How to date a girl with her boyfriend on the same table
- Han, Marina, et al.
- 2009
(Show Context)
Citation Context ...thors address the power allocation problem for interference relay channels. They model the problem as a strategic non-cooperative game and show that this game always has a unique Nash equilibrium. In =-=[17]-=-, the authors investigate the interaction between the source and friendly jammers, they introduce a game theoretic approach in order to obtain a distributed solution. Moreover, in [18], the authors in... |

4 |
Gaussian channels with arbitrary inputs: Optimal precoding and power allocation
- Ghanem, “MAC
- 2012
(Show Context)
Citation Context ... that aim to maximize the secure and reliable information rates are existing in the literature. Such designs were done for different channel models, for example, for the two user MAC Gaussian channel =-=[2]-=-, or for cooperative virtual MIMOs [3] by directly maximizing the mutual information, or via optimizing other design criterion such as, minimizing the mean square error [4], or minimizing the bit erro... |

3 |
A zero-sum power allocation game in the parallel Gaussian wiretap channel with an unfriendly jammer
- Ara, Reboredo, et al.
- 2012
(Show Context)
Citation Context ...t channel models with cooperative relaying and with the existence of a jammer are considered in [12]. Optimal power allocation strategies were derived for a zero sum game with an unfriendly jammer in =-=[13]-=-. In [14], the authors studied the achievable secrecy rates for a non-cooperative zero sum game with a jamming relay 2assisting the eavesdropper. They found a saddle point solution of such game. In [1... |

2 |
power allocation and optimal precoding with multi-cell processing
- “Optimal
- 2013
(Show Context)
Citation Context ...eliable information rates are existing in the literature. Such designs were done for different channel models, for example, for the two user MAC Gaussian channel [2], or for cooperative virtual MIMOs =-=[3]-=- by directly maximizing the mutual information, or via optimizing other design criterion such as, minimizing the mean square error [4], or minimizing the bit error rate [5]. In [6], the authors addres... |

2 | Filter Design with Secrecy Constraints: The Degraded Multiple-Input Multiple-Output Gaussian Wiretap Channel
- Reboredo, Ara, et al.
(Show Context)
Citation Context ...o user MAC Gaussian channel [2], or for cooperative virtual MIMOs [3] by directly maximizing the mutual information, or via optimizing other design criterion such as, minimizing the mean square error =-=[4]-=-, or minimizing the bit error rate [5]. In [6], the authors address secure communications of one source-destination pair with the help of multiple cooperating relays in the presence of one or more eav... |

2 | Power Allocation Strategies for OFDM Gaussian Wiretap Channels with a Friendly Jammer
- Ara, Reboredo, et al.
(Show Context)
Citation Context ...equilibrium. In [17], the authors investigate the interaction between the source and friendly jammers, they introduce a game theoretic approach in order to obtain a distributed solution. Moreover, in =-=[18]-=-, the authors investigate optimal power allocation strategies for OFDM wiretap channels with the existence of friendly jammers. In this paper, the wiretap channel model of interest has no jammers, how... |

1 | A Secrecy Game with an Informed Jammer Relay
- Yuksel, Liu, et al.
- 2010
(Show Context)
Citation Context ... models with cooperative relaying and with the existence of a jammer are considered in [12]. Optimal power allocation strategies were derived for a zero sum game with an unfriendly jammer in [13]. In =-=[14]-=-, the authors studied the achievable secrecy rates for a non-cooperative zero sum game with a jamming relay 2assisting the eavesdropper. They found a saddle point solution of such game. In [15], the a... |

1 |
A Game Theoritic Approach for Power Allocation
- Janzamin, Pakravan, et al.
(Show Context)
Citation Context ...3]. In [14], the authors studied the achievable secrecy rates for a non-cooperative zero sum game with a jamming relay 2assisting the eavesdropper. They found a saddle point solution of such game. In =-=[15]-=-, the authors propose a distributed game-theoretic method for power allocation in bi-directional cooperative communication. They showed that their method reaches equilibrium in one stage, and proved t... |

1 |
Interference channels
- Kramer
- 2011
(Show Context)
Citation Context ... can consider that the achievable secrecy rate regions for the model in Figure 1 with two relay devices and one eavesdropper coincide with that of the MAC with one common eavesdropper, see [7], [19], =-=[20]-=-. Therefore, we can conclude the following theorem. Theorem 1: (Achievability): The achievable secure rate regions for the model in Figure 1 is upper bounded by the 2Notice that the channel gains are ... |