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## The Gaussian Many-to-One Interference Channel with Confidential Messages

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Citations: | 11 - 5 self |

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359 |
The Gaussian wiretap channel
- Leung-Yan-Cheong, Hellman
- 1978
(Show Context)
Citation Context ... this work, we study this problem in the framework of information theoretic secrecy. Information theoretic secrecy was first proposed by Shannon in [1] and was later extended to noisy channels by [2]–=-=[4]-=-. In this framework, the eavesdropper is assumed to be passive and has unbounded computation power. Secrecy is measured with mutual information: A message is said to be secure from eavesdropping if th... |

301 |
The wire-tap channel,” Bell Syst
- Wyner
- 1975
(Show Context)
Citation Context .... In this work, we study this problem in the framework of information theoretic secrecy. Information theoretic secrecy was first proposed by Shannon in [1] and was later extended to noisy channels by =-=[2]-=-–[4]. In this framework, the eavesdropper is assumed to be passive and has unbounded computation power. Secrecy is measured with mutual information: A message is said to be secure from eavesdropping i... |

167 |
Communication theory of secrecy systems,” Bell Sys
- Shannon
- 1949
(Show Context)
Citation Context ...ch that its benefit for secrecy can be harvested. In this work, we study this problem in the framework of information theoretic secrecy. Information theoretic secrecy was first proposed by Shannon in =-=[1]-=- and was later extended to noisy channels by [2]–[4]. In this framework, the eavesdropper is assumed to be passive and has unbounded computation power. Secrecy is measured with mutual information: A m... |

159 | Discrete memoryless interference and broadcast channels with confidential messages: Secrecy rate regions
- Liu, Maric, et al.
(Show Context)
Citation Context ...fit of interference on secrecy, the fundamental model to study is the interference channel with confidential messages. Indeed, this model with two users has been studied extensively up to date, e.g., =-=[1]-=-–[6]. The case with more than two users, by comparison, is not well explored. Difficulties in solving the K-user case, K ≥ 3, exist in both the achievability and the converse. For achievability, there... |

134 | The approximate capacity of the many-to-one and one-to-many Gaussian interference channels
- Bresler, Parekh, et al.
- 2010
(Show Context)
Citation Context ... use of lattice codes, which is essentially interference alignment in signal space. This approach allows decoding the sum of interference without knowing each component in it. Notable results include =-=[8]-=- where lattice codes are used for interference alignment for a many-to-one Gaussian interference channel. The same idea also applies to a fully connected interference channel [9], [10]. In this work, ... |

131 | Gaussian interference networks: Sum capacity in the low interference regime and new outer bounds on the capacity region
- Annapureddy, Veeravalli
- 2009
(Show Context)
Citation Context ...e of could mitigate this adverse effect. Theorem 2: The secrecy sum rate is upper bounded by (14) where . . Remark 3: The upper bound in Theorem 2 applies for any set of gains . It was shown in [16], =-=[20]-=- that when there are no secrecy constraints and, the set of satisfies (15) the sum capacity of the -user many-to-one interference channel is given by (16) It is clear that (16) can be used as an upper... |

114 |
Achieving 1/2 log (1+SNR) on the AWGN channel with lattice encoding and decoding
- Erez, Zamir
- 2004
(Show Context)
Citation Context ...e in the context of secrecy. We use lattice codes to achieve secrecy for this model and use the tool first introduced in [11] which computes secrecy rates when the lattice code has a nested structure =-=[12]-=-. Notably, the structure of the lattice we use differs from that used in interference channels without secrecy constraints [8]–[10], and accordingly so does its error probability analysis [12]. For th... |

88 | The General Gaussian Multiple Access and Two-Way Wire-Tap Channels: Achievable Rates and Cooperative Jamming - Tekin, Yener - 2008 |

51 | Generalized entropy power inequalities and monotonicity properties of information
- Madiman, Barron
(Show Context)
Citation Context ...= 1, ..., K − 1. Then it can be shown that the first limit in (45) is upper bounded by ) K−1 ∑ i=1 C (Pi) + C ( ∑K−1 i=1 hiPi K − 1 (48) The main technique is the generalized entropy power inequality =-=[14]-=-. Since no secrecy constraint is invoked in its derivation, its result is still applicable here. This, along with the fact that I ( Xn K ; Y n K |Xn ) 1,...,K−1 ≤ nC(PK), gives us the result in the th... |

45 | A layered lattice coding scheme for a class of three user Gaussian interference channels,” ArXiv pre-print cs.IT/0809.4316
- Sridharan, Jafarian, et al.
- 2008
(Show Context)
Citation Context ... results include [8] where lattice codes are used for interference alignment for a many-to-one Gaussian interference channel. The same idea also applies to a fully connected interference channel [9], =-=[10]-=-. In this work, we focus on the Gaussian many-to-one interference channel first studied in [8], in an effort to investigate the effects of interference in the context of secrecy. We use lattice codes ... |

44 | Providing secrecy with structured codes: Tools and applications to two-user Gaussian channels,” submitted to
- He, Yener
(Show Context)
Citation Context ...mitters and their receivers [7], and upper bounding the secrecy sum rate of the multiple access wiretap channel part [8]. To derive the achievable rate, we utilize structured codes and layered coding =-=[11]-=-, [15], [18]. The design of the layers follows [15], though for each layer, we use nested lattice codes from [19] instead of the sphere shaped lattice codes as in [15]. The merit of using nested latti... |

43 | Capacity of symmetric k-user gaussian very strong interference channels.” [Online]. Available: http://arxiv.org/abs/0808.2314
- Sridharan, Jafarian, et al.
(Show Context)
Citation Context ...table results include [8] where lattice codes are used for interference alignment for a many-to-one Gaussian interference channel. The same idea also applies to a fully connected interference channel =-=[9]-=-, [10]. In this work, we focus on the Gaussian many-to-one interference channel first studied in [8], in an effort to investigate the effects of interference in the context of secrecy. We use lattice ... |

40 | On the secrecy of multiple access wiretap channel
- Ekrem, Ulukus
- 2008
(Show Context)
Citation Context ...and accordingly so does its error probability analysis [12]. For the converse, known results are limited to the case where the eavesdropper observes a weaker channel than the legitimate receiver [3], =-=[4]-=-. The upper bound from [1] is general, yet is difficult to evaluate for the Gaussian case due to the presence of the auxiliary random variables. While the upper bound in [2] is applicable to the stron... |

23 | K-user interference channels: Achievable secrecy rate and degrees of freedom
- He, Yener
- 2009
(Show Context)
Citation Context ...user Gaussian many-to-one interference channel, and an upper bound on the secrecy sum rate. The achievability technique is general and applies to the full connected Kuser interference channel as well =-=[15]-=-. The converse utilizes a combination of techniques in [3], [4]. Although both techniques were designed for weak interference, we show their combination provides a good sum rate upper bound for the st... |

19 | Cognitive interference channels with confidential messages
- Liang, Somekh-Baruch, et al.
(Show Context)
Citation Context ...of interference on secrecy, the fundamental model to study is the interference channel with confidential messages. Indeed, this model with two users has been studied extensively up to date, e.g., [1]–=-=[6]-=-. The case with more than two users, by comparison, is not well explored. Difficulties in solving the K-user case, K ≥ 3, exist in both the achievability and the converse. For achievability, there is ... |

18 | A new outer bound for the Gaussian interference channel with confidential messages - He, Yener - 2009 |

15 | Interference-Assisted Secret Communication - Tang, Liu, et al. - 2008 |

14 | Providing Secrecy with Lattice Codes
- He, Yener
- 2008
(Show Context)
Citation Context ...el first studied in [8], in an effort to investigate the effects of interference in the context of secrecy. We use lattice codes to achieve secrecy for this model and use the tool first introduced in =-=[11]-=- which computes secrecy rates when the lattice code has a nested structure [12]. Notably, the structure of the lattice we use differs from that used in interference channels without secrecy constraint... |

12 |
Secrecy capacity region of a class of one-sided interference channel
- Li, Yates, et al.
(Show Context)
Citation Context ...10], and accordingly so does its error probability analysis [12]. For the converse, known results are limited to the case where the eavesdropper observes a weaker channel than the legitimate receiver =-=[3]-=-, [4]. The upper bound from [1] is general, yet is difficult to evaluate for the Gaussian case due to the presence of the auxiliary random variables. While the upper bound in [2] is applicable to the ... |

9 |
Interference Alignment for Secrecy. Submited to
- Koyluoglu, El-Gamal, et al.
- 2008
(Show Context)
Citation Context ...e intended message. Yet, in secrecy problems, we have to face the question on how to remove the interference when the receiver is not supposed to decode the interference. This problem is addressed in =-=[7]-=- for the case where all links are i.i.d. fading under a continuous distribution, and interference alignment in temporal domain leads to achievable rates. Yet, if the channel is static, this method is ... |

6 | Secrecy Generation for Multiple Input Multiple Output Channel Models - Csiszár, Narayan - 2009 |

4 | Cooperative binning and channel prefixing for secrecy in interference channels”, Submitted to - Koyluoglu, El-Gamal |

3 | Interference Alignment Via Random Coding and the Capacity of a Class of Deterministic Interference Channels - Cadambe, Jafar - 2009 |

1 | Secure communication on interference channels,” presented at the - Yates, Tse, et al. - 2008 |

1 |
interference channels: Achievable secrecy rate and degrees of freedom,” presented at the
- Koyluoglu, El-Gamal, et al.
(Show Context)
Citation Context ...city region within 0.5 bit for the very strong interference condition. Interference channel with more than two users has also been studied. A symmetric static -user interference channel is studied in =-=[13]-=-. Reference [14] has studied the -user interference channel where all links were i.i.d. fading and sampled from a continuous distribution. Again the results in both cases are limited to achievable rat... |

1 |
Interference alignment for secrecy
- Poor
(Show Context)
Citation Context ...in 0.5 bit for the very strong interference condition. Interference channel with more than two users has also been studied. A symmetric static -user interference channel is studied in [13]. Reference =-=[14]-=- has studied the -user interference channel where all links were i.i.d. fading and sampled from a continuous distribution. Again the results in both cases are limited to achievable rates and no outer ... |

1 |
The approximate capacity of the many-to-one and one-to-many Gaussian interference channels,” presented at
- Tse
- 2007
(Show Context)
Citation Context ...ion for studying this channel is to be able to comprehensively characterize the role of interference in this simplified -user setting. This model without secrecy constraints has first been studied by =-=[15]-=- and recently by [16]. Reference [15] derives the inner and outer bound for the channel model and shows that their gap is bounded by a constant which is only a function of the number of users . When p... |

1 |
lattices and linear codes
- Sridharan, Jafarian, et al.
- 1997
(Show Context)
Citation Context ...hows that their gap is bounded by a constant which is only a function of the number of users . When proving the inner bound, [15] uses layered coding and the sphere shaped lattice code for each layer =-=[17]-=-. Doing so aligns signals from the first transmitters at the th receiver, and facilitates the decoding process at this receiver. Reference [16] characterizes a set of channel gains for which the sum c... |

1 |
A layered lattice coding scheme for a class of three user Gaussian interference channels,” presented at the 46th Allerton Conf
- Jafar, Shamai
- 2008
(Show Context)
Citation Context ...their receivers [7], and upper bounding the secrecy sum rate of the multiple access wiretap channel part [8]. To derive the achievable rate, we utilize structured codes and layered coding [11], [15], =-=[18]-=-. The design of the layers follows [15], though for each layer, we use nested lattice codes from [19] instead of the sphere shaped lattice codes as in [15]. The merit of using nested lattice codes for... |

1 |
1/2 log (1+ SNR) on the AWGN channel with lattice encoding and decoding
- Annapureddy, V
- 2004
(Show Context)
Citation Context ...art [8]. To derive the achievable rate, we utilize structured codes and layered coding [11], [15], [18]. The design of the layers follows [15], though for each layer, we use nested lattice codes from =-=[19]-=- instead of the sphere shaped lattice codes as in [15]. The merit of using nested lattice codes for secrecy problems has recently been demonstrated in [11]. Specifically, it has been found that the eq... |

1 |
On network interference management
- Viswanath
(Show Context)
Citation Context ...case where only user is allowed to transmit, we obtain the following secure degrees of freedom region: (17) (18) Since this is the same degrees of freedom region when there are no secrecy constraints =-=[21]-=-, we conclude that when the power ratio between each node is fixed, imposing secrecy constraints does not lead to any loss in terms of the secure degrees of freedom region. 3) Constant Gap Results: Se... |

1 |
Lattices which are good for (almost) everything
- Zamir
- 2005
(Show Context)
Citation Context ... . We next describe a result on decoding nested lattice codes when interference is present. Consider -dimensional lattices , such that is Rogers-good for covering and Poltyrev-good for channel coding =-=[22]-=-. Construct the fine lattice as in [19, Section 7] such that . Hence, forms a nested lattice pair. Define independent random variables , such that is uniformly distributed over the fundamental region ... |

1 |
general Gaussian multiple access and two-way wire-tap channels: Achievable rates and cooperative jamming
- Madiman, Barron
- 2008
(Show Context)
Citation Context ...ceptionally well reception. Otherwise, let be the user in with the largest value for , where . is the user that will transmit jamming signals to protect the confidential messages from the other users =-=[23]-=-. We do not use this cooperative jamming scheme for the th layer. Also note that when , this scheme is clearly not applicable. To simplify and unify the notation, we define the set of users excluding ... |

1 |
entropy power inequalities and monotonicity properties of information
- He, Yener
- 2007
(Show Context)
Citation Context ...em 4] corresponds to the case with . Let . We start with (178) (179) We next derive an upper bound on the first two terms in (179). The main tool used is the generalized entropy power inequality [8], =-=[24]-=-: Let be lengthcontinuous random vector. Let be arbitrary subset of . Then (180) where is the maximum number of sets in in which any appears. Without loss of generality, we assume . Define . Define as... |