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## On the secrecy rate of interference networks using structured codes (2009)

Venue: | in Proceedings of the IEEE International Symposium on Information Theory (ISIT 2009), (Seoul, South Korea |

Citations: | 6 - 2 self |

### Citations

12425 |
Elements of Information Theory
- Cover, Thomas
- 1991
(Show Context)
Citation Context ... features of the lattice coding argument. To explain this further, let us reconsider the symmetric interference channel with a wiretapper (Figure 1) and use randomly generated codebooks as defined in =-=[17]-=- for the legitimate channel. Note that randomly generated codebooks with joint (typicalset) decoding is the conventional achievability argument for the multiple-access channel. As shown in [17], as lo... |

753 |
Broadcast channels with confidential messages
- Csiszár, Körner
- 1978
(Show Context)
Citation Context ...ctives on this problem. From an information theoretic perspective, the capacity of a wiretap channel, a model for eavesdropping attack on a point to point channel, was introduced and analyzed in [7], =-=[6]-=-. A combination of random-coding 2 with binning was used to achieve the capacity of the wiretap channel. Subsequently, structured binning arguments (as in [3]) were used instead of random binning to o... |

478 |
A new achievable rate region for the interference channel
- Han, Kobayashi
- 1981
(Show Context)
Citation Context ...weak. For an interference channel with two transmitreceive pairs, the nested lattice coding strategy described in [10] achieves a rate region that is, in general, a subset of the Han-Kobayashi region =-=[19]-=-. Thus, for general values of a, it is not yet known if lattice codebooks can be used to achieve the same rate region for the unconstrained two-user Gaussian interference channel as the Han-Kobayashi ... |

126 | Lattices which are good for (almost) everything - Erez, Litsyn, et al. - 2005 |

114 | Achieving 1 log(1 + SNR) on the AWGN channel with lattice encoding and decoding - Erez, Zamir - 2004 |

99 |
A case where interference does not reduce capacity
- Carleial
- 1975
(Show Context)
Citation Context ...2 log |C| − (log(|C|) + n) ≥ log |C| − n I(X1; X1 + X2) = H(X1) − H(X1|X1 + X2) ≤ log |C| − log |C| + nA. Very Strong Interference Channel The “very strong” interference channel was first studied in =-=[14]-=-. By very strong, we mean that the interference channel gain (a in equation (1)) is large enough such that the interfering signal (for e.g. from Transmitter 1) can be successfully decoded at the recei... |

99 | Averaging bounds for lattices and linear codes
- Loeliger
- 1997
(Show Context)
Citation Context ... n × n matrix and G is an n × k matrix with elements from GF(p). The details behind this construction and the fact that matrices G, G ′ exist such that these lattices are “good” can be found in [11], =-=[18]-=-. Then we have, Λ mod L ≡ G ′ [p −1 GZ k p + Z n ] mod G ′ (Z n ) where modulo Z n is intersection with the Voronoi region of Z n (as defined in [11]), and ≡ denotes the fact that there is an invertib... |

91 | Multiple access channels with confidential messages,”
- Liang, Poor
- 2008
(Show Context)
Citation Context ...ng to obtain the same results for wiretap channel capacity. Subsequently, the wiretap channel framework has been generalized to multiple other settings, including channels such as the multiple access =-=[4]-=- and cognitive-interference [5] channels and also to network models such as the wireless erasure network [8]. In all of these cases, as in [6], random coding and binning arguments form the basis for a... |

87 |
The Wire-Tap Channel,” The Bell System
- Wyner
- 1975
(Show Context)
Citation Context ...erspectives on this problem. From an information theoretic perspective, the capacity of a wiretap channel, a model for eavesdropping attack on a point to point channel, was introduced and analyzed in =-=[7]-=-, [6]. A combination of random-coding 2 with binning was used to achieve the capacity of the wiretap channel. Subsequently, structured binning arguments (as in [3]) were used instead of random binning... |

52 | The case for structured random codes in network capacity theorems
- Nazer, Gastpar
- 2008
(Show Context)
Citation Context ...r achieving the secrecy rate (region). In recent years, there is an increasing interest in structured coding schemes, particularly for enhancing the rates achievable in interference/wireless networks =-=[13]-=-, [10]. Lattice codes are shown to induce an alignment in the interference seen at each node, thus enhancing the degrees of freedom [10] and the secure degrees of freedom for an interference network [... |

43 | Capacity of symmetric k-user gaussian very strong interference channels
- Sridharan, Jafarian, et al.
- 2008
(Show Context)
Citation Context ...d using lattice codes with 1-bit secrecy for the channel given by Figure 1. Symmetric interference channels with multiple (> 2) transmit-receive pairs and very strong interference are investigated in =-=[15]-=- using a lattice coding framework. In [15], it is shown that if a2 (P +1)2 ≥ P , then codebooks that are nested subsets of the same lattice can be used such that each legitimate communication channel ... |

40 | Capacity of cognitive interference channels with and without secrecy,”
- Liang, Somekh-Baruch, et al.
- 2009
(Show Context)
Citation Context ...or wiretap channel capacity. Subsequently, the wiretap channel framework has been generalized to multiple other settings, including channels such as the multiple access [4] and cognitive-interference =-=[5]-=- channels and also to network models such as the wireless erasure network [8]. In all of these cases, as in [6], random coding and binning arguments form the basis for achieving the secrecy rate (regi... |

29 | Secure nested codes for type ii wiretap channels
- Liu, Liang, et al.
- 2007
(Show Context)
Citation Context ...nnel, was introduced and analyzed in [7], [6]. A combination of random-coding 2 with binning was used to achieve the capacity of the wiretap channel. Subsequently, structured binning arguments (as in =-=[3]-=-) were used instead of random binning to obtain the same results for wiretap channel capacity. Subsequently, the wiretap channel framework has been generalized to multiple other settings, including ch... |

29 | Sum capacity of the Gaussian interference channel in the low interference regime
- Annapureddy, Veeravalli
- 2008
(Show Context)
Citation Context ...(b) are due to the data processing inequality and (c) is due to Lemma 2. B. Weak Interference Channels Weak interference channels, where a < 1, have received significant attention in recent years. In =-=[16]-=-, the authors determine that, for all a such that |a + a3P | ≤ 1 2 , treating interference as noise in the legitimate (unconstrained) channel is optimal, i.e., that R1 = R2 = 1 2 log ( P 1 + a2 ) P + ... |

13 | Manjunath: A Robust Data Hiding Technique using Multidimensional Lattices
- Chae, Mukherjee, et al.
- 1998
(Show Context)
Citation Context ... the degrees of freedom [10] and the secure degrees of freedom for an interference network [9]. Simultaneously, lattice coding has also been shown to possess security benefits, for information hiding =-=[12]-=- and for information relaying in wireless networks [1], [2]. In this work, we emphasize the gains of using lattice coding schemes over random coding schemes for the interference 1 This work is support... |

2 |
Sriram Vishwanath, Syed Ali Jafar, and Shlomo Shamai. A layered lattice coding scheme for a class of three user gaussian interference channels
- Sridharan, Jafarian
- 2008
(Show Context)
Citation Context ...eving the secrecy rate (region). In recent years, there is an increasing interest in structured coding schemes, particularly for enhancing the rates achievable in interference/wireless networks [13], =-=[10]-=-. Lattice codes are shown to induce an alignment in the interference seen at each node, thus enhancing the degrees of freedom [10] and the secure degrees of freedom for an interference network [9]. Si... |

1 |
Aylin Yener,“Providing Secrecy with Lattice Codes
- He
- 2008
(Show Context)
Citation Context ...freedom for an interference network [9]. Simultaneously, lattice coding has also been shown to possess security benefits, for information hiding [12] and for information relaying in wireless networks =-=[1]-=-, [2]. In this work, we emphasize the gains of using lattice coding schemes over random coding schemes for the interference 1 This work is supported by DARPA IAMANET and a grant from the Air Force Off... |

1 |
Aylin Yener, “Two-hop Secure Communication Using an Untrusted Relay
- He
(Show Context)
Citation Context ...om for an interference network [9]. Simultaneously, lattice coding has also been shown to possess security benefits, for information hiding [12] and for information relaying in wireless networks [1], =-=[2]-=-. In this work, we emphasize the gains of using lattice coding schemes over random coding schemes for the interference 1 This work is supported by DARPA IAMANET and a grant from the Air Force Office o... |