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## Nested lattice codes for Gaussian relay networks with interference (2011)

Venue: | IEEE Trans. Inf. Theory |

Citations: | 23 - 1 self |

### Citations

12171 |
Elements of information theory
- Cover, Thomas
- 1991
(Show Context)
Citation Context ... the interference nature was also incorporated, and an achievable multicast rate was computed. This achievable rate has a cut-set-like representation and meets the information theoretic cut-set bound =-=[27]-=- in some special cases. To incorporate the noise, erasure networks with broadcast or interference only were considered in [7], [8]. However, the network models in [7], [8] assumed that the side inform... |

2071 | Information Theory and Reliable Communication - Gallager - 1968 |

1927 | Network information flow - Ahlswede, Cai, et al. - 2000 |

1166 |
Gamal, “Capacity theorems for the relay channel
- Cover, El
- 1979
(Show Context)
Citation Context ... interest to the capacity of single source multicast relay networks, which is still an open problem. For instance, the capacity of single relay channels is still unknown except for some special cases =-=[1]-=-. However, if we confine the class of networks further, there are several cases in which the capacity is characterized. Recently, in [2], the multicast capacity of wireline networks was characterized.... |

341 | Nested linear/lattice codes for structured multiterminal binning
- Zamir, Shamai, et al.
- 2002
(Show Context)
Citation Context ...n which ΛC is used as codewords and Λ is used for shaping. The coding rate of the nested lattice code is given by 1 n log |C| = log ρ. Nested lattice codes have been studied in many previous articles =-=[18]-=-, [19], [23], [24], and proved to have many useful properties, such as achieving the capacity of the AWGN channel. In the next subsection, we deal with the nested lattice codes for the achievability p... |

174 | Joint physical layer coding and network coding for bi-directional relaying
- Narayanan, Wilson, et al.
- 2007
(Show Context)
Citation Context ...the equal power case, i.e., Pu,v = P , the achievable multicast rate (3) has terms in the form of log ( 1 K + P ) for some integer K ≥ 1. Similar forms of achievable rate were observed in [10], [15], =-=[16]-=-, [25] for some equal power Gaussian networks. The following subsections are devoted to proving Theorem 1. A. Upper bound The cut-set bound [27] of the network is given by R ≤ max p(xV,V ) min S∈Γ I (... |

147 | Capacity of wireless erasure networks
- Dana, Gowaikar, et al.
- 2006
(Show Context)
Citation Context ...set-like representation and meets the information theoretic cut-set bound [27] in some special cases. To incorporate the noise, erasure networks with broadcast or interference only were considered in =-=[7]-=-, [8]. However, the network models in [7], [8] assumed that the side information on the location of all erasures in the network is provided to destination nodes. Noisy networks without side informatio... |

139 | Computation over multiple-access channels
- Nazer, Gastpar
- 2007
(Show Context)
Citation Context ...node can interfere with each other. Since wireless networks are often interference limited, our setup focuses on the more important aspect of them. This model covers those networks considered in [8], =-=[9]-=-, [10], [12]. Our interest in the relay networks with interference was inspired by [14], in which the capacity of single relay channels with interference was established. In this paper, we focus on tw... |

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

113 |
Achieving 1 log (1 + SNR) on the AWGN channel with lattice encoding and decoding
- Erez, Zamir
- 2004
(Show Context)
Citation Context ...ian relay networks with interference and linear finite-field symmetric networks with interference. For the Gaussian relay networks with interference, we propose a scheme based on nested lattice codes =-=[19]-=- which are formed from a lattice chain and compute an achievable multicast rate. The basic idea of using lattice codes is to exploit the structural gain of computation coding [11], which corresponds t... |

101 | Capacity of the Gaussian two-way relay channel to within 1/2 bit
- Nam, Chung, et al.
- 2010
(Show Context)
Citation Context ... As an extension to multiple source networks, we showed that the same lattice coding scheme considered in this work can achieve the capacity of the Gaussian two-way relay channel within 1 2 bit [15], =-=[17]-=-. As another direction of extension, we can consider applying structured codes to networks with non-orthogonal broadcast channels. There is a recent work on the interference channel [26] which is rela... |

93 | Averaging bounds for lattices and linear codes
- Loeliger
- 1997
(Show Context)
Citation Context ...lity of R1 directly followed. However, if we are only interested in finding the achievability of R1, not in the error exponent, we can use the argument on the bounding behavior of lattice decoding in =-=[21]-=-, which gives the same result in a much simpler way. Remark 3: Since P1 ≥ · · · ≥ PK , we have R∗1 ≥ · · · ≥ R∗K . Now, consider the case that, for some î < K, the rates R∗i , î+ 1 ≤ i ≤ K, are zero... |

68 |
On coding without restrictions for the AWGN channel
- Poltyrev
- 1994
(Show Context)
Citation Context ...g for the additive white Gaussian noise (AWGN) channel. A sequence of lattices is said to be Poltyrev-good if, for Z̄ ∼ N (0, σ̄2I), Pr{Z̄ /∈ R} ≤ e−nEP (µ), (8) where EP (·) is the Poltyrev exponent =-=[22]-=- and µ is the volume-to-noise ratio (VNR) defined as µ = (Vol(R))2/n 2πeσ̄2 . Note that (8) upper bounds the error probability of the nearest lattice point decoding (or equivalently, Euclidean lattice... |

64 | Capacity of a class of relay channels with orthogonal components
- Gamal, Zahedi
- 2005
(Show Context)
Citation Context ...ited, our setup focuses on the more important aspect of them. This model covers those networks considered in [8], [9], [10], [12]. Our interest in the relay networks with interference was inspired by =-=[14]-=-, in which the capacity of single relay channels with interference was established. In this paper, we focus on two special subclasses of general networks with interference; Gaussian relay networks wit... |

62 | Capacity bounds for two-way relay channel
- Nam, Chung, et al.
- 2008
(Show Context)
Citation Context ...t, in the equal power case, i.e., Pu,v = P , the achievable multicast rate (3) has terms in the form of log ( 1 K + P ) for some integer K ≥ 1. Similar forms of achievable rate were observed in [10], =-=[15]-=-, [16], [25] for some equal power Gaussian networks. The following subsections are devoted to proving Theorem 1. A. Upper bound The cut-set bound [27] of the network is given by R ≤ max p(xV,V ) min S... |

56 |
Information Flow in Relay Networks
- Aref
- 1980
(Show Context)
Citation Context ...ding technique called network coding. Starting from this seminal work, many efforts have been made to incorporate wireless effects in the network model, such as broadcast, interference, and noise. In =-=[3]-=-, the broadcast nature was incorporated into the network model by requiring each relay node to send the same signal on all outgoing channels, and the unicast capacity was determined. However, the mode... |

56 | Lattice strategies for the dirty multiple access channel
- Philosof, Khisti, et al.
(Show Context)
Citation Context ...ual power case, i.e., Pu,v = P , the achievable multicast rate (3) has terms in the form of log ( 1 K + P ) for some integer K ≥ 1. Similar forms of achievable rate were observed in [10], [15], [16], =-=[25]-=- for some equal power Gaussian networks. The following subsections are devoted to proving Theorem 1. A. Upper bound The cut-set bound [27] of the network is given by R ≤ max p(xV,V ) min S∈Γ I (XS,V ;... |

54 | Wireless Network Information Flow
- Avestimehr, Diggavi, et al.
- 2007
(Show Context)
Citation Context ...ity was determined. However, the model assumed that the network is deterministic (noiseless) and has no interference in reception at each node. In [4], the work was extended to multicast capacity. In =-=[5]-=-, the interference nature was also incorporated, and an achievable multicast rate was computed. This achievable rate has a cut-set-like representation and meets the information theoretic cut-set bound... |

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 ...1 2 bit [15], [17]. As another direction of extension, we can consider applying structured codes to networks with non-orthogonal broadcast channels. There is a recent work on the interference channel =-=[26]-=- which is related to this issue. 18 APPENDIX A. Proof of Theorem 2 Consider a lattice (more precisely, a sequence of lattices) Λn1 with σ2(Λn1 ) = P1, which is simultaneously Rogers-good and Poltyrev-... |

43 |
The multicast capacity of deterministic relay networks with no interference
- Ratnakar, Kramer
- 2006
(Show Context)
Citation Context ...ignal on all outgoing channels, and the unicast capacity was determined. However, the model assumed that the network is deterministic (noiseless) and has no interference in reception at each node. In =-=[4]-=-, the work was extended to multicast capacity. In [5], the interference nature was also incorporated, and an achievable multicast rate was computed. This achievable rate has a cut-set-like representat... |

15 |
Unicast transmission over multiple access erasure networks: Capacity and duality
- Smith, Vishwanath
- 2007
(Show Context)
Citation Context ...ike representation and meets the information theoretic cut-set bound [27] in some special cases. To incorporate the noise, erasure networks with broadcast or interference only were considered in [7], =-=[8]-=-. However, the network models in [7], [8] assumed that the side information on the location of all erasures in the network is provided to destination nodes. Noisy networks without side information at ... |

10 |
On the role of MMSE estimation in approaching the information theoretic limits of linear Gaussian channels: Shannon meets Wiener
- Jr
- 2003
(Show Context)
Citation Context ...me preliminaries for the lattices and nested lattice codes, which are key ingredients of our achievability proof. For a more comprehensive review on lattices and nested lattice codes, see [19], [20], =-=[23]-=-. An n-dimensional lattice Λ is defined as a discrete subgroup of Euclidean space Rn with ordinary vector addition. This implies that for any lattice points λ, λ′ ∈ Λ, we have λ + λ′ ∈ Λ, λ − λ′ ∈ Λ, ... |

6 | Relay networks with orthogonal components - Nam, Chung |

2 |
A proof of the existence of good nested lattices. available at http://www.eecs.umich.edu/techreports/systems/cspl/cspl384.pdf
- Krithivasan, Pradhan
(Show Context)
Citation Context ... as codewords and Λ is used for shaping. The coding rate of the nested lattice code is given by 1 n log |C| = log ρ. Nested lattice codes have been studied in many previous articles [18], [19], [23], =-=[24]-=-, and proved to have many useful properties, such as achieving the capacity of the AWGN channel. In the next subsection, we deal with the nested lattice codes for the achievability proof of Theorem 1.... |