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## Nested lattice codes for gaussian two-way relay channels,” arXiv:1301.6291v1 (2013)

Citations: | 1 - 0 self |

### Citations

12171 |
Elements of information theory
- Cover, Thomas
- 1991
(Show Context)
Citation Context ...obability of error is defined as Pe = Pr { Ŵ1 6= W1 or Ŵ2 6= W2 } . A rate pair (R1, R2) of non-negative real values is achievable if there exists encoding and decoding functions with Pe → 0 as n→∞ =-=[37]-=-. The capacity region of the GTRC is the convex closure of the set of achievable rate pairs (R1, R2). Note that the model depicted in Fig. 1 is referred to as the symmetric model if all source and rel... |

1927 | Network information flow
- Ahlswede, Cai, et al.
- 2000
(Show Context)
Citation Context ...ombined on the symbol level, where the relay sends the linear sum of the decoded symbols from both nodes. Shortly after the introduction of the two-way relay channel, its connection to network coding =-=[9]-=- was observed and investigated. The network coding schemes combine the data from nodes on the bit level using the XOR operation, see e.g., [10], [11], [12], [13], [14], [15]. Lattice coding uses modul... |

341 | Nested linear/lattice codes for structured multiterminal binning
- Zamir, Shamai, et al.
- 2002
(Show Context)
Citation Context ...nsive review on lattices and their performance analysis, we refer the reader to the study of [28], [29], [30]. Nested lattice codes have been shown to be capacity achieving for the AWGN channel [31], =-=[32]-=-, AWGN broadcast channel [32] and the AWGN multiple access channel [1]. Song and Devroye [33], using list decoding technique, show that lattice codes can achieve the DF rate of single source, single d... |

228 | Two-way communication channels
- Shannon
- 1961
(Show Context)
Citation Context ...tween several earth stations where there is no direct link between the stations. Two-way or bi-directional communication between two nodes without a relay was first proposed and studied by Shannon in =-=[3]-=-. In this setup, two nodes want to exchange messages with each other, and act as transmitters and receivers at the same time. For this setup, the capacity region is not known in general and only inner... |

196 | Information exchange in wireless networks with network coding and physical-layer broadcast
- Wu, Chou, et al.
- 2004
(Show Context)
Citation Context ...e two-way relay channel, its connection to network coding [9] was observed and investigated. The network coding schemes combine the data from nodes on the bit level using the XOR operation, see e.g., =-=[10]-=-, [11], [12], [13], [14], [15]. Lattice coding uses modulo addition in a multi-dimensional space and utilizes nonlinear operations for combining the data. Applying lattice coding in two-way relaying s... |

174 | Joint physical layer coding and network coding for bi-directional relaying
- Narayanan, Wilson, et al.
- 2007
(Show Context)
Citation Context ...ng uses modulo addition in a multi-dimensional space and utilizes nonlinear operations for combining the data. Applying lattice coding in two-way relaying systems was considered in, e.g., [16], [17], =-=[18]-=-. In general, as in CF or partial DF relaying strategies, the relay node need not to decode the source messages, but only need to pass sufficient information to the destination nodes. In this paper, w... |

157 | Compute-and-Forward: Harnessing Interference Through Structured Codes
- Nazer, Gastpar
- 2011
(Show Context)
Citation Context ...attice codes for the uplink (i.e., MAC phase), and structured binning for the downlink (i.e., broadcast phase), we propose two achievable schemes. Scheme 1 is based on “compute and forward” scheme of =-=[1]-=- while scheme 2 utilizes two different lattices for source nodes based on a three-stage lattice partition chain. We show that scheme 2 can achieve capacity region at the high signal-to-noise ratio (SN... |

130 | A Deterministic Approach to Wireless Relay Networks
- Avestimehr, Diggavi, et al.
- 2007
(Show Context)
Citation Context ...stpar by introducing compute-and-forward scheme obtain significantly higher rates between users than previous results in the literature over a relay network [1]. By utilizing a deterministic approach =-=[34]-=- and a simple AF or a particular superposition coding strategy at the relay, [6] achieves full-duplex GTRC capacity region within 3 bits from the cut-set bound for all values of channel gains. A gener... |

126 | Noisy network coding
- Lim, Kim, et al.
- 2011
(Show Context)
Citation Context ... node can achieve capacity region at the high SNR. Lim et.al, using noisy network coding for GTRC, show that the achievable rate of their scheme for each user is within 12 bit from the cut-set bound. =-=[36]-=-. The achievable sum rate in [36] is within 1 bit from the cut-set bound. Here, we apply nested lattice codes at the relay to obtain linear combination of messages. By comparing with the cut-set outer... |

123 |
Lattices which are good for (almost) everything
- Erez, Litsyn, et al.
- 2005
(Show Context)
Citation Context ...5], [24], [17], [25], [26], [27]. Similar to [18], [17], we apply the nested lattice coding. For a comprehensive review on lattices and their performance analysis, we refer the reader to the study of =-=[28]-=-, [29], [30]. Nested lattice codes have been shown to be capacity achieving for the AWGN channel [31], [32], AWGN broadcast channel [32] and the AWGN multiple access channel [1]. Song and Devroye [33]... |

118 | Physical Network Coding in Two-Way Wireless Relay Channels
- Popovski, Yomo
- 2007
(Show Context)
Citation Context ...lay channel, its connection to network coding [9] was observed and investigated. The network coding schemes combine the data from nodes on the bit level using the XOR operation, see e.g., [10], [11], =-=[12]-=-, [13], [14], [15]. Lattice coding uses modulo addition in a multi-dimensional space and utilizes nonlinear operations for combining the data. Applying lattice coding in two-way relaying systems was c... |

114 |
Achieving 1/2 log (1+SNR) on the AWGN channel with lattice encoding and decoding
- Erez, Zamir
- 2004
(Show Context)
Citation Context ...mprehensive review on lattices and their performance analysis, we refer the reader to the study of [28], [29], [30]. Nested lattice codes have been shown to be capacity achieving for the AWGN channel =-=[31]-=-, [32], AWGN broadcast channel [32] and the AWGN multiple access channel [1]. Song and Devroye [33], using list decoding technique, show that lattice codes can achieve the DF rate of single source, si... |

113 | Lattice Coding and Decoding Achieve the Optimal Diversity-Multiplexing Tradeoff of MIMO Channels - Gamal, Caire, et al. - 2004 |

109 | On lattice quantization noise
- Zamir, Feder
- 1996
(Show Context)
Citation Context ... good for mean-squared error December 12, 2013 DRAFT 5(MSE) quantization if lim n→∞ G ( Λ(n) ) = 1 2πe . The sequence is indexed by the lattice dimension n. The existence of such lattices is shown in =-=[39]-=-, [28]. Definition 7. (AWGN channel coding goodness or Poltyrev-good): Let Z be a length-i.i.d Gaussian vector, Z ∼ N (0, σ2ZIn). The volume-to-noise ratio of a lattice is given by µ (Λ, ǫ) = ( Vol(V)... |

101 | Capacity of the Gaussian two-way relay channel to within 1/2 bit
- Nam, Chung, et al.
- 2010
(Show Context)
Citation Context ...e coding uses modulo addition in a multi-dimensional space and utilizes nonlinear operations for combining the data. Applying lattice coding in two-way relaying systems was considered in, e.g., [16], =-=[17]-=-, [18]. In general, as in CF or partial DF relaying strategies, the relay node need not to decode the source messages, but only need to pass sufficient information to the destination nodes. In this pa... |

101 | Performance Bounds for Bi-Directional Coded Cooperation Protocols
- Kim, Mitran, et al.
- 2008
(Show Context)
Citation Context ...1 and 2 want to communicate with each other at rates R1 and R2, respectively, while a relay node facilitates the communication between them. TRC with a direct link between nodes 1 and 2 is studied in =-=[19]-=-, [20], [21], [22], [23]. Here, we consider a GTRC without a direct link between nodes 1 and 2. Our model is an extension of [18] and it is essentially the same as those considered in [5], [24], [17],... |

78 |
Coded bi-directional relaying
- Larsson, Johansson, et al.
- 2005
(Show Context)
Citation Context ...way relay channel, its connection to network coding [9] was observed and investigated. The network coding schemes combine the data from nodes on the bit level using the XOR operation, see e.g., [10], =-=[11]-=-, [12], [13], [14], [15]. Lattice coding uses modulo addition in a multi-dimensional space and utilizes nonlinear operations for combining the data. Applying lattice coding in two-way relaying systems... |

68 |
On coding without restrictions for the AWGN channel
- Poltyrev
- 1994
(Show Context)
Citation Context ...-good if lim n→∞ µ ( Λ(n), ǫ ) = 2πe, ∀ǫ ∈ (0, 1) and, for fixed volume-to-noise ratio greater than 2πe, Pr {Z /∈ Vn} decays exponentially in n . Poltyrev showed that sequences of such lattices exist =-=[40]-=-. The existence of a sequence of lattices Λ(n) which are good in both senses (i.e., simultaneously are Poltyrev-good and Rogers-good) has been shown in [28]. Definition 8. (Nested Lattices): A lattice... |

62 | Capacity bounds for two-way relay channel
- Nam, Chung, et al.
- 2008
(Show Context)
Citation Context ... [20], [21], [22], [23]. Here, we consider a GTRC without a direct link between nodes 1 and 2. Our model is an extension of [18] and it is essentially the same as those considered in [5], [24], [17], =-=[25]-=-, [26], [27]. Similar to [18], [17], we apply the nested lattice coding. For a comprehensive review on lattices and their performance analysis, we refer the reader to the study of [28], [29], [30]. Ne... |

55 | Channel coding and decoding in a relay system operated with physical-layer network coding
- Zhang, Liew
- 2009
(Show Context)
Citation Context ...annel, its connection to network coding [9] was observed and investigated. The network coding schemes combine the data from nodes on the bit level using the XOR operation, see e.g., [10], [11], [12], =-=[13]-=-, [14], [15]. Lattice coding uses modulo addition in a multi-dimensional space and utilizes nonlinear operations for combining the data. Applying lattice coding in two-way relaying systems was conside... |

43 |
Rate regions for the separated twoway relay channel
- Gunduz, Tuncel, et al.
- 2010
(Show Context)
Citation Context ...so known as the bi-directional relay channel, consists of two nodes communicating with each other in a bi-directional manner via a relay. This setup was first introduced in [4]; later studied in [4], =-=[5]-=-, [6] and an approximate characterization of the capacity region of the Gaussian case is derived. The traditional relaying protocols require four channel uses to exchange the data of two nodes whereas... |

39 | Lattices are everywhere
- Zamir
- 2009
(Show Context)
Citation Context ...4], [17], [25], [26], [27]. Similar to [18], [17], we apply the nested lattice coding. For a comprehensive review on lattices and their performance analysis, we refer the reader to the study of [28], =-=[29]-=-, [30]. Nested lattice codes have been shown to be capacity achieving for the AWGN channel [31], [32], AWGN broadcast channel [32] and the AWGN multiple access channel [1]. Song and Devroye [33], usin... |

32 | Network coding for two-way relay channels using lattices
- Baik, Chung
- 2008
(Show Context)
Citation Context ...Lattice coding uses modulo addition in a multi-dimensional space and utilizes nonlinear operations for combining the data. Applying lattice coding in two-way relaying systems was considered in, e.g., =-=[16]-=-, [17], [18]. In general, as in CF or partial DF relaying strategies, the relay node need not to decode the source messages, but only need to pass sufficient information to the destination nodes. In t... |

31 |
Capacity of the two-way relay channel within a constant gap
- Avestimehr, Sezgin, et al.
- 2010
(Show Context)
Citation Context ...own as the bi-directional relay channel, consists of two nodes communicating with each other in a bi-directional manner via a relay. This setup was first introduced in [4]; later studied in [4], [5], =-=[6]-=- and an approximate characterization of the capacity region of the Gaussian case is derived. The traditional relaying protocols require four channel uses to exchange the data of two nodes whereas the ... |

28 | Achievable rate regions and performance comparison of half duplex bi-directional relaying protocols
- Kim, Devroye, et al.
- 2011
(Show Context)
Citation Context ...2 want to communicate with each other at rates R1 and R2, respectively, while a relay node facilitates the communication between them. TRC with a direct link between nodes 1 and 2 is studied in [19], =-=[20]-=-, [21], [22], [23]. Here, we consider a GTRC without a direct link between nodes 1 and 2. Our model is an extension of [18] and it is essentially the same as those considered in [5], [24], [17], [25],... |

23 | Joint source channel coding with side information using hybrid digital analog codes
- Wilson, Narayanan, et al.
- 2010
(Show Context)
Citation Context ...bits from the sum capacity, which was the best gap-to-capacity. Communication over a symmetric GTRC when all source and relay nodes have the same transmit powers and noise variances, is considered in =-=[35]-=-. It is shown that lattice codes and lattice decoding at the relay node can achieve capacity region at the high SNR. Lim et.al, using noisy network coding for GTRC, show that the achievable rate of th... |

23 | Nested lattice codes for gaussian relay networks with interference
- Nam, Chung, et al.
- 2011
(Show Context)
Citation Context ...n. To reach this goal, we choose a as the closest integer to √g i.e., a = ⌈√ g ⌋ . 2) Scheme 2: Our proposed scheme: Let us first consider a theorem that is a key to our code construction. Theorem 1. =-=[42]-=- For any P1 ≥ P2 ≥ 0, a sequence of n-dimensional lattice partition chains Λ(n)C /Λ(n)2 /Λ(n)1 , i.e., Λ(n)1 ⊆ Λ (n) 2 ⊆ Λ(n)C , exists that satisfies the following properties: • Λ(n)1 and Λ (n) 2 are... |

22 |
Achievable rates for the restricted half-duplex two-way relay channel
- Schnurr, Oechtering, et al.
- 2007
(Show Context)
Citation Context ...ere exist several strategies for the processing at the relay node, e.g., an amplify-and-forward (AF) strategy [4], a decode-and-forward (DF) strategy [4], [7], or a compress-and-forward (CF) strategy =-=[8]-=-. The AF protocol is a simple scheme, which amplifies the signal transmitted from both nodes and retransmit it to them, and unlike the DF protocol, no decoding at the relay is performed. In the two-wa... |

22 | Title: Approximate capacity of the two-way relay channel: A deterministic approach
- Avestimehr, Sezgin, et al.
- 2008
(Show Context)
Citation Context ...ied in [19], [20], [21], [22], [23]. Here, we consider a GTRC without a direct link between nodes 1 and 2. Our model is an extension of [18] and it is essentially the same as those considered in [5], =-=[24]-=-, [17], [25], [26], [27]. Similar to [18], [17], we apply the nested lattice coding. For a comprehensive review on lattices and their performance analysis, we refer the reader to the study of [28], [2... |

12 | Superimposed XOR: A new physical layer network coding scheme for two-way relay channels
- Liu, Tao, et al.
- 2009
(Show Context)
Citation Context ... its connection to network coding [9] was observed and investigated. The network coding schemes combine the data from nodes on the bit level using the XOR operation, see e.g., [10], [11], [12], [13], =-=[14]-=-, [15]. Lattice coding uses modulo addition in a multi-dimensional space and utilizes nonlinear operations for combining the data. Applying lattice coding in two-way relaying systems was considered in... |

12 | Decode-and-Forward Two-Way Relaying with Network Coding and Opportunistic Relay Selection
- Zhou, Li, et al.
- 2010
(Show Context)
Citation Context ...onnection to network coding [9] was observed and investigated. The network coding schemes combine the data from nodes on the bit level using the XOR operation, see e.g., [10], [11], [12], [13], [14], =-=[15]-=-. Lattice coding uses modulo addition in a multi-dimensional space and utilizes nonlinear operations for combining the data. Applying lattice coding in two-way relaying systems was considered in, e.g.... |

12 | Lattice codes for the Gaussian relay channel: Decode-and-forward and compress-and-forward,” submitted to
- Song, Devroye
(Show Context)
Citation Context ...[28], [29], [30]. Nested lattice codes have been shown to be capacity achieving for the AWGN channel [31], [32], AWGN broadcast channel [32] and the AWGN multiple access channel [1]. Song and Devroye =-=[33]-=-, using list decoding technique, show that lattice codes can achieve the DF rate of single source, single destination Gaussian relay channels with one or more relays. It is also shown that the lattice... |

11 |
Two-way wireless communication via a relay station
- Knopp
- 2007
(Show Context)
Citation Context ... [21], [22], [23]. Here, we consider a GTRC without a direct link between nodes 1 and 2. Our model is an extension of [18] and it is essentially the same as those considered in [5], [24], [17], [25], =-=[26]-=-, [27]. Similar to [18], [17], we apply the nested lattice coding. For a comprehensive review on lattices and their performance analysis, we refer the reader to the study of [28], [29], [30]. Nested l... |

10 |
Spectral efficient protocols for nonregenerative half-duplex relaying
- Rankov, Wittneben
- 2005
(Show Context)
Citation Context ...e two-way relay channel, also known as the bi-directional relay channel, consists of two nodes communicating with each other in a bi-directional manner via a relay. This setup was first introduced in =-=[4]-=-; later studied in [4], [5], [6] and an approximate characterization of the capacity region of the Gaussian case is derived. The traditional relaying protocols require four channel uses to exchange th... |

8 |
Molisch, “Asymmetric twoway relay with doubly nested lattice codes
- Tian, Wu, et al.
- 2012
(Show Context)
Citation Context ...ate with each other at rates R1 and R2, respectively, while a relay node facilitates the communication between them. TRC with a direct link between nodes 1 and 2 is studied in [19], [20], [21], [22], =-=[23]-=-. Here, we consider a GTRC without a direct link between nodes 1 and 2. Our model is an extension of [18] and it is essentially the same as those considered in [5], [24], [17], [25], [26], [27]. Simil... |

8 |
On the role of MMSE estimation in approaching the information theoretic limits of linear Gaussian channels: Shannon meets Wiener
- Forney
- 2003
(Show Context)
Citation Context ...7], [25], [26], [27]. Similar to [18], [17], we apply the nested lattice coding. For a comprehensive review on lattices and their performance analysis, we refer the reader to the study of [28], [29], =-=[30]-=-. Nested lattice codes have been shown to be capacity achieving for the AWGN channel [31], [32], AWGN broadcast channel [32] and the AWGN multiple access channel [1]. Song and Devroye [33], using list... |

7 | Outer bounds for the capacity region of a Gaussian two-way relay channel
- K, Prathyusha, et al.
- 2012
(Show Context)
Citation Context ... to communicate with each other at rates R1 and R2, respectively, while a relay node facilitates the communication between them. TRC with a direct link between nodes 1 and 2 is studied in [19], [20], =-=[21]-=-, [22], [23]. Here, we consider a GTRC without a direct link between nodes 1 and 2. Our model is an extension of [18] and it is essentially the same as those considered in [5], [24], [17], [25], [26],... |

3 |
Optimal resource allocation for a bidirectional regenerative half-duplex relaying
- Oechtering, Boche
- 2006
(Show Context)
Citation Context ...d data back to both nodes. For this phase, there exist several strategies for the processing at the relay node, e.g., an amplify-and-forward (AF) strategy [4], a decode-and-forward (DF) strategy [4], =-=[7]-=-, or a compress-and-forward (CF) strategy [8]. The AF protocol is a simple scheme, which amplifies the signal transmitted from both nodes and retransmit it to them, and unlike the DF protocol, no deco... |

2 | Analysis and design of communication techniques in spectrally efficient wireless relaying systems - Zhao - 2010 |

2 | Partial decode-forward coding schemes for the Gaussian two-way relay channel
- Zhong, Vu
- 2012
(Show Context)
Citation Context ...mmunicate with each other at rates R1 and R2, respectively, while a relay node facilitates the communication between them. TRC with a direct link between nodes 1 and 2 is studied in [19], [20], [21], =-=[22]-=-, [23]. Here, we consider a GTRC without a direct link between nodes 1 and 2. Our model is an extension of [18] and it is essentially the same as those considered in [5], [24], [17], [25], [26], [27].... |

2 | On achievable rate regions of the asymmetric awgn two-way relay channel
- Ong, Kellett, et al.
- 2011
(Show Context)
Citation Context ... [22], [23]. Here, we consider a GTRC without a direct link between nodes 1 and 2. Our model is an extension of [18] and it is essentially the same as those considered in [5], [24], [17], [25], [26], =-=[27]-=-. Similar to [18], [17], we apply the nested lattice coding. For a comprehensive review on lattices and their performance analysis, we refer the reader to the study of [28], [29], [30]. Nested lattice... |

2 |
A proof of the existence of good lattices,” tech
- Krithivasan, Pradhan
- 2007
(Show Context)
Citation Context ... lattice code is R = 1 n log |C| = 1 n log Vol (V) Vol (V1) . The existence of nested lattices where the coarse lattice as well as the fine lattice are good in both senses has also been shown in [1], =-=[41]-=-. An interesting property of these codes is that any integer combinations of transmitted codewords are themselves codewords. In the following, we present a key property of dithered nested lattice code... |