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## Compute-and-Forward Two-Way Relaying

Venue: | IET Commun |

Citations: | 2 - 2 self |

### Citations

7184 | Convex Optimization
- Boyd, Vandenberghe
- 2004
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Citation Context ...lowing equation, must be nonnegative. ( βih1ia1i β2i h 2 1i + µi )2 + ( βih2ia2i β2i h 2 2i + µi )2 = P1 + P2 (23) This equation has not a straightforward answer and can be solved by bisection method =-=[21]-=-. On the other hand, when the answer is inside the feasible region, we should have ( βihkiaki β2i h 2 ki )2 + ( βihkiaki β2i h 2 ki )2 < P1 + P2 (24) 8 and the PAV is given by αk = aki βihki , ∀k = 1,... |

430 | A simple Cooperative diversity method based on network path selection
- Bletsas, Khisti, et al.
- 2006
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Citation Context ... the assumation of Pr ≥ max (P1, P2) we can easily rewrite (31) as m = argmax i Rri (48) Now, the best relay, after the multiple access phase, is selected based on (48), using the approach similar to =-=[22]-=-. That is the relay i, i = 1, 2, ...,M , sets a timer with the value Ti proportional to the inverse of its corresponding rate, i.e. Rri . The first relay that its timer reaches zero (which has the hig... |

196 | Hot Topic: Physical-Layer Network Coding
- Zhang, Liew, et al.
- 2006
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Citation Context ...mmunication scenario, two users attempt to communicate with each 1 ar X iv :1 40 8. 28 55 v2s[ cs .IT ]s10sO cts20 14 other with the help of a relay. To this end, physical layer network coding (PLNC) =-=[1]-=- along with the conventional DF or AF relaying strategy has been commonly considered [2-4]. It has been shown that PLNC can achieve within 1/2 bit of the capacity of a Gaussian TWRC (Two Way Relay Cha... |

174 | Joint physical layer coding and network coding for bi-directional relaying - Narayanan, Wilson, et al. - 2007 |

168 | Capacity of Rayleigh fading channels under different adaptive transmission and diversity-combining techniques
- Alouini, Goldsmith
- 1999
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Citation Context ...2l ) − . . .+ (−1)M−1I1 ( M∑ k=1 1 P1σ21k + 1 P2σ22k ) } (58) where In (µ) = ∞ ∫ 0 tn−1 ln (1 + t) e−µtdt = (n− 1)!eµ n∑ l=1 Γ(l−n,µ) µl and Γ (., .) is the upper incomplete gamma function defined in =-=[24]-=-. V NUMERICAL RESULTS For numerical evaluation, target rate Rt = 1 is considered. The Rayleigh channel parameters equal to σ2ji = 1, j = 1, 2, i = 1, ...,M , are assumed. The parameter δ in algorithm ... |

157 | Compute-and-Forward: Harnessing Interference Through Structured Codes
- Nazer, Gastpar
- 2011
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Citation Context ...rward it to the users. Due to noise amplification in the relay, this scheme shows a poor performance [2]. The novel relaying strategy known as compute-and-forward (CMF), proposed by Nazer and Gastpar =-=[8]-=-, is proved to be efficient for multiuser communication scenarios. The CMF strategy can exploit the interference to achieve a higher throughput. CMF strategy is also known as a reliable physical layer... |

133 |
Space-Time Coding: Theory and Practice
- Jafarkhani
- 2005
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Citation Context ...i=1 ( 2Rt − 1 P )( 1 σ21i + 1 σ22i ) = (2Rt − 1)M PM M∏ i=1 ( 1 σ21i + 1 σ22i ) (55) 13 Hence, the acheivable diversity order from the outage bound with the definition G = − lim P→∞ log(Pout) log(P ) =-=[23]-=- is equal to M, i.e. the number of relays. According to the Theorem1 and with the assumation of Pr ≥ max (P1, P2), an upperbound on the sum rate conditioned on each channel realizations can be derived... |

118 | Physical Network Coding in Two-Way Wireless Relay Channels
- Popovski, Yomo
- 2007
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Citation Context ...se, which results in a performance loss. As a solution, an optimum ML decoder can be utilized at the relay at the expense of a very high complexity [3]. The three-step DF two-way relaying proposed in =-=[2]-=- requires three time slots that results in a throughput reduction. As an alternative, the relay can exploit AF strategy to simply amplify the received signal from the users, and then forward it to the... |

114 |
Achieving 1/2 log (1+SNR) on the AWGN channel with lattice encoding and decoding
- Erez, Zamir
- 2004
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Citation Context ...y receiving sufficient number of decoded equations from the relays. For codewords, lattice codes are commonly utilized, which can achieve the capacity of additive white Gaussian noise (AWGN) channels =-=[10]-=-. While CMF strategy has been considered in different scenarios in the literature, such as multi-antenna systems [11], cooperative distributed antenna systems [12], multi-access relay channels [13], g... |

103 |
Optimum decision feedback multiuser equalization with successive decoding achieves the total capacity of the Gaussian multiple-access channel
- Varanas, Guess
- 1997
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Citation Context ..., in the first step, both users simultaneously transmit their messages, and the relay recovers both messages in turn, using a linear receiver structure like successive interference cancellation (SIC) =-=[7]-=-. In the second step, the relay sends a combination of the recovered messages to the users. The problem with the scheme proposed is that, when recovering one of the messages, the other message is cons... |

101 | Capacity of the Gaussian two-way relay channel to within 1/2 bit - Nam, Chung, et al. - 2010 |

101 | Performance Bounds for Bi-Directional Coded Cooperation Protocols
- Kim, Mitran, et al.
- 2008
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Citation Context ... zero-mean Gaussian distribution with variance 1. III COMPUTE AND FORWARD TWO WAY RELAYING In our proposed CMF based scheme, Multiple Access Broadcast (MABC) protocol for two way transmission is used =-=[19]-=-. In the first time slot (named multiple access phase), two users simultaneously transmit their codewords to the relays. Each relay receives a noisy linear combination of users’ codewords, and using t... |

55 | Reliable Physical Layer Network Coding - Nazer, Gastpar - 2011 |

38 | Memoryless relay strategies for two-way relay channels - Cui, Ho, et al. - 2009 |

16 | Integer-Forcing Linear Receivers
- Zhan, Nazer, et al.
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Citation Context ...d, which can achieve the capacity of additive white Gaussian noise (AWGN) channels [10]. While CMF strategy has been considered in different scenarios in the literature, such as multi-antenna systems =-=[11]-=-, cooperative distributed antenna systems [12], multi-access relay channels [13], generalized multi-way relay channels [14], two transmitter multi-relay systems [15], and finally multi-source multi-re... |

15 |
Compute-and-Forward Strategies for Cooperative Distributed Antenna Systems
- Hong, Caire
- 2013
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Citation Context ...white Gaussian noise (AWGN) channels [10]. While CMF strategy has been considered in different scenarios in the literature, such as multi-antenna systems [11], cooperative distributed antenna systems =-=[12]-=-, multi-access relay channels [13], generalized multi-way relay channels [14], two transmitter multi-relay systems [15], and finally multi-source multi-relay network [16]; however, to our best knowled... |

12 | Decode-and-Forward Two-Way Relaying with Network Coding and Opportunistic Relay Selection
- Zhou, Li, et al.
- 2010
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Citation Context ...the messages, the other message is considered as noise, which results in a performance loss. As a solution, an optimum ML decoder can be utilized at the relay at the expense of a very high complexity =-=[3]-=-. The three-step DF two-way relaying proposed in [2] requires three time slots that results in a throughput reduction. As an alternative, the relay can exploit AF strategy to simply amplify the receiv... |

7 | Efficient compute-and-forward network codes search for twoway relay channel
- Wei, Chen
- 2012
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Citation Context ...recovering the equation, ai = arg max a∈Z2,a6=0 log+ (||a||2 − ∣∣hiTa∣∣2 1 + ||hi||2 )−1 = arg min a∈Z2,a6=0 ( aTHia ) (4) where log+ (x) = max (log (x) , 0). The solution of (4) can be expressed =-=[20]-=- as scaling the received signal by the following factor βi = hi Ta 1 + ||hi||2 (5) That is the recovered equation is expressed as si = Q(βiy r i ) = ai1x1 + ai2x2 (6) where Q(.) shows the lattice quan... |

5 |
Compute-and-Forward on a Multiaccess Relay Channel: Coding and Symmetric-Rate Optimization
- Soussi, Zaidi, et al.
- 2014
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Citation Context ...ls [10]. While CMF strategy has been considered in different scenarios in the literature, such as multi-antenna systems [11], cooperative distributed antenna systems [12], multi-access relay channels =-=[13]-=-, generalized multi-way relay channels [14], two transmitter multi-relay systems [15], and finally multi-source multi-relay network [16]; however, to our best knowledge the application of CMF in two-w... |

3 | Simplified compute-and-forward and its performance analysis
- Hejazi, Nasiri-Kenari
- 2013
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Citation Context ...ure, such as multi-antenna systems [11], cooperative distributed antenna systems [12], multi-access relay channels [13], generalized multi-way relay channels [14], two transmitter multi-relay systems =-=[15]-=-, and finally multi-source multi-relay network [16]; however, to our best knowledge the application of CMF in two-way relaying hasn’t been considered so far, just from information theory aspect in [17... |

3 |
Asymptotically optimal error-rate performance of linear physical-layer network coding in Rayleigh fading two-way relay channels
- Yang, Collings
- 2010
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Citation Context ...he best relay be real-valued Rayleigh channels. This assumption was commonly used in the literature when considering the performance analysis of CMF based strategies, for instance please see [15] and =-=[18]-=-. However for simulation evaluations, we consider general Rayliegh fading channel (Complex Gaussian Coefficient) with both phase and amplitude variations. We analitically derive, an upper bound on the... |

2 |
K.B.: ’Compute-and-Forward: Optimization Over Multi-Source-MultiRelay Networks
- Chen, Fan, et al.
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Citation Context ...e distributed antenna systems [12], multi-access relay channels [13], generalized multi-way relay channels [14], two transmitter multi-relay systems [15], and finally multi-source multi-relay network =-=[16]-=-; however, to our best knowledge the application of CMF in two-way relaying hasn’t been considered so far, just from information theory aspect in [17]. In this paper, we propose a new practical framew... |

1 |
Jinhong Yuan: ’Outage Performance for Compute-and-Forward in Generalized Multi-Way Relay Channels
- Wang, Xiang
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Citation Context ...ered in different scenarios in the literature, such as multi-antenna systems [11], cooperative distributed antenna systems [12], multi-access relay channels [13], generalized multi-way relay channels =-=[14]-=-, two transmitter multi-relay systems [15], and finally multi-source multi-relay network [16]; however, to our best knowledge the application of CMF in two-way relaying hasn’t been considered so far, ... |

1 |
K.: ’An analysis of the joint compute-and-forward decoder for the binaryinput two-way relay channel
- Hern, Narayanan
(Show Context)
Citation Context ...15], and finally multi-source multi-relay network [16]; however, to our best knowledge the application of CMF in two-way relaying hasn’t been considered so far, just from information theory aspect in =-=[17]-=-. In this paper, we propose a new practical framework for two-way relaying based on CMF strategy, in which we use a linear receiver and a general lattice encoding previously proposed by Nazer [8]. We ... |