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## Simplified compute-and-forward and its performance analysis (2013)

Venue: | IET Commun |

Citations: | 4 - 1 self |

### Citations

356 |
Improved methods for calculating vectors of short length in a lattice, including a complexity analysis
- Fincke, Pohst
- 1985
(Show Context)
Citation Context ... I− gmgm T 1 + ‖gm‖ 2 ) . (7) The above integer optimization problem is equivalent to the shortest vector problem (SVP), and has no closed-form solution [10, 16]. Lattice reduction algorithms such as =-=[17]-=- can be applied to calculate the optimum ECV numerically. However, due to the large search space of the problem on hand, the complexity of the system is considerably high. In the following, we introdu... |

158 | Compute-and-forward: Harnessing interference through structured codes,” Information Theory
- Nazer, Gastpar
- 2011
(Show Context)
Citation Context ...considered. Index Term- compute-and-forward, outage probability, performance analysis, channel estimation error, wireless relay network. 1 I INTRODUCTION The CMF method, proposed by Nazer and Gastpar =-=[1]-=-, enables exploiting, rather than combating, the multiple access interference in a wireless relay network, and thus results in improved network throughput [2]. In this method, relays, instead of recov... |

137 | Computation over multiple-access channels
- Nazer, Gastpar
- 2007
(Show Context)
Citation Context ...‖ek‖ 2 − ∣∣gTek∣∣2 1 + ‖g‖2 = ek TGek (16) and, in a similar way, b̃T G̃b̃ = bTGb. This yields that minimization in (14) is the same as the one in (12) and this proves the lemma. As an example, e25 = =-=[2, 7]-=- T is a permutation of e24 = [7, 2] T , in Table 1, and hence we have ‖gmin (e25)‖ = ‖gmin (e24)‖. 8 C. Simplified Compute-and-Forward (Proposed Scheme) As mentioned in the previous subsection, the id... |

54 | Reliable physical layer network coding
- Nazer, Gastpar
- 2011
(Show Context)
Citation Context ...t to 2000 (33 dB), in the case of L = 2 sources. The results are sorted and provided in Tabel 1. As an example, in Fig. 3, the distance between point F and the origin is equal to ‖gmin (ek)‖ for ek = =-=[2, 1]-=- T . Now, according to the Lemma 4, for a given gm, equivalent to a constant instantaneous sum SNR, only ECVs that satisfy ‖gmin (am)‖ ≤ ‖gm‖ are needed to be searched. These ECVs can be found from Ta... |

41 | An algebraic approach to physical-layer network coding - Feng, Silva, et al. |

22 | Multilevel coding schemes for compute-and-forward with flexible decoding,” Computing Research Repository (CoRR - Hern, Narayanan |

19 | Successive compute-and-forward
- Nazer
(Show Context)
Citation Context ... case of multiple antenna sources and relays, and compute the corresponding achievable rate based on an optimization problem. Successive recovering of messages in relays for CMF method is proposed in =-=[5]-=-. The idea is similar to successive interference cancellation (SIC) technique and leads to a higher recovering rate at each relay. In [6], the impact of inter-symbol interference on the CMF method, fo... |

10 |
Lattice codes for the compute-and-forward protocol: The flatness factor
- Belfiore
(Show Context)
Citation Context ... an information theory viewpoint which involves finding an achievable rate or a capacity region [7–9]. On the other hand, some works concentrate on the practical aspects and implementation of the CMF =-=[10]-=-. Efficient design of proper codes and lattices are discussed in [11–14]. Reference [15] considers the problem of lattice decoding and proposes some practical and efficient approaches to this end. Fin... |

9 | Practical code design for compute-and-forward - Ordentlich, Zhan, et al. |

5 | Concatenated signal codes with applications to compute and forward - Tunali, Narayanan |

5 | Lattice decoding for the compute-and-forward protocol
- Mejri, Othman, et al.
- 2012
(Show Context)
Citation Context ... region [7–9]. On the other hand, some works concentrate on the practical aspects and implementation of the CMF [10]. Efficient design of proper codes and lattices are discussed in [11–14]. Reference =-=[15]-=- considers the problem of lattice decoding and proposes some practical and efficient approaches to this end. Finding an optimum integer Equation Coefficient Vector (ECV), coefficients of recovered com... |

5 |
Outage performance for compute-and-forward in generalized multi-way relay channels,”
- Wang, Xiang, et al.
- 2012
(Show Context)
Citation Context ...ent Vector (ECV), coefficients of recovered combination at a relay, is computationally complex. This issue in not addressed considerably and will be investigated in this paper. The authors in [1] and =-=[16]-=- have calculated the outage performance of the CMF method in the cases of three-transmitter multiple-access channel (MAC) and Multi-Way relay channels, respectively. However, in these works, the achie... |

4 | The approximate sum capacity of the symmetric K-user gaussian interference channel - Ordentlich, Erez, et al. - 2012 |

2 |
The degrees of freedom of compute-and-forward,” Information Theory
- Niesen, Whiting
- 2012
(Show Context)
Citation Context ...over desired messages. In recent years, the CMF method as a promising approach, has received a lot of attention. There have been an increasing number of works on theoretical aspects of CMF method. In =-=[3]-=-, by analyzing asymptotic behavior, the number of degrees of freedom of CMF method is derived. The authors in [4] generalize the CMF method to the case of multiple antenna sources and relays, and comp... |

2 |
Mimo compute-and-forward
- Jiening, Erez, et al.
(Show Context)
Citation Context ...There have been an increasing number of works on theoretical aspects of CMF method. In [3], by analyzing asymptotic behavior, the number of degrees of freedom of CMF method is derived. The authors in =-=[4]-=- generalize the CMF method to the case of multiple antenna sources and relays, and compute the corresponding achievable rate based on an optimization problem. Successive recovering of messages in rela... |

1 |
A compute-and-forward scheme for gaussian bidirectional relaying with inter-symbol interference
- Huang, Tunali, et al.
- 2013
(Show Context)
Citation Context ...recovering of messages in relays for CMF method is proposed in [5]. The idea is similar to successive interference cancellation (SIC) technique and leads to a higher recovering rate at each relay. In =-=[6]-=-, the impact of inter-symbol interference on the CMF method, for the bi-directional relay case, is evaluated. Most of the analytical studies, including aforementioned works, consider the CMF from an i... |

1 | Compute-and-forward in the two-hop multi-antenna x-channel - Jorswieck, Richter |