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## An Algebraic Approach to Physical-Layer Network Coding (2013)

Citations: | 40 - 4 self |

### Citations

1012 | Linear network coding - Li, Yeung, et al. - 2003 |

958 | Factoring polynomials with rational coefficients - LENSTRA, LENSTRA, et al. - 1982 |

856 | An algebraic approach to network coding - Koetter, Médard - 2003 |

291 | Wireless network information flow: A deterministic approach - Avestimehr, Diggavi, et al. - 2011 |

258 | Coding for errors and erasures in random network coding - Kötter, Kschischang - 2008 |

230 | An Introduction to the Geometry of Numbers - Cassels - 1997 |

170 | Joint physical layer coding and network coding for bidirectional relaying - Wilson, Narayanan, et al. - 2010 |

161 | Insufficiency of linear coding in network information flow - Dougherty, Freiling, et al. - 2005 |

156 | Compute-and-Forward: Harnessing interference through structured codes
- Nazer, Gastpar
(Show Context)
Citation Context ...nal transmission schemes [1]. Due to its remarkable potential, PNC has received considerable research attention in recent years, with a particular focus on two-way relay systems [2]. In a recent work =-=[3]-=-, Nazer and Gastpar extended PNC from two-way relay systems to general network scenarios. Their approach allows each relay to map an interfering signal into some linear combination of transmitted mess... |

137 | Computation over multiple-access channels - Nazer, Gastpar - 2007 |

128 | Noisy network coding - Lim, Kim, et al. - 2011 |

113 | Physical network coding in two-way wireless relay channels - Popovski, Yomo |

109 | Lattice-reduction-aided detectors for MIMO communication systems - Yao, Wornell - 2002 |

97 | Averaging bounds for lattices and linear codes - Loeliger - 1997 |

76 | The anti-packets can increase the achievable throughput of a wireless multi-hop network - Popovski, Yomo - 2006 |

68 | V.Tarokh, “Optimized constellation for two-way wireless relaying with physical network coding
- Koike-Akino
- 2009
(Show Context)
Citation Context ...l compared to traditional transmission schemes [1]. Due to its remarkable potential, PNC has received considerable research attention in recent years, with a particular focus on two-way relay systems =-=[2]-=-. In a recent work [3], Nazer and Gastpar extended PNC from two-way relay systems to general network scenarios. Their approach allows each relay to map an interfering signal into some linear combinati... |

62 |
Physical layer network coding
- Zhang, Liew, et al.
- 2006
(Show Context)
Citation Context ...e apply our framework for PNC to a Gaussian relay network and demonstrate its advantage over conventional PNC schemes. I. INTRODUCTION Physical-layer network coding (PNC) was proposed by Zhang et al. =-=[1]-=- to embrace interference in wireless networks. In a nutshell, each relay in the network maps an interfering signal into an XOR combination of simultaneously transmitted codewords. Surprisingly, this s... |

60 | Capacity bounds for two-way relay channels - Nam, Chung, et al. - 2008 |

58 | Complex lattice reduction algorithm for low-complexity full-diversity MIMO detection - Gan, Ling, et al. - 2009 |

57 | Multidimensional constellations—part II: Voronoi constellations - Forney - 1989 |

53 | A Fast Encoding Method for Lattice Codes and Quantizers - Conway, Sloane - 1983 |

52 | Reliable physical layer network coding - Nazer, Gastpar - 2011 |

44 | Approximately achieving gaussian relay network capacity with lattice codes - Ozgur, Diggavi |

38 | Hot topic: Physical layer network coding - Zhang, Liew, et al. - 2006 |

38 | Low-dimensional lattice basis reduction revisited - Nguyen, Stehle - 2004 |

31 | Capacity of the two-way relay channel within a constant gap - Avestimehr, Sezgin, et al. - 2010 |

30 | Linear algebra over commutative rings - McDonald - 1984 |

30 | Matrices over Commutative Rings - Brown - 1993 |

29 |
On the role of MMSE estimation in approaching the information-theoretic limits of linear Gaussian channels
- Forney
- 2003
(Show Context)
Citation Context .... In fact, we set v` = 0 for ` = 1, . . . , L. In other words, we remove all the dithers. This is because the dither v` is just a tactic to simplify some proof, but is not actually needed in practice =-=[8]-=-. We apply the Tomlinson-Harashima shaping as suggested in [7], which is a special case of the shaping operations defined in Sec. III-C. As a result, our encoder E is identical to that used in [7]. 3)... |

22 | Closest vectors, successive minima, and dual HKZ bases of lattices - Blömer - 2000 |

21 | K.Narayanan , “Multilevel Coding Schemes for Computeand-Forward - Hern - 2011 |

18 | The degrees of freedom of compute-and-forward - Niesen, Whiting - 2012 |

17 | algorithm revisited - Vallée, Gauss’ - 1991 |

16 | A generalized of the LLL-algorithm over Euclidean rings or orders,” J. Théorie des Nombres de Bordeaux - Napias - 1996 |

15 | Compute-and-forward strategies for cooperative distributed antenna systems,” Computing Research Repository (CoRR - Hong, Caire |

14 | Coded bidirectional relaying in wireless networks - Popovski, Koike-Akino - 2009 |

13 | Lattice Coding for Signals and Networks - Zamir - 2013 |

11 | Power allocation strategies and lattice based coding schemes for bi-directional relaying - Wilson, Narayanan |

10 | Low Density Lattice Codes
- Sommer, Feder, et al.
- 2008
(Show Context)
Citation Context ...lattice shaping [7] may be used such that additional 1.53 dB of shaping gain can be potentially obtained. Another candidate of practical, high coding gain lattices is low density lattice codes (LDLC) =-=[9]-=-. It has recently been reported that a 100-dimensional LDLC 5 10 15 20 25 300 0.2 0.4 0.6 0.8 SNR (dB) N et w or ksTh ro ug hp uts(1 00 %) ←s8.3dB gain Signal Codes 9−QAM Fig. 3. Comparison of achieva... |

10 | MIMO compute-and-forward - Zhan, Nazer, et al. |

10 | Lattice codes for the compute-and-forward protocol: The flatness factor - Belfiore |

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

9 | An improvement to the Minkowski-Hlawka bound for packing superballs - Rush, Sloane - 1987 |

7 | Lattices over Eisenstein integers for compute-and-forward - Tunali, Narayanan, et al. - 2012 |

7 | Shaping methods for low-density lattice codes - Sommer, Feder, et al. |

6 | Signal codes: Convolutional lattice codes - Shalvi, Sommer, et al. - 2011 |

5 | Communication over finite-chain-ring matrix channels,” Computing Research Repository (CoRR - Feng, Nóbrega, et al. |

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

4 | Lattice network codes based on Eisenstein integers - Qifu, Yuan - 2012 |

4 | Turbo lattices: Construction and performance analysis,” submitted to - Sakzad, Sadeghi, et al. - 2010 |

3 | Kurkoski “Powerconstrained communications using LDLC lattices
- Dauwels, Loeliger, et al.
(Show Context)
Citation Context ...8.3dB gain Signal Codes 9−QAM Fig. 3. Comparison of achievable throughput of PNC schemes using signal codes and uncoded QAM. using nested lattice shaping can be made only 3.6 dB from the sphere bound =-=[10]-=-. This makes it very attractive to be used in our framework. VI. CONCLUSION In this paper, we have followed the framework of Nazer and Gastpar [3] towards the design of PNC schemes via lattice partiti... |

3 | codes I: Algebraic structure - “Convolutional - 1970 |

3 | Achieving the gains promised by integer-forcing equalization with binary codes - Ordentlich, Erez - 2010 |

1 |
Signal Codes,” submitted to
- Shalvi, Sommer, et al.
- 2008
(Show Context)
Citation Context ...tices to produce a Z[i]-lattice Λ with sublattice Λ′, which is however very difficult to implement in practice. In contrast, we use existing practical, high coding gain lattices, such as signal codes =-=[7]-=-. Signal codes are a special class of Z[i]-lattices whose generator matrix is given by G k×(k+m) Λ = 1 f1 · · · fm 0 · · · 0 0 0 1 · · · fm−1 fm · · · 0 0 . . . . . . · · · ... ... · · · ... ..... |

1 | Managing interference through space-time codes, lattice reduction and network coding - Belfiore, Castro |

1 | Lattice network coding via signal codes - Feng, Silva, et al. |

1 | criteria for lattice network coding - “Design |