### Abstract

In this work, we propose phase precoding for the compute-and-forward (CoF) protocol. We derive the phase precoded computation rate and show that it is greater than the original computation rate of CoF protocol without precoder. To maximize the phase precoded computation rate, we need to 'jointly' find the optimum phase precoding matrix and the corresponding network equation coefficients. This is a mixed integer programming problem where the optimum precoders should be obtained at the transmitters and the network equation coefficients have to be computed at the relays. To solve this problem, we introduce phase precoded CoF with partial feedback. It is a quantized precoding system where the relay jointly computes both a quasi-optimal precoder from a finite codebook and the corresponding network equations. The index of the obtained phase precoder within the codebook will then be fedback to the transmitters. A 'deep hole phase precoder' is presented as an example of such a scheme. We further simulate our scheme with a lattice code carved out of the Gosset lattice and show that significant coding gains can be obtained in terms of equation error performance.

Original language | English |
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Title of host publication | 2014 IEEE International Symposium on Information Theory, ISIT 2014 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 2117-2121 |

Number of pages | 5 |

ISBN (Print) | 9781479951864 |

DOIs | |

Publication status | Published - 1 Jan 2014 |

Event | 2014 IEEE International Symposium on Information Theory, ISIT 2014 - Honolulu, HI, United States Duration: 29 Jun 2014 → 4 Jul 2014 |

### Publication series

Name | IEEE International Symposium on Information Theory - Proceedings |
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ISSN (Print) | 2157-8095 |

### Other

Other | 2014 IEEE International Symposium on Information Theory, ISIT 2014 |
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Country | United States |

City | Honolulu, HI |

Period | 29/6/14 → 4/7/14 |

### Fingerprint

### Keywords

- Compute-and-forward
- lattice codes
- phase precoding

### ASJC Scopus subject areas

- Theoretical Computer Science
- Information Systems
- Modelling and Simulation
- Applied Mathematics

### Cite this

*2014 IEEE International Symposium on Information Theory, ISIT 2014*(pp. 2117-2121). [6875207] (IEEE International Symposium on Information Theory - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2014.6875207