## Abstract

A novel construction of lattices is proposed. This construction can be thought of as a special class of Construction A from codes over finite rings that can be represented as the Cartesian product of L linear codes over F-p1 , ... , F-pL, respectively, and hence is referred to as Construction pi(A). The existence of a sequence of such lattices that is good for channel coding (i.e., Poltyrev-limit achieving) under multistage decoding is shown. A new family of multilevel nested lattice codes based on Construction pi(A) lattices is proposed and its achievable rate for the additive white Gaussian noise channel is analyzed. A generalization named Construction pi(D) is also investigated, which subsumes Construction A with codes over prime fields, Construction D, and Construction pi(A) as special cases.

Original language | English |
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Pages (from-to) | 5718-5733 |

Number of pages | 16 |

Journal | IEEE Transactions on Information Theory |

Volume | 63 |

Issue number | 9 |

DOIs | |

State | Published - Sep 2017 |

## Keywords

- Lattices
- lattice codes
- linear codes
- COMPUTE-AND-FORWARD
- EISENSTEIN INTEGERS
- AWGN CHANNEL
- COSET CODES
- INTERFERENCE
- PACKINGS
- CAPACITY
- ERROR