## Abstract

Trellis diagrams of lattices and the Viterbi algorithm can be used for decoding. It has been known that the numbers of states and labels at every level of any finite trellis diagrams of a lattice L and its dual L* under the same coordinate system are the same. In the paper, we present concrete expressions of the numbers of distinct paths in the trellis diagrams of L and L* under the same coordinate system, which are more concrete than Theorem 2 of [1], We also give a relation between the numbers of edges in the trellis diagrams of L and L*. Furthermore, we provide the upper bounds on the state numbers of a trellis diagram of the lattice L_{1} ⊗ L _{2} by the state numbers of trellis diagrams of lattices L_{1} and L_{2}.

Original language | English |
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Pages (from-to) | 1979-1986 |

Number of pages | 8 |

Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

Volume | E88-A |

Issue number | 7 |

DOIs | |

Publication status | Published - Jul 2005 |

Externally published | Yes |

## Keywords

- Dual lattices
- Lattice
- Tensor product
- Trellis diagrams