Some trellis properties on lattices

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 L₁ ⊗ L ₂ by the state numbers of trellis diagrams of lattices L₁ and L₂.