Some Trellis Properties on Lattices

Haibin KAN; Hong SHEN

doi:10.1093/ietfec/e88-a.7.1979

Some Trellis Properties on Lattices

Haibin KAN, Hong SHEN

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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 L₁L₂ by the state numbers of trellis diagrams of lattices L₁ and L₂.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E88-A No.7 pp.1979-1986

Publication Date: 2005/07/01

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DOI: 10.1093/ietfec/e88-a.7.1979

Type of Manuscript: PAPER

Category: Coding Theory

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Haibin KAN, Hong SHEN, "Some Trellis Properties on Lattices" in IEICE TRANSACTIONS on Fundamentals, vol. E88-A, no. 7, pp. 1979-1986, July 2005, doi: 10.1093/ietfec/e88-a.7.1979.
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 L₁L₂ by the state numbers of trellis diagrams of lattices L₁ and L₂.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e88-a.7.1979/_p

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@ARTICLE{e88-a_7_1979,
author={Haibin KAN, Hong SHEN, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Some Trellis Properties on Lattices},
year={2005},
volume={E88-A},
number={7},
pages={1979-1986},
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 L₁L₂ by the state numbers of trellis diagrams of lattices L₁ and L₂.},
keywords={},
doi={10.1093/ietfec/e88-a.7.1979},
ISSN={},
month={July},}

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TY - JOUR
TI - Some Trellis Properties on Lattices
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1979
EP - 1986
AU - Haibin KAN
AU - Hong SHEN
PY - 2005
DO - 10.1093/ietfec/e88-a.7.1979
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E88-A
IS - 7
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - July 2005
AB - 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 L₁L₂ by the state numbers of trellis diagrams of lattices L₁ and L₂.
ER -