State-Complexity Reduction for Convolutional Codes Using Trellis-Module Integration

Masato TAJIMA; Koji OKINO; Takashi MIYAGOSHI

doi:10.1093/ietfec/e89-a.10.2466

State-Complexity Reduction for Convolutional Codes Using Trellis-Module Integration

Masato TAJIMA, Koji OKINO, Takashi MIYAGOSHI

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Assume that G(D) is a k₀n₀ canonical generator matrix. Let G^(L)(D) be the generator matrix obtained by integrating L consecutive trellis-modules associated with G(D). We also consider a modified version of G^(L)(D) using a column permutation. Then take notice of the corresponding minimal trellis-module T^(L). In this paper, we show that there is a case where the minimum number of states over all levels in T^(L) is less than the minimum attained for the minimal trellis-module associated with G(D). In this case, combining with a shifted sectionalization of the trellis, we can construct a trellis-module with further reduced number of states. We actually present such an example. We also clarify the mechanism of state-space reduction. That is, we show that trellis-module integration combined with an appropriate column permutation and a shifted sectionalization of the trellis is equivalent to shifting some particular bits of the original code bits by L time units.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E89-A No.10 pp.2466-2474

Publication Date: 2006/10/01

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Online ISSN: 1745-1337

DOI: 10.1093/ietfec/e89-a.10.2466

Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)

Category: Coding Theory

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Masato TAJIMA, Koji OKINO, Takashi MIYAGOSHI, "State-Complexity Reduction for Convolutional Codes Using Trellis-Module Integration" in IEICE TRANSACTIONS on Fundamentals, vol. E89-A, no. 10, pp. 2466-2474, October 2006, doi: 10.1093/ietfec/e89-a.10.2466.
Abstract: Assume that G(D) is a k₀n₀ canonical generator matrix. Let G^(L)(D) be the generator matrix obtained by integrating L consecutive trellis-modules associated with G(D). We also consider a modified version of G^(L)(D) using a column permutation. Then take notice of the corresponding minimal trellis-module T^(L). In this paper, we show that there is a case where the minimum number of states over all levels in T^(L) is less than the minimum attained for the minimal trellis-module associated with G(D). In this case, combining with a shifted sectionalization of the trellis, we can construct a trellis-module with further reduced number of states. We actually present such an example. We also clarify the mechanism of state-space reduction. That is, we show that trellis-module integration combined with an appropriate column permutation and a shifted sectionalization of the trellis is equivalent to shifting some particular bits of the original code bits by L time units.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e89-a.10.2466/_p

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@ARTICLE{e89-a_10_2466,
author={Masato TAJIMA, Koji OKINO, Takashi MIYAGOSHI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={State-Complexity Reduction for Convolutional Codes Using Trellis-Module Integration},
year={2006},
volume={E89-A},
number={10},
pages={2466-2474},
abstract={Assume that G(D) is a k₀n₀ canonical generator matrix. Let G^(L)(D) be the generator matrix obtained by integrating L consecutive trellis-modules associated with G(D). We also consider a modified version of G^(L)(D) using a column permutation. Then take notice of the corresponding minimal trellis-module T^(L). In this paper, we show that there is a case where the minimum number of states over all levels in T^(L) is less than the minimum attained for the minimal trellis-module associated with G(D). In this case, combining with a shifted sectionalization of the trellis, we can construct a trellis-module with further reduced number of states. We actually present such an example. We also clarify the mechanism of state-space reduction. That is, we show that trellis-module integration combined with an appropriate column permutation and a shifted sectionalization of the trellis is equivalent to shifting some particular bits of the original code bits by L time units.},
keywords={},
doi={10.1093/ietfec/e89-a.10.2466},
ISSN={1745-1337},
month={October},}

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TY - JOUR
TI - State-Complexity Reduction for Convolutional Codes Using Trellis-Module Integration
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2466
EP - 2474
AU - Masato TAJIMA
AU - Koji OKINO
AU - Takashi MIYAGOSHI
PY - 2006
DO - 10.1093/ietfec/e89-a.10.2466
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E89-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 2006
AB - Assume that G(D) is a k₀n₀ canonical generator matrix. Let G^(L)(D) be the generator matrix obtained by integrating L consecutive trellis-modules associated with G(D). We also consider a modified version of G^(L)(D) using a column permutation. Then take notice of the corresponding minimal trellis-module T^(L). In this paper, we show that there is a case where the minimum number of states over all levels in T^(L) is less than the minimum attained for the minimal trellis-module associated with G(D). In this case, combining with a shifted sectionalization of the trellis, we can construct a trellis-module with further reduced number of states. We actually present such an example. We also clarify the mechanism of state-space reduction. That is, we show that trellis-module integration combined with an appropriate column permutation and a shifted sectionalization of the trellis is equivalent to shifting some particular bits of the original code bits by L time units.
ER -