A Method for Obtaining the Optimum Sectionalization of the RMLD Algorithm for Non-Linear Rectangular Codes
Summary :
A recursive maximum likelihood decoding (RMLD) algorithm is more efficient than the Viterbi algorithm. The decoding complexity of the RMLD algorithm depends on the recursive sectionalization. The recursive sectionalization which minimizes the decoding complexity is called the optimum sectionalization. In this paper, for a class of non-linear codes, called rectangular codes, it is shown that a near optimum sectionalization can be obtained with a dynamic programming approach. Furthermore, for a subclass of rectangular codes, called C-rectangular codes, it is shown that the exactly optimum sectionalization can be obtained with the same approach. Following these results, an efficient algorithm to obtain the optimum sectionalization is proposed. The optimum sectionalizations for the minimum weight subcode of some Reed-Muller codes and of a BCH code are obtained with the proposed algorithm.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E82-A No.10 pp.2052-2060
- Publication Date
- 1999/10/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- Special Section PAPER (Special Section on Information Theory and Its Applications)
- Category
- Coding Theory
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Yasuhiro MATSUMOTO, Toru FUJIWARA, "A Method for Obtaining the Optimum Sectionalization of the RMLD Algorithm for Non-Linear Rectangular Codes" in IEICE TRANSACTIONS on Fundamentals,
vol. E82-A, no. 10, pp. 2052-2060, October 1999, doi: .
Abstract: A recursive maximum likelihood decoding (RMLD) algorithm is more efficient than the Viterbi algorithm. The decoding complexity of the RMLD algorithm depends on the recursive sectionalization. The recursive sectionalization which minimizes the decoding complexity is called the optimum sectionalization. In this paper, for a class of non-linear codes, called rectangular codes, it is shown that a near optimum sectionalization can be obtained with a dynamic programming approach. Furthermore, for a subclass of rectangular codes, called C-rectangular codes, it is shown that the exactly optimum sectionalization can be obtained with the same approach. Following these results, an efficient algorithm to obtain the optimum sectionalization is proposed. The optimum sectionalizations for the minimum weight subcode of some Reed-Muller codes and of a BCH code are obtained with the proposed algorithm.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e82-a_10_2052/_p
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@ARTICLE{e82-a_10_2052,
author={Yasuhiro MATSUMOTO, Toru FUJIWARA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Method for Obtaining the Optimum Sectionalization of the RMLD Algorithm for Non-Linear Rectangular Codes},
year={1999},
volume={E82-A},
number={10},
pages={2052-2060},
abstract={A recursive maximum likelihood decoding (RMLD) algorithm is more efficient than the Viterbi algorithm. The decoding complexity of the RMLD algorithm depends on the recursive sectionalization. The recursive sectionalization which minimizes the decoding complexity is called the optimum sectionalization. In this paper, for a class of non-linear codes, called rectangular codes, it is shown that a near optimum sectionalization can be obtained with a dynamic programming approach. Furthermore, for a subclass of rectangular codes, called C-rectangular codes, it is shown that the exactly optimum sectionalization can be obtained with the same approach. Following these results, an efficient algorithm to obtain the optimum sectionalization is proposed. The optimum sectionalizations for the minimum weight subcode of some Reed-Muller codes and of a BCH code are obtained with the proposed algorithm.},
keywords={},
doi={},
ISSN={},
month={October},}
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TY - JOUR
TI - A Method for Obtaining the Optimum Sectionalization of the RMLD Algorithm for Non-Linear Rectangular Codes
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2052
EP - 2060
AU - Yasuhiro MATSUMOTO
AU - Toru FUJIWARA
PY - 1999
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E82-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 1999
AB - A recursive maximum likelihood decoding (RMLD) algorithm is more efficient than the Viterbi algorithm. The decoding complexity of the RMLD algorithm depends on the recursive sectionalization. The recursive sectionalization which minimizes the decoding complexity is called the optimum sectionalization. In this paper, for a class of non-linear codes, called rectangular codes, it is shown that a near optimum sectionalization can be obtained with a dynamic programming approach. Furthermore, for a subclass of rectangular codes, called C-rectangular codes, it is shown that the exactly optimum sectionalization can be obtained with the same approach. Following these results, an efficient algorithm to obtain the optimum sectionalization is proposed. The optimum sectionalizations for the minimum weight subcode of some Reed-Muller codes and of a BCH code are obtained with the proposed algorithm.
ER -
English
