IEICE TRANSACTIONS on Fundamentals
List Decoding of Reed-Muller Codes Based on a Generalized Plotkin Construction
Summary :
Gopalan, Klivans, and Zuckerman proposed a list-decoding algorithm for Reed-Muller codes. Their algorithm works up to a given list-decoding radius. Dumer, Kabatiansky, and Tavernier improved the complexity of the algorithm for binary Reed-Muller codes by using the well-known Plotkin construction. In this study, we propose a list-decoding algorithm for non-binary Reed-Muller codes as a generalization of Dumer et al.'s algorithm. Our algorithm is based on a generalized Plotkin construction, and is more suitable for parallel computation than the algorithm of Gopalan et al. Since the list-decoding algorithms of Gopalan et al., Dumer et al., and ours can be applied to more general codes than Reed-Muller codes, we give a condition for codes under which these list-decoding algorithms works.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E96-A No.7 pp.1662-1666
- Publication Date
- 2013/07/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E96.A.1662
- Type of Manuscript
- LETTER
- Category
- Coding Theory
Authors
Kenji YASUNAGA
Kanazawa University
Keyword
Latest Issue
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Kenji YASUNAGA, "List Decoding of Reed-Muller Codes Based on a Generalized Plotkin Construction" in IEICE TRANSACTIONS on Fundamentals,
vol. E96-A, no. 7, pp. 1662-1666, July 2013, doi: 10.1587/transfun.E96.A.1662.
Abstract: Gopalan, Klivans, and Zuckerman proposed a list-decoding algorithm for Reed-Muller codes. Their algorithm works up to a given list-decoding radius. Dumer, Kabatiansky, and Tavernier improved the complexity of the algorithm for binary Reed-Muller codes by using the well-known Plotkin construction. In this study, we propose a list-decoding algorithm for non-binary Reed-Muller codes as a generalization of Dumer et al.'s algorithm. Our algorithm is based on a generalized Plotkin construction, and is more suitable for parallel computation than the algorithm of Gopalan et al. Since the list-decoding algorithms of Gopalan et al., Dumer et al., and ours can be applied to more general codes than Reed-Muller codes, we give a condition for codes under which these list-decoding algorithms works.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E96.A.1662/_p
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@ARTICLE{e96-a_7_1662,
author={Kenji YASUNAGA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={List Decoding of Reed-Muller Codes Based on a Generalized Plotkin Construction},
year={2013},
volume={E96-A},
number={7},
pages={1662-1666},
abstract={Gopalan, Klivans, and Zuckerman proposed a list-decoding algorithm for Reed-Muller codes. Their algorithm works up to a given list-decoding radius. Dumer, Kabatiansky, and Tavernier improved the complexity of the algorithm for binary Reed-Muller codes by using the well-known Plotkin construction. In this study, we propose a list-decoding algorithm for non-binary Reed-Muller codes as a generalization of Dumer et al.'s algorithm. Our algorithm is based on a generalized Plotkin construction, and is more suitable for parallel computation than the algorithm of Gopalan et al. Since the list-decoding algorithms of Gopalan et al., Dumer et al., and ours can be applied to more general codes than Reed-Muller codes, we give a condition for codes under which these list-decoding algorithms works.},
keywords={},
doi={10.1587/transfun.E96.A.1662},
ISSN={1745-1337},
month={July},}
Copy
TY - JOUR
TI - List Decoding of Reed-Muller Codes Based on a Generalized Plotkin Construction
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1662
EP - 1666
AU - Kenji YASUNAGA
PY - 2013
DO - 10.1587/transfun.E96.A.1662
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E96-A
IS - 7
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - July 2013
AB - Gopalan, Klivans, and Zuckerman proposed a list-decoding algorithm for Reed-Muller codes. Their algorithm works up to a given list-decoding radius. Dumer, Kabatiansky, and Tavernier improved the complexity of the algorithm for binary Reed-Muller codes by using the well-known Plotkin construction. In this study, we propose a list-decoding algorithm for non-binary Reed-Muller codes as a generalization of Dumer et al.'s algorithm. Our algorithm is based on a generalized Plotkin construction, and is more suitable for parallel computation than the algorithm of Gopalan et al. Since the list-decoding algorithms of Gopalan et al., Dumer et al., and ours can be applied to more general codes than Reed-Muller codes, we give a condition for codes under which these list-decoding algorithms works.
ER -
English
