IEICE TRANSACTIONS on Fundamentals
Algebraic Decoding of BCH Codes over Symbol-Pair Read Channels: Cases of Two-Pair and Three-Pair Error Correction
Summary :
In this paper, we discuss an algebraic decoding of BCH codes over symbol-pair read channels. The channels output overlapping pairs of symbols in storage applications. The pair distance and pair error are used in the channels. We define a polynomial that represents the positions of the pair errors as the error-locator polynomials and a polynomial that represents the positions of the pairs of a received pair vector in conflict as conflict-locator polynomial. In this paper, we propose algebraic methods for correcting two-pair and three-pair errors for BCH codes. First, we show the relation between the error-locator polynomials and the conflict-locator polynomial. Second, we show the relation among these polynomials and the syndromes. Finally, we provide how to correct the pair errors by solving equations including the relational expression by algebraic methods.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E99-A No.12 pp.2179-2191
- Publication Date
- 2016/12/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E99.A.2179
- Type of Manuscript
- Special Section PAPER (Special Section on Information Theory and Its Applications)
- Category
- Coding Theory and Techniques
Authors
Makoto TAKITA
Kobe University
Masanori HIROTOMO
Saga University
Masakatu MORII
Kobe University
Keyword
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Makoto TAKITA, Masanori HIROTOMO, Masakatu MORII, "Algebraic Decoding of BCH Codes over Symbol-Pair Read Channels: Cases of Two-Pair and Three-Pair Error Correction" in IEICE TRANSACTIONS on Fundamentals,
vol. E99-A, no. 12, pp. 2179-2191, December 2016, doi: 10.1587/transfun.E99.A.2179.
Abstract: In this paper, we discuss an algebraic decoding of BCH codes over symbol-pair read channels. The channels output overlapping pairs of symbols in storage applications. The pair distance and pair error are used in the channels. We define a polynomial that represents the positions of the pair errors as the error-locator polynomials and a polynomial that represents the positions of the pairs of a received pair vector in conflict as conflict-locator polynomial. In this paper, we propose algebraic methods for correcting two-pair and three-pair errors for BCH codes. First, we show the relation between the error-locator polynomials and the conflict-locator polynomial. Second, we show the relation among these polynomials and the syndromes. Finally, we provide how to correct the pair errors by solving equations including the relational expression by algebraic methods.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E99.A.2179/_p
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@ARTICLE{e99-a_12_2179,
author={Makoto TAKITA, Masanori HIROTOMO, Masakatu MORII, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Algebraic Decoding of BCH Codes over Symbol-Pair Read Channels: Cases of Two-Pair and Three-Pair Error Correction},
year={2016},
volume={E99-A},
number={12},
pages={2179-2191},
abstract={In this paper, we discuss an algebraic decoding of BCH codes over symbol-pair read channels. The channels output overlapping pairs of symbols in storage applications. The pair distance and pair error are used in the channels. We define a polynomial that represents the positions of the pair errors as the error-locator polynomials and a polynomial that represents the positions of the pairs of a received pair vector in conflict as conflict-locator polynomial. In this paper, we propose algebraic methods for correcting two-pair and three-pair errors for BCH codes. First, we show the relation between the error-locator polynomials and the conflict-locator polynomial. Second, we show the relation among these polynomials and the syndromes. Finally, we provide how to correct the pair errors by solving equations including the relational expression by algebraic methods.},
keywords={},
doi={10.1587/transfun.E99.A.2179},
ISSN={1745-1337},
month={December},}
Copy
TY - JOUR
TI - Algebraic Decoding of BCH Codes over Symbol-Pair Read Channels: Cases of Two-Pair and Three-Pair Error Correction
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2179
EP - 2191
AU - Makoto TAKITA
AU - Masanori HIROTOMO
AU - Masakatu MORII
PY - 2016
DO - 10.1587/transfun.E99.A.2179
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E99-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2016
AB - In this paper, we discuss an algebraic decoding of BCH codes over symbol-pair read channels. The channels output overlapping pairs of symbols in storage applications. The pair distance and pair error are used in the channels. We define a polynomial that represents the positions of the pair errors as the error-locator polynomials and a polynomial that represents the positions of the pairs of a received pair vector in conflict as conflict-locator polynomial. In this paper, we propose algebraic methods for correcting two-pair and three-pair errors for BCH codes. First, we show the relation between the error-locator polynomials and the conflict-locator polynomial. Second, we show the relation among these polynomials and the syndromes. Finally, we provide how to correct the pair errors by solving equations including the relational expression by algebraic methods.
ER -
English
