On a Characterization of a State of Rank-Modulation Scheme Over Multi-Cell Ranking by a Group Action
Summary :
In this paper, we propose a group theoretic representation suitable for the rank-modulation (RM) scheme over the multi-cell ranking presented by En Gad et al. By introducing an action of the group of all permutation matrices on the set of all permutations, the scheme is clearly reformulated. Moreover, we introduce the concept of r-dominating sets over the multi-cell ranking, which is a generalization of conventional dominating sets, in the design of rank-modulation rewriting codes. The concept together with the proposed group theoretic representation yields an explicit formula of an upper bound on the size of the set of messages that can be stored in the memory by using RM rewriting codes over multi-cell ranking. This bound enables us to consider the trade-off between the size of the storable message set and the rewriting cost more closely. We also provide a concrete example of RM rewriting code that is not available by conventional approaches and whose size of the storable message set can not be achieved by conventional codes.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E100-A No.12 pp.2558-2571
- Publication Date
- 2017/12/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E100.A.2558
- Type of Manuscript
- Special Section PAPER (Special Section on Information Theory and Its Applications)
- Category
- Coding Theory and Techniques
Authors
Tomoharu SHIBUYA
Sophia University
Takeru SUDO
Sophia University
Keyword
Latest Issue
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Tomoharu SHIBUYA, Takeru SUDO, "On a Characterization of a State of Rank-Modulation Scheme Over Multi-Cell Ranking by a Group Action" in IEICE TRANSACTIONS on Fundamentals,
vol. E100-A, no. 12, pp. 2558-2571, December 2017, doi: 10.1587/transfun.E100.A.2558.
Abstract: In this paper, we propose a group theoretic representation suitable for the rank-modulation (RM) scheme over the multi-cell ranking presented by En Gad et al. By introducing an action of the group of all permutation matrices on the set of all permutations, the scheme is clearly reformulated. Moreover, we introduce the concept of r-dominating sets over the multi-cell ranking, which is a generalization of conventional dominating sets, in the design of rank-modulation rewriting codes. The concept together with the proposed group theoretic representation yields an explicit formula of an upper bound on the size of the set of messages that can be stored in the memory by using RM rewriting codes over multi-cell ranking. This bound enables us to consider the trade-off between the size of the storable message set and the rewriting cost more closely. We also provide a concrete example of RM rewriting code that is not available by conventional approaches and whose size of the storable message set can not be achieved by conventional codes.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E100.A.2558/_p
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@ARTICLE{e100-a_12_2558,
author={Tomoharu SHIBUYA, Takeru SUDO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={On a Characterization of a State of Rank-Modulation Scheme Over Multi-Cell Ranking by a Group Action},
year={2017},
volume={E100-A},
number={12},
pages={2558-2571},
abstract={In this paper, we propose a group theoretic representation suitable for the rank-modulation (RM) scheme over the multi-cell ranking presented by En Gad et al. By introducing an action of the group of all permutation matrices on the set of all permutations, the scheme is clearly reformulated. Moreover, we introduce the concept of r-dominating sets over the multi-cell ranking, which is a generalization of conventional dominating sets, in the design of rank-modulation rewriting codes. The concept together with the proposed group theoretic representation yields an explicit formula of an upper bound on the size of the set of messages that can be stored in the memory by using RM rewriting codes over multi-cell ranking. This bound enables us to consider the trade-off between the size of the storable message set and the rewriting cost more closely. We also provide a concrete example of RM rewriting code that is not available by conventional approaches and whose size of the storable message set can not be achieved by conventional codes.},
keywords={},
doi={10.1587/transfun.E100.A.2558},
ISSN={1745-1337},
month={December},}
Copy
TY - JOUR
TI - On a Characterization of a State of Rank-Modulation Scheme Over Multi-Cell Ranking by a Group Action
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2558
EP - 2571
AU - Tomoharu SHIBUYA
AU - Takeru SUDO
PY - 2017
DO - 10.1587/transfun.E100.A.2558
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E100-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2017
AB - In this paper, we propose a group theoretic representation suitable for the rank-modulation (RM) scheme over the multi-cell ranking presented by En Gad et al. By introducing an action of the group of all permutation matrices on the set of all permutations, the scheme is clearly reformulated. Moreover, we introduce the concept of r-dominating sets over the multi-cell ranking, which is a generalization of conventional dominating sets, in the design of rank-modulation rewriting codes. The concept together with the proposed group theoretic representation yields an explicit formula of an upper bound on the size of the set of messages that can be stored in the memory by using RM rewriting codes over multi-cell ranking. This bound enables us to consider the trade-off between the size of the storable message set and the rewriting cost more closely. We also provide a concrete example of RM rewriting code that is not available by conventional approaches and whose size of the storable message set can not be achieved by conventional codes.
ER -
English
