Ring Theoretic Approach to Reversible Codes Based on Circulant Matrices
Summary :
Recently, Haley and Grant introduced the concept of reversible codes – a class of binary linear codes that can reuse the decoder architecture as the encoder and encodable by the iterative message-passing algorithm based on the Jacobi method over F2. They also developed a procedure to construct parity check matrices of a class of reversible codes named type-I reversible codes by utilizing properties specific to circulant matrices. In this paper, we refine a mathematical framework for reversible codes based on circulant matrices through a ring theoretic approach. This approach enables us to clarify the necessary and sufficient condition on which type-I reversible codes exist. Moreover, a systematic procedure to construct all circulant matrices that constitute parity check matrices of type-I reversible codes is also presented.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E94-A No.11 pp.2121-2126
- Publication Date
- 2011/11/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E94.A.2121
- Type of Manuscript
- Special Section PAPER (Special Section on Information Theory and Its Applications)
- Category
- Coding Theory
Authors
Keyword
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Tomoharu SHIBUYA, "Ring Theoretic Approach to Reversible Codes Based on Circulant Matrices" in IEICE TRANSACTIONS on Fundamentals,
vol. E94-A, no. 11, pp. 2121-2126, November 2011, doi: 10.1587/transfun.E94.A.2121.
Abstract: Recently, Haley and Grant introduced the concept of reversible codes – a class of binary linear codes that can reuse the decoder architecture as the encoder and encodable by the iterative message-passing algorithm based on the Jacobi method over F2. They also developed a procedure to construct parity check matrices of a class of reversible codes named type-I reversible codes by utilizing properties specific to circulant matrices. In this paper, we refine a mathematical framework for reversible codes based on circulant matrices through a ring theoretic approach. This approach enables us to clarify the necessary and sufficient condition on which type-I reversible codes exist. Moreover, a systematic procedure to construct all circulant matrices that constitute parity check matrices of type-I reversible codes is also presented.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E94.A.2121/_p
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@ARTICLE{e94-a_11_2121,
author={Tomoharu SHIBUYA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Ring Theoretic Approach to Reversible Codes Based on Circulant Matrices},
year={2011},
volume={E94-A},
number={11},
pages={2121-2126},
abstract={Recently, Haley and Grant introduced the concept of reversible codes – a class of binary linear codes that can reuse the decoder architecture as the encoder and encodable by the iterative message-passing algorithm based on the Jacobi method over F2. They also developed a procedure to construct parity check matrices of a class of reversible codes named type-I reversible codes by utilizing properties specific to circulant matrices. In this paper, we refine a mathematical framework for reversible codes based on circulant matrices through a ring theoretic approach. This approach enables us to clarify the necessary and sufficient condition on which type-I reversible codes exist. Moreover, a systematic procedure to construct all circulant matrices that constitute parity check matrices of type-I reversible codes is also presented.},
keywords={},
doi={10.1587/transfun.E94.A.2121},
ISSN={1745-1337},
month={November},}
Copy
TY - JOUR
TI - Ring Theoretic Approach to Reversible Codes Based on Circulant Matrices
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2121
EP - 2126
AU - Tomoharu SHIBUYA
PY - 2011
DO - 10.1587/transfun.E94.A.2121
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E94-A
IS - 11
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - November 2011
AB - Recently, Haley and Grant introduced the concept of reversible codes – a class of binary linear codes that can reuse the decoder architecture as the encoder and encodable by the iterative message-passing algorithm based on the Jacobi method over F2. They also developed a procedure to construct parity check matrices of a class of reversible codes named type-I reversible codes by utilizing properties specific to circulant matrices. In this paper, we refine a mathematical framework for reversible codes based on circulant matrices through a ring theoretic approach. This approach enables us to clarify the necessary and sufficient condition on which type-I reversible codes exist. Moreover, a systematic procedure to construct all circulant matrices that constitute parity check matrices of type-I reversible codes is also presented.
ER -
English
