Ring Theoretic Approach to Reversible Codes Based on Circulant Matrices

• SHIBUYA Tomoharu

  Department of Information and Communication Sciences, Sophia University

抄録

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 $\\mathbb{F}_2$. 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.

収録刊行物

• IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

  IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E94-A (11), 2121-2126, 2011

  一般社団法人 電子情報通信学会

キーワード

• LDPC codes
• reversible codes
• encoding of linear codes
• Jacobi method
• circulant matrices
• message-passing algorithm

詳細情報

• CRID: 1390001206311967744
• NII論文ID: 10030191481
• NII書誌ID: AA10826239
• DOI: 10.1587/transfun.e94.a.2121
• ISSN: 17451337
• ISSN: 09168508
• Web Site: http://www.jstage.jst.go.jp/article/transfun/E94.A/11/E94.A_11_2121/_pdf
• 本文言語コード: en
• データソース種別:
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  • Crossref
  • CiNii Articles
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