IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Online ISSN : 1745-1337
Print ISSN : 0916-8508
Special Section on Information Theory and Its Applications
Ring Theoretic Approach to Reversible Codes Based on Circulant Matrices
Tomoharu SHIBUYA
Author information
JOURNAL RESTRICTED ACCESS

2011 Volume E94.A Issue 11 Pages 2121-2126

Details
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 $\\mathbb{F}_2$. 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.

Content from these authors
© 2011 The Institute of Electronics, Information and Communication Engineers
Previous article Next article
feedback
Top