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Discrete Applied Mathematics
Volume 140, Issues 1-3, 15 May 2004, Pages 35-48
 
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doi:10.1016/j.dam.2003.02.001    How to Cite or Link Using DOI (Opens New Window)
Copyright © 2003 Elsevier B.V. All rights reserved.

New upper and lower bounds on the channel capacity of read/write isolated memory*1

M.J.Mordecai J. GolinE-mail The Corresponding Author, a, Xuerong YongE-mail The Corresponding Author, a, Yuanping ZhangE-mail The Corresponding Author, a, b and Li ShengE-mail The Corresponding Author, c

a Department of Computer Science, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China b Department of Mathematics, Hunan Normal University, Changsha 410081, People's Republic of China c Department of Mathematics, Drexel University, 3141 Chestnut Street, Philadelphia, PA 19104, USA

Received 30 November 2000; 
Revised 15 April 2002; 
accepted 7 February 2003. 
Available online 14 November 2003.

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Abstract

In this paper, we refine upper and lower bounds for the channel capacity of a serial, binary rewritable medium in which no consecutive locations may store 1's and no consecutive locations may be altered during a single rewriting pass. This problem was originally examined by Cohn (Discrete. Appl. Math. 56 (1995) 1) who proved that C, the channel capacity of the memory, in bits per symbol per rewrite, satisfies

0.50913cdots, three dots, centeredless-than-or-equals, slantCless-than-or-equals, slant0.56029cdots, three dots, centered .
In this paper, we show how to model the problem as a constrained two-dimensional binary matrix problem and then modify recent techniques for dealing with such matrices to derive improved bounds of

0.53500cdots, three dots, centeredless-than-or-equals, slantCless-than-or-equals, slant0.55209cdots, three dots, centered .

Author Keywords: Capacity; Channel graph; Eigenvalue; Two-dimensional codes; Runlength-limited codes; Constrained arrays

Article Outline

1. Introduction
2. Constrained matrices
Kato and Zeger [7]
3. A second transfer matrix
4. The maximum principle and better lower bounds
5. Conclusion and open problems
Acknowledgements
References




 
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