doi:10.1016/j.dam.2003.02.001
Copyright © 2003 Elsevier B.V. All rights reserved.
New upper and lower bounds on the channel capacity of read/write isolated memory*1
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
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
Author Keywords: Capacity; Channel graph; Eigenvalue; Two-dimensional codes; Runlength-limited codes; Constrained arrays
Fig. 1. B1 is a good matrix. B2 is not a good matrix for two reasons: the two consecutive bold 1's in the second row contradict the read restriction and the bold 2×2 submatrix in the lower right corner contradicts the write restriction.
Fig. 2. The transfer matrices A1, A2, A3, A4.
Fig. 3. The horizontal transfer matrices , , and associated matrices B1, B2 and B3.
Table 1. Fk is the kth Fibonacci number. λk is the largest eigenvalue of the Fk+2×Fk+2 transfer matrix Ak. The λk values are from Table 1 in [4]

Table 2. μr is the largest eigenvalue of the 2r×2r transfer matrix Not-foundr
