Entropy of bit-stuffing-induced measures for two-dimensional checkerboard constraints

IEEE Transactions on Information Theory

Volumn 53, Issue 4, 2007, Pages 1537-1546

  Forchhammer, Søren ^a   Laursen, Torben V ^a,b  

^a TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

^b TrygVesta   (Denmark)

Author keywords

2 D constraints; Bit stuffing encoding; Cascading two dimensional (2 D) arrays; Run length limited (RLL) constraints

Indexed keywords

BIT ERROR RATE; CONSTRAINT THEORY; INFORMATION THEORY; PROBABILITY;

BIT-STUFFING ENCODING; PERIODIC MERGING ARRAYS; UPPER BOUND;

ENCODING (SYMBOLS);

EID: 34147136554     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2007.892781     Document Type: Article

References (18)

1. K. A. S. Immink, P. H. Siegel, and J. K. Wolf, "Codes for digital recorders," IEEE Trans. Inf. Theory, vol. 44, no. 6, pp. 2260-2299, Oct. 1998.
2. P. Vettiger, G. Cross, M. Despont, U. Drechsler, U. Durig, B. Gotsmann, W. Haberle, W. M. Lantz, H. Rothuizen, R. Stutz, and G. Binnig, "The "millipede" -nanotechnology entering data storage," IEEE Trans. Nanotechnol., vol. 1, no. 1, pp. 39-55, 2002.
3. E. Eleftheriou, T. Antonakopoulos, G. Binnig, G. Cherubini, M. Despont, A. Dholakia, U. Duerig, M. Lantz, H. Pozidisand, H. Rothuizen, and P. Vettiger, "Millipede-a mems-based scanning-probe data-storage system," IEEE Trans. Magn., vol. 39, no. 2, pp. 938-945, Mar. 2003.
4. R. Roth, P. H. Siegel, and J. K. Wolf, "Efficient coding schemes for the hard-square model," IEEE Trans. Inf. Theory, vol. 47, no. 3, pp. 1166-76, Mar. 2001.
5. d subshifts of finite type," Linear Algebra Appl., pp. 199-220, 1997.
6. v symbolic dynamics," Proc. London Math. Soc., vol. 43, pp. 251-272, 1981.
7. A. Kato and K. Zeger, "On the capacity of two-dimensional run-length constrained channels," IEEE Trans. Inf. Theory, vol. 45, no. 5, pp. 1527-1540, Jul. 1999.
8. W. Weeks, IV and R. Blahut, "The capacity and coding gain of certain checkerboard codes," IEEE Trans. Inf. Theory, vol. 44, no. 3, pp. 1193-1204, May 1998.
9. Z. Nagy and K. Zeger, "Asymptotic capacity of two-dimensional channels with checkerboard constraints," IEEE Trans. Inf. Theory, vol. 49, no. 9, pp. 2115-2125, Sep. 2003.
10. S. Forchhammer and J. Justesen, "Entropy bounds for constrained two-dimensional random fields," IEEE Trans. Inf. Theory, vol. 45, no. 1, pp. 118-127, Jan. 1999.
11. S. Halevy, J. Chen, R. M. Roth, P. H. Siegel, and J. K. Wolf, "Improved bit-stuffing bounds on two-dimensional constraints," IEEE Trans. Inf. Theory, vol. 50, no. 5, pp. 824-838, May 2004.
12. Z. Nagy and K. Zeger, "Entropy bounds for the hard-triangle model," in Proc. IEEE Int. Symp. Information Theory, Chicago, IL, 2004, p. 162.
13. C. E. Shannon, "A mathematical theory of communication," Bell Syst. Tech. J., vol. 27, pp. 379-423, Jul. 1948.
14. T. Etzion, "Cascading methods for runlength-limited arrays," IEEE Trans. Inf. Theory, vol. 43, no. 1, pp. 319-324, Jan. 1997.
15. S. Forchhammer and T. V. Laursen, "Cascading 2d constrained arrays using periodic merging arrays," in Proc. IEEE Int. Symp. Information Theory, Yokohama, Japan, 2003, p. 109.
16. A. Berman and R. J. Plemmons, Nonnegative Matrices in th Mathematical Sciences. Philadelphia, PA: SIAM, 1994.
17. S. Forchhammer and J. Justesen, "Bounds on the capacity of constrained two-dimensional codes," IEEE Trans. Inf. Theory, vol. 46, no. 7, pp. 2659-2666, Nov. 2000.
18. T. B. Schultz, "Coding for Nanotech Storage," Master Thesis, Tech. Univ. Denmark, Lyngby, Denmark, 2005.