Embedding Information in Grayscale Images - Signal Processing ...

1
0.9
0.8
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0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
Figure 6: Rate-distortion curve, time-sharing R = 1 LSB modulation (...), binary Hamming
codes (o), ternary Hamming codes (*), the Golay codes (x), and the 5-ary codes (+).
8 Conclusion
We have only looked at small distortions here. Moreover we have concentrated on perfect
codes since this was so easy. It can be shown that Hamming codes are quite good for D → 0.
For a moderate rate we have seen that Golay codes are rather good, but what about even better
codes for even higher rates? How do we generalize the coloring results to larger number of
colors and more dimensions?
References
[1] J. Chou, S. Pradhan, L. El Ghaoui and K. Ramchandran, “A Robust Optimization Solution
to the Data Hiding Problem Using Distributed Source Coding Principles,” preprint,
2000.
[2] S. Gelfand and M. Pinsker, “Coding for a Channel with Random Parameters”, Problems
of Control and Information Theory, vol. 9, pp. 19-31, 1980.
[3] P. Moulin and J. O’Sullivan, “Information-theoretic Analysis of Information Hiding,”
preprint, 1999.
[4] F.M.J. Willems, ”An Informationtheoretical Approach to Information Embedding,”
Proc. 21st Symp. Inform. Theory in the Benelux, pp. 255-260, Wassenaar, May 25-26,
2000.