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IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. XX, NO. 2 −5 3 −4 −3 −2 −1 ù Fig. 21. 4 ➤ ➅✛➆ Predicted Measured 0 1 2 [ ➅✱➆ ] 4 5 Fig. 22. Distortion improvement for inverse SCS mapping after AWGN attack with ❘❚❙❯✕➤❱❘❚❙❯❳❲ ❨ ) 3 ✧✬✥ → ❩➘↔✵❬✜❭ . 2 Achievable Distortion Reduction Finally, the achieved distortion improvement is investigated. The improvement is measured in terms of the difference between the Ó❫❪❬➩ (document-to-attack power ratio) before (Ó❫❪❬➩②✺ ) and after (Ó❴❪➫➩ ✕ ✥ ) the mapping, which is given by Ó❫❪➫➩➫Ñ ê ❇ Unfortunately, the result for ➧❨➨❬➩ ❇ Ó ❪➫➩ ✕ ✥ ➓ ❫ ➓ ① Ó❫❪❬➩②✺ ➧❂➨➫➩ ⑦ ✡ ✟ Ñ ✻ë ✎✍ ➓⑤➛❅➔✃➱ ❐✴❮ ➘❚❰ Ó ➾✪✍ ü✴➪ ✗ Ó✗➾✪✍ ➷ ➷ ✍ ✌ ➪ Ü❫Ý❬Û (52) is rather disappointing with a maximal distortion improvement of Ó❫❪➫➩➫Ñ ê ➼ ê❛❵❝❜ ➓❛➔✽Û✤➔❺Ô✧Ü❫Ý .
Shamai and B. M. Zaidel, “Applying the dirty paper approach to the downlink of a cellular system,” Tech. , Technion-Israel Institute of Technology, 2002, In Preparation. [22] R. Zamir, S. Shamai, and U. Erez, “Nested linear/lattice codes for structured multiterminal binning,” IEEE Transactions on Information Theory, vol. 48, no. 6, pp. 1250–1276, June 2002. [23] J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, Springer-Verlag, New York, Berlin, Heidelberg, 1988. [24] L. Schuchman, “Dither signals and their effect on quantization noise,” IEEE Transaction on Communication Technology (COM), vol.
Y, MONTH 2002 é➎ 31 , respectively. ✎ is known to the watermark receiver so that þ the correlation ø õ between ü and ✎ , that is ▲ ▼➘❖ ◗✪❘ ø õ ➓ ❇ ➛ ➱ ➏ ➎✷ö ➎ Û ❍ Ñ❊❉ ☎ Ò ➎ç✃ ➘ The unbiased estimate þ õ of þ derived from ø õ is derived as follows: ➓ E ✇úù ➎ ③ E ✇ üõ ③ ö E ✇❅þ✄➾✑÷ ➎ ➬ ➓ ▲◆➱ ▼✞❖ ◗✪❘ ➎ ➪✿➬û ➎ ❬ ③ ➓ þ E ✇✦÷ ③ ➬ E ✇◆ ▲✷➱ ▼✞❖ ◗✪❘ ③ ➬⑧þ ö can be estimated from ü based on (37) ➎ (38) ▲◆➱ ▼✞❖ ◗✪❘ þ ❇❍ ➛ Ñ❊❉ ☎ Ò ❇❍ ➛ Ñ❊❉ ☎ Ò ➾þ E ✇✦÷ ③ ➬ E ✇◆ ③ ➪ ö ➎ ➬ ❇ E ✇úù ➎ ③ ö ➎ ➓ ❍ Ñ❊❉ ☎ Ò ➎❺✃ ➘ ö ➎➯ ➎❺✃ ➘ ➎❺✃ ➘ ▲✷▼✞❖ ◗✪❘ ✷▲ ➱ ▼✞❖ ◗✪❘ ▲✷➱ ▼✞❖ ◗✪❘ þ E ✇✠÷ ③ ➬ E ✇❝ ③ ➱ þ þ ö ➎ ➬ ❍ ❇ Ñ❊❉ ☎ Ò ö ➎➯ ➓ ❍ ❇ Ñ❊❉ ☎ Ò ö ➎ ➯ ➓ þ ☞ ➯✕ (39) ➓ ❍ ❇ ❊Ñ ❉ ☎ Ò ➘ ➘ ➘ ➎ç✃ ➎ç✃ ý ➎❺✃ þÐÿ ✃❰ ü E✇ õ ③ þ ➓ (40) ☞ ➯✕ øõ (41) þõ ➓ ☞ ➯✕ (41) describes the estimation rule for þ õ using the SS pilot watermark ✎ that is known to the receiver.