TY - GEN
T1 - Infonnation-theoretic analysis of spherical fingerprinting
AU - Moulin, Pierre
AU - Wang, Ying
PY - 2009
Y1 - 2009
N2 - Information-theoretic performance limits of digital fingerprinting systems subject to almost-sure squared-error distortion constraints on the fingerprint embedder and the colluders are derived in this paper. The rate of the fingerprinting code is R= 1/N log M where is codelength and is the number of users. No assumption is made on the host signal statistics, but the collusion channel is also subject to a location-invariant condition. The receiver knows neither the collusion channel nor even the number of colluders. Capacity is the supremum of achievable rates and is shown to be equal to 1/2K log( 1+D f/KDc) where is the number of colluders, and Df and Dc are the L2-distortion tolerance levels for the fingerprint embedder and the colluders, respectively. The worst collusion is shown to consist of uniform linear averaging of the coalition's marked copies followed by addition of independent spherical noise. Positive error exponents are achieved at all rates below capacity using random spherical fingerprinting codes and a new universal decoding criterion based on empirical Gaussian mutual information. It is also shown that minimum-distance decoding fails for this problem, and that a simple single-user decoder is almost as good as the universal decoder for large Geometric interpretations for all the results are given.
AB - Information-theoretic performance limits of digital fingerprinting systems subject to almost-sure squared-error distortion constraints on the fingerprint embedder and the colluders are derived in this paper. The rate of the fingerprinting code is R= 1/N log M where is codelength and is the number of users. No assumption is made on the host signal statistics, but the collusion channel is also subject to a location-invariant condition. The receiver knows neither the collusion channel nor even the number of colluders. Capacity is the supremum of achievable rates and is shown to be equal to 1/2K log( 1+D f/KDc) where is the number of colluders, and Df and Dc are the L2-distortion tolerance levels for the fingerprint embedder and the colluders, respectively. The worst collusion is shown to consist of uniform linear averaging of the coalition's marked copies followed by addition of independent spherical noise. Positive error exponents are achieved at all rates below capacity using random spherical fingerprinting codes and a new universal decoding criterion based on empirical Gaussian mutual information. It is also shown that minimum-distance decoding fails for this problem, and that a simple single-user decoder is almost as good as the universal decoder for large Geometric interpretations for all the results are given.
KW - Capacity
KW - Digital fingerprinting
KW - Error exponents
KW - Gaussian random variables
KW - Model order selection
KW - Multiple-access channels
KW - Normalized correlation
KW - Randomized codes
KW - Typical sets
KW - Universal coding
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U2 - 10.1109/ITA.2009.5044950
DO - 10.1109/ITA.2009.5044950
M3 - Conference contribution
AN - SCOPUS:70349292666
SN - 9781424439904
T3 - Information Theory and Applications Workshop, ITA 2009
SP - 229
EP - 236
BT - Information Theory and Applications Workshop, ITA 2009
T2 - Information Theory and Applications Workshop, ITA 2009
Y2 - 8 February 2009 through 13 February 2009
ER -