Experimental Assessment of Probabilistic Fingerprinting Codes over AWGN Channel

Abstract

The estimation of the false-positive probability has been an important concern for fingerprinting codes, and the formula of the probability has been derived under a restricted assumption and statistic model. In this paper, we first analyze the statistic behavior of the value of score derived from the correlation between a pirated codeword and codewords of all users when some bits are flipped. Then, the derivation of the score is adaptively designed to consider the attack model such that a pirated codeword is distorted by additive white Gaussian noise. The traceability and probability of false-positive are estimated by Monte-Carlo simulation, and the validity of the Gaussian approximation for the distribution of score is evaluated for probabilistic fingerprinting codes.

Toward Practical Joint Decoding of Binary Tardos Fingerprinting Codes

“…As far as we know, our paper presents for the first time experimental results on such a large scale for the Tardos code. Soft watermark decoding achieves tangible performance enhancements contrary to the conclusions drawn in [14]. Overall, the comparisons to related works with their exact setup show the benefits of our decoder: better decoding performance with a controlled probability of false alarm and an acceptable runtime.…”

“…In the combined digit model assumed in [18] and [19], the watermark decoder is indeed composed of multiple binary detectors, one per symbol of the alphabets: for the binary alphabet, both symbols may be detected in case of a merge. In [14] and [15], the watermark decoder has a single but scalar output . In brief, this soft decision is clearly negative (positive) if symbol "0" (respectively "1") is detected, and around 0 in case of a merge.…”

“…3, for a spread spectrum watermarking where a symbol is embedded per block of content with an antipodal [a.k.a. binary phase shift keying (BPSK)] modulation of a secret carrier [14], [16].…”

“…It is interesting to see that our decoder obtains competitive lengths while keeping the original code construction. The second part uses the soft outputs of a watermarking decoder as tested with the Tardos code in [14] and with the error correction code (ECC)-based fingerprinting code in [15] and [16]. The number of users ranges from 10 to more than 10 .…”

Universal Threshold Calculation for Fingerprinting Decoders using Mixture Models

“…The seminal work of probabilistic or bias-based fingerprinting codes is the well known Tardos Codes introduced by Tardos [19] proving that a fingerprinting scheme must satisfy l ∝ c 2 ln nε −1 1 for a large number of fingerprints n, with code length l, number of colluders c and upper bound on the probability of accusing a specific innocent ε1. It followed a long list of descendants, that proposed optimizations by sharpening the bounds ( [22], [15], [16], [9]), improving the distribution function ( [5], [1], 1 For binary fingerprints, both models are equal [7]) or introducing a more discriminative or practical accusation score function ( [20], [10], [6], [17]). …”