Communication theoretic analysis of digital fingerprinting under linear averaging Gaussian attack

Abstract

In this thesis, performance of correlation detector is investigated from a communication theoretic perspective for additive fingerprinting under Gaussian averaging attack. First, digital fingerprinting problem is modeled as a communication system: Presence of users in the collusion is embodied by binary messages, fingerprints are represented as modulating waveforms and linear averaging collusion attack is modeled as a multiple-access channel. It is stated that correlation detector, which calculates the correlation between a specific fingerprint and the colluded copy, is an analogue of the well known matched filter. It is obvious that matched filter is suboptimum for colluder detection so multiple-access interference causing this suboptimality is quantified. Because of the focused detection and decision at the receiver bit error probability is considered as the basic performance measure and generic bit error probability expression that is valid for any additive codebook is derived. In terms of fingerprint codebooks orthogonal, simplex and Gaussian fingerprints are studied. For each codebook minimum achievable bit error probability is obtained and collusion resistance expression is derived based on bit error probability. Furthermore asymptotic behavior of minimum bit error probability is investigated with respect to signal length, number of users and noise power. Error exponents are also calculated and rate of variation of bit error probability at asymptotes is studied.