Minimum Bit Error Probability Research Articles

A Detection Theoretic Approach to Digital Fingerprinting With Focused Receivers Under Uniform Linear Averaging Gaussian Attacks

We consider the digital fingerprinting (FP) problem and model it as a multiuser communications problem and develop a detection theoretic framework. In the general case, colluders apply uniform linear averaging followed by additive colored Gaussian noise. For each user, the receiver computes the correlation between the attacked signal and a linear-transformed version of that user's fingerprint, and performs thresholding (focused detection). Assuming independent colluders with potentially unequal priors, we derive generic exact bit-error probability (BEP) expressions, together with tight bounds, for arbitrary FP codes. Then, we specialize our results to orthogonal, simplex and Gaussian codes in the presence of additive white Gaussian noise; under mean squared error distortion constraints on the embedder and the colluders, we analytically quantify the optimal detection rule, the resulting minimum BEP and its asymptotic behavior, the collusion resistance, and the error exponent for the aforementioned codes, and compare their performances. We show that the minimum BEP expressions for these codes obey the same functional form and that they can be ordered as simplex, orthogonal, and Gaussian in terms of increasing BEP.

Comments on "Carrier tracking in RAKE reception of wide-band DSSS in Ricean fading"

In an earlier paper by Ziemer et al. (see ibid., vol.47, no.6, pp.681-6, 1999), the effect of phase-tracking error in the fingers of a coherent RAKE receiver was characterized. This paper gives additional results for the case where the phase tracking error is due jointly to input noise to the receiver and phase noise internal to the phase tracking device. An optimum number of paths exists, giving a minimum bit-error probability.