Combining an information-theoretic approach to fingerprinting with a more constructive, statistical approach, we derive new results on the fingerprinting capacities for various informed settings, as well as new log-likelihood decoders with provable code lengths that asymptotically match these capacities. The simple decoder built against the interleaving attack is further shown to achieve the simple capacity for unknown attacks, and is argued to be an improved version of the recently proposed decoder of With this new universal decoder, cut-offs on the bias distribution function can finally be dismissed. Besides the application of these results to fingerprinting, a direct consequence of our results to group testing is that (i) a simple decoder asymptotically requires a factor 1.44 more tests to find defectives than a joint decoder, and (ii) the simple decoder presented in this paper provably achieves this bound.
Recently Abbe and Zheng @cite_18 showed that, in the context of fingerprinting @cite_29 , if the set of allowed collusion channels satisfies a certain one-sidedness condition, then a decoder that achieves capacity against the information-theoretic worst-case attack is a universal decoder achieving capacity against arbitrary attacks. The main drawback of using this result is that the worst-case attack is hard to compute, but this does lead to more insight why e.g. @cite_37 obtained a universal decoder by considering the decoder against the interleaving attack', which is known to be the asymptotic worst-case attack.
@cite_18 @cite_29 @cite_37
2083594366 1546855683 2143664144 1485005937
We study a fingerprinting game in which the number of colluders and the collusion channel are unknown. The encoder embeds fingerprints into a host sequence and provides the decoder with the capability to trace back pirated copies to the colluders. Fingerprinting capacity has recently been derived as the limit value of a sequence of maximin games with mutual information as their payoff functions. However, these games generally do not admit saddle-point solutions and are very hard to solve numerically. Here under the so-called Boneh-Shaw marking assumption, we reformulate the capacity as the value of a single two-person zero-sum game, and show that it is achieved by a saddle-point solution. If the maximal coalition size is k and the fingerprinting alphabet is binary, we show that capacity decays quadratically with k. Furthermore, we prove rigorously that the asymptotic capacity is 1 (k221n2) and we confirm our earlier conjecture that Tardos' choice of the arcsine distribution asymptotically maximizes the mutual information payoff function while the interleaving attack minimizes it. Along with the asymptotics, numerical solutions to the game for small k are also presented. We compute the channel capacity of non-binary fingerprinting under the Marking Assumption, in the limit of large coalition size c. The solution for the binary case was found by Huang and Moulin. They showed that asymptotically, the capacity is 1 (c22 ln 2), the interleaving attack is optimal and the arcsine distribution is the optimal bias distribution. In this paper we prove that the asymptotic capacity for general alphabet size q is (q - 1) (c22 lnq). Our proof technique does not reveal the optimal attack or bias distribution. The fact that the capacity is an increasing function of q shows that there is a real gain in going to non-binary alphabets. We consider the generalized dirty-paper channel Y=X+S+N,E X sup 2 spl les P sub X , where N is not necessarily Gaussian, and the interference S is known causally or noncausally to the transmitter. We derive worst case capacity formulas and strategies for "strong" or arbitrarily varying interference. In the causal side information (SI) case, we develop a capacity formula based on minimum noise entropy strategies. We then show that strategies associated with entropy-constrained quantizers provide lower and upper bounds on the capacity. At high signal-to-noise ratio (SNR) conditions, i.e., if N is weak relative to the power constraint P sub X , these bounds coincide, the optimum strategies take the form of scalar lattice quantizers, and the capacity loss due to not having S at the receiver is shown to be exactly the "shaping gain" 1 2log(2 spl pi e 12) spl ap 0.254 bit. We extend the schemes to obtain achievable rates at any SNR and to noncausal SI, by incorporating minimum mean-squared error (MMSE) scaling, and by using k-dimensional lattices. For Gaussian N, the capacity loss of this scheme is upper-bounded by 1 2log2 spl pi eG( spl Lambda ), where G( spl Lambda ) is the normalized second moment of the lattice. With a proper choice of lattice, the loss goes to zero as the dimension k goes to infinity, in agreement with the results of Costa. These results provide an information-theoretic framework for the study of common communication problems such as precoding for intersymbol interference (ISI) channels and broadcast channels. In this paper, we consider the problem of min- imizing the multicast decoding delay of generalized instantly decodable network coding (G-IDNC) over persistent forward and feedback erasure channels with feedback intermittence. In such an environment, the sender does not always receive acknowledgement from the receivers after each transmission. Moreover, both the forward and feedback channels are subject to persistent erasures, which can be modelled by a two state (good and bad states) Markov chain known as Gilbert-Elliott channel (GEC). Due to such feedback imperfections, the sender is unable to determine subsequent instantly decodable packets combination for all receivers. Given this harsh channel and feedback model, we first derive expressions for the probability distributions of decoding delay increments and then employ these expressions in formulating the minimum decoding problem in such environment as a maximum weight clique problem in the G-IDNC graph. We also show that the problem formulations in simpler channel and feedback models are special cases of our generalized formulation. Since this problem is NP-hard, we design a greedy algorithm to solve it and compare it to blind approaches proposed in literature. Through extensive simulations, our adaptive algorithm is shown to outperform the blind approaches in all situations and to achieve significant improvement in the decoding delay, especially when the channel is highly persistent. Index Terms—Multicast Channels, Persistent Erasure Chan- nels, G-IDNC, Decoding Delay, Lossy Intermittent Feedback, Maximum Weight Clique Problem.