Digital fingerprinting is a technique for identifying users who might try to use multimedia content for unintended purposes, such as redistribution. These fingerprints are typically embedded into the content using watermarking techniques that are designed to be robust to a variety of attacks. A cost-e#ective attack against such digital fingerprints is collusion, where several di#erently marked copies of the same content are combined to disrupt the underlying fingerprints. In this paper, we investigate the problem of designing fingerprints that can withstand collusion and allow for the identification of colluders. We begin by introducing the collusion problem for additive embedding. We then study the e#ect that averaging collusion has upon orthogonal modulation. We introduce an e#cient detection algorithm for identifying the fingerprints associated with K colluders that requires log(n/K)) correlations for a group of n users. We next develop a fingerprinting scheme based upon code modulation that does not require as many basis signals as orthogonal modulation. We propose a new class of codes, called anti-collusion codes (ACC), which have the property that the composition of any subset of K or fewer codevectors is unique. Using this property, we can therefore identify groups of K or fewer colluders. We present a construction of binary-valued ACC under the logical AND operation that uses the theory of combinatorial designs and is suitable for both the on-o# keying and antipodal form of binary code modulation. In order to accommodate n users, our code construction requires only # n) orthogonal signals for a given number of colluders. We introduce four di#erent detection strategies that can be used with our ACC for identifying a suspect set of colluders. We demonstrate th...

In a WDM network, routing a request consists in assigning it a route in the physical network and a wavelength. If each request uses at most 1/C of the bandwidth of the wavelength, we will say that the grooming factor is C. That means that on a given edge of the network we can groom (group) at most C requests on the same wavelength. With this constraint the objective can be either to minimize the number of wavelengths (related to the transmission cost) or minimize the number of Add Drop Multiplexers (shortly ADM) used in the network (related to the cost of the nodes). We consider here the case where the network is a path on N nodes, PN. Thus the routing is unique. For a given grooming factor C minimizing the number of wavelengths is an easy problem, well known and related to the load problem. But minimizing the number of ADM’s is NP-complete for a general set of requests and no results are known. Here we show how to model the problem as a graph partition problem and using tools of design theory we completely solve the case where C = 2 and where we have a static uniform all-to-all traffic (one request for each pair of vertices).

Abstract—The noiseless wire-tap channel of type II with coset coding scheme was provided by Ozarow and Wyner. In this correspondence, the user is split into multiple parties who are coordinated in coding their data symbols by using the same encoder. The adversary can tap not only partial transmitted symbols but also partial data symbols. We are interested in the equivocation of the data symbols to this adversary who has more power than that of Ozarow and Wyner. The generalized Hamming weight of Wei and the dimension/length profile (DLP) of Forney are extended to two-code formats: relative generalized Hamming weight and relative dimension/length profile (RDLP). Upper and lower bounds of the new concepts are investigated. They are useful to design a perfect secrecy coding scheme for the coordinated multiparty model. Under a general secrecy standard, the coordinated model can provide a higher transmission rate than an uncoordinated (time-sharing) model. Index Terms—Dimension/length profile (DLP), generalized Hamming weight, relative dimension/length profile (RDLP), relative generalized Hamming weight, wire-tap channel of type II. I.

Optical packet switching is a long-term strategy to provide high-speed transmission, data transparency, and reconfigurability. Optical buffers are used in the switches to resolve contentions that occur whenever two packets are destined to the same output at the same time slot. Due to the lack of optical random access memory, fiber delay line (FDL) is cur-rently the only way to implement optical buffering. In general, optical buffering structures can be categorized in two classes: feed-forward and feedback, both of which have advan-tages and disadvantages. In this research, we proposed a more effective hybrid buffering architecture that combines the merits of both schemes. It requires smaller optical device sizes and fewer wavelengths and has less noise than feedback architecture. At the same time, it can facilitate preemptive priority routing which feed-forward architecture cannot support. Based on this architecture, we described two switch designs—single plane and multiple plane. The numerical results showed that the new switch architecture can signifi-cantly reduce the packet loss probability. The objective of traffic grooming is to save electronics cost by effectively assigning low-rate circuits onto high-speed channels. Generally, we can treat the traffic grooming

A critical set in a Latin square of order n is a set of entries in an n x n array which can be embedded in precisely one Latin square of order n, with the property that if any entry of the critical set is deleted, the remaining set can be embedded in more than one Latin square of order n. The number of

It is well known that certain combinatorial structures in the Tanner graph of a low-density parity-check code exhibit a strong influence on its performance under iterative decoding. These structures include cycles, stopping/trapping sets and parameters such as the diameter of the code. In general, it is very hard to find a complete characterization of such configurations in an arbitrary code, and even harder to understand the intricate relationships that exist between these entities. It is therefore of interest to identify a simple setting in which all the described combinatorial structures can be enumerated and studied within a joint framework. One such setting is developed in this paper, for the purpose of analyzing the distribution of short cycles and the structure of stopping and trapping sets in Tanner graphs of LDPC codes based on idempotent and symmetric Latin squares. The parity-check matrices of LDPC codes based on Latin squares have a special form that allows for connecting combinatorial parameters of the codes with the number of certain sub-rectangles in the Latin squares. Sub-rectangles of interest can be easily identified, and in certain instances, completely enumerated. The presented study can be extended in several different directions, one of which is concerned with modifying the code design process in order to eliminate or reduce the number of configurations bearing a negative influence on the performance of the code. Another application of the results includes determining to which extent a configuration governs the behavior of the bit error rate (BER) curve in the waterfall and error-floor regions.

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A 4-cycle system of order n is said to be almost resolvable provided its 4-cycles can be partitioned into (n − 1)/2 almost parallel classes ( = (n − 1)/4 vertex disjoint 4-cycles) and a half parallel class ( = (n−1)/8 vertex disjoint 4-cycles.) We construct an almost resolvable 4-cycle system of every order n ≡ 1 (mod 8) except 9 (for which no such system exists) and possibly 33, 41 and 57. 1

A line in (Z/nZ) 2 is any translate of a cyclic subgroup of order n. A subset X ⊂ (Z/nZ) 2 is a cap if no three of its points are collinear, and X is complete if it is not properly contained in another cap. We determine bounds on Φ(n), the minimum size of a complete cap in (Z/nZ) 2. The other natural extremal question of determining the maximum size of a cap in (Z/nZ) 2 is considered in [8]. These questions are closely related to well-studied questions in finite affine and projective geometry. If p is the smallest prime divisor of n, weprovethat max{4, √ 2p + 1}≤Φ(n) ≤ max{4,p+1}. 2 We conclude the paper with a large number of open problems in this area. 1

We consider two well-known constructions for Steiner triple systems and show that by using the right ingredients, the resultant systems are nonresolvable. The first