We show that the Gaussian multipleaccess channel (MAC) and broadcast channel (BC) are duals. The dual channels we consider have the same channel gains and the same noise power at all receivers. We nd an expression for the capacity region of the BC in terms of the capacity region of the dual MAC, and vice versa. Duality applies to many dierent channel models and capacity de nitions.

This tutorial paper reviews the theory and design of codes for hiding or embedding information in signals such as images, video, audio, graphics, and text. Such codes have also been called watermarking codes; they can be used in a variety of applications, including copyright protection for digital media, content authentication, media forensics, data binding, and covert communications. Some of these applications imply the presence of an adversary attempting to disrupt the transmission of information to the receiver; other applications involve a noisy, generally unknown, communication channel. Our focus is on the mathematical models, fundamental principles, and code design techniques that are applicable to data hiding. The approach draws from basic concepts in information theory, coding theory, game theory, and signal processing, and is illustrated with applications to the problem of hiding data in images. Keywords—Coding theory, data hiding, game theory, image processing, information theory, security, signal processing, watermarking. I.

Abstract — We develop coding strategies for estimation under communication constraints in tree-structured sensor networks. The strategies have a modular and decentralized architecture. This promotes the flexibility, robustness, and scalability that wireless sensor networks need to operate in uncertain, changing, and resource-constrained environments. The strategies are based on a generalization of Wyner-Ziv source coding with decoder side information. We develop solutions for general trees, and illustrate our results in serial (pipeline) and parallel (hub-and-spoke) networks. Additionally, the strategies can be applied to other network information theory problems. They have a successive coding structure that gives an inherently less complex way to attain a number of prior results, as well as some novel results, for the CEO problem, multiterminal source coding, and certain classes of relay channels. Index Terms — sensor networks, distributed estimation, data fusion, side information, Wyner-Ziv coding, rate distortion theory, CEO problems, multiterminal source coding, distributed detection, relay channels. I.

We consider the problem of lossy joint source-channel coding in a communication system where the encoder has access to channel state information (CSI) and the decoder has access to side information that is correlated to the source. This configuration combines the Wyner-Ziv model of pure lossy source coding with side information at the decoder and the Shannon/Gel'fand-Pinsker model of pure channel coding with CSI at the encoder. We prove a separation theorem for this communication system, which asserts that there is no loss in asymptotic optimality in applying first, an optimal Wyner-Ziv source code and then, an optimal Gel'fand-Pinsker channel code. We then derive conditions for the optimality of a symbol-by-symbol (scalar) source-channel code, and demonstrate situations where these conditions are met. Finally, we discuss a few practical applications, including of overlaid communication where the model under discussion is useful.

We present simple, practical codes designed for the binary and Gaussian dirty-paper chan-nels. We show that the dirty paper decoding problem can be transformed into an equivalent multiple-access decoding problem, for which we apply superposition coding. Our concept is a generalization of the nested lattices approach of Zamir, Shamai and Erez. In a theoretical setting, our constructions are capable of achieving capacity using random component codes and maximum-likelihood decoding. We also present practical implementations of the con-structions, and simulation results for both dirty-paper channels. Our results for the Gaussian dirty-paper channel are on par with the best known results for nested-lattices. We discuss the binary dirty-tape channel, for which we present a simple, effective coding technique. Finally, we propose a framework for extending our approach to general Gel’fand-Pinsker channels. Index Terms- dirty paper, dirty tape, multiple-access channel, side information, superposition coding.

Driven by a host of applications, distributed source coding (DSC) has assumed renewed interest in recent years. Wyner-Ziv coding (WZC), which deals with the rate-distortion problem with side information available only at the decoder, is one case of DSC. In this paper, we focus on successive refinement of the Wyner-Ziv problem described in [1]. Similar to the problem in classic source coding, a successive refinement coding scheme for the Wyner-Ziv problem consists of multi-stage encoders and decoders where each decoder uses all the information generated from previous encoding stages and the side information, which could be different from stage to stage. We call such a scheme successively refinable if the rate-distortion pair associated with any stage falls on the same Wyner-Ziv rate-distortion curve given the corresponding side information. It was shown in [1] that if the side information for all stages are identical, the jointly Gaussian source with squared error distortion measure is successively refinable. We extend successive refinability from jointly Gaussian source to the more general type of sources that the difference between the source and the side information is Gaussian and independent of the side information. As a by-product, we give an alternative proof that the Wyner-Ziv problem for these sources has no rate loss, where this statement was recently shown in [2]. We then propose a layered (successive) coding scheme using nested scalar quantization and Slepian-Wolf coding of bit planes based on LDPC codes for the type of sources described above. Moreover, when ideal Slepian-Wolf coding is assumed, we show that our scheme is practically successively refinable, i.e., there is no performance loss due to layering. For the jointly Gaussian source, our layered coder performs 1.33 to 2.83 dB from the Wyner-Ziv bound for rates ranging from 0.47 to 5.65 bits per sample. The full paper is available at

∗ Both authors contributed equally The problem of extracting the relevant aspects of data was addressed through the information bottleneck (IB) method, by (soft) clustering one variable while preserving information about another- relevance- variable. An interesting question addressed in the current work is the extension of these ideas to obtain continuous representations (embeddings) that preserve relevant information, rather than discrete clusters. We give a formal definition of the general continuous IB problem and obtain an analytic solution for the optimal representation for the important case of multivariate Gaussian variables. The obtained optimal representation is a noisy linear projection to eigenvectors of the normalized correlation ma-trix Σ x|yΣ −1 x, which is also the basis obtained in Canonical Correlation Analysis. However, in Gaussian IB, the compression tradeoff parameter uniquely determines the dimension, as well as the scale of each eigenvector. This introduces a novel interpretation where solutions of different ranks lie on a continuum parametrized by the compression level. Our analysis also provides analytic expression for the optimal tradeoff- the information curve- in terms of the eigenvalue spectrum. 1

This paper extends recent results on steganographic capacity. We derive capacity expressions for perfectly-secure steganographic systems. The warden may be passive, or active using a memoryless attack channel, or active using an arbitrarily varying channel. Neither encoder nor decoder know which channel was selected by the warden. In some cases, the steganographic constraint does not result in any capacity loss. To achieve steganographic capacity, encoder and decoder generally need to share a secret codebook.

We explore a mathematical characterization of the functional duality between classical source and channel coding, formulating the precise conditions under which the optimal encoder for one problem is functionally identical to the optimal decoder for the other problem. We then extend this functional duality to the case of coding with side information. We consider several examples corresponding to both discrete-valued and continuous-valued cases to illustrate our formulation.

Fingerprinting systems in the presence of collusive attacks are analyzed as a game between a fingerprinter and a decoder, on the one hand, and a coalition of two or more attackers, on the other hand. The fingerprinter distributes, to different users, different fingerprinted copies of a host data (covertext), drawn from a memoryless stationary source, embedded with different fingerprints. The coalition members create a forgery of the data while aiming at erasing the fingerprints in order not to be detected. Their action is modelled by a multiple access channel (MAC). We analyze the performance of two classes of decoders, associated with different kinds of error events. The decoder of the first class aims at detecting the entire coalition, whereas the second is satisfied with the detection of at least one member of the coalition. Both decoders have access to the original covertext data and observe the forgery in order to identify member/s of the coalition. Motivated by a worst-case approach, we assume that the coalition of attackers is informed of the hiding strategy taken by the fingerprinter and the decoder, while they are uninformed of the attacking scheme. Single letter expressions for the error exponents of the two kinds are obtained, a decoder that is optimal with respect to the two kinds of errors is introduced, and the worst-case attack channel is characterized. 1