Relaxing the Gaussian AVC

The arbitrarily varying channel (AVC) is a conservative way of modeling an unknown interference, and the corresponding capacity results are pessimistic. We reconsider the Gaussian AVC by relaxing the classical model and thereby weakening the adversarial nature of the interference. We examine three different relaxations. First, we show how a very small amount of common randomness between transmitter and receiver is sufficient to achieve the rates of fully randomized codes. Second, akin to the dirty paper coding problem, we study the impact of an additional interference known to the transmitter. We provide partial capacity results that differ significantly from the standard AVC. Third, we revisit a Gaussian MIMO AVC in which the interference is arbitrary but of limited dimension.Comment: Submitted to the IEEE Transactions on Information Theor

A Practical Dirty Paper Coding Applicable for Broadcast Channel

In this paper, we present a practical dirty paper coding scheme using trellis coded modulation for the dirty paper channel $Y=X+S+W,$ $\mathbb{E}\{X^2\} \leq P$, where $W$ is white Gaussian noise with power $\sigma_w ^2$, $P$ is the average transmit power and $S$ is the Gaussian interference with power $\sigma_s ^2$ that is non-causally known at the transmitter. We ensure that the dirt in our scheme remains distinguishable to the receiver and thus, our designed scheme is applicable to broadcast channel. Following Costa's idea, we recognize the criteria that the transmit signal must be as orthogonal to the dirt as possible. Finite constellation codes are constructed using trellis coded modulation and by using a Viterbi algorithm at the encoder so that the code satisfies the design criteria and simulation results are presented with codes constructed via trellis coded modulation using QAM signal sets to illustrate our results.Comment: 10 page

Trellis-coded quantization for public-key steganography

This paper deals with public-key steganography in the presence of a passive warden. The aim is to hide secret messages within cover-documents without making the warden suspicious, and without any preliminar secret key sharing. Whereas a practical attempt has been already done to provide a solution to this problem, it suffers of poor flexibility (since embedding and decoding steps highly depend on cover-signals statistics) and of little capacity compared to recent data hiding techniques. Using the same framework, this paper explores the use of trellis-coded quantization techniques (TCQ and turbo TCQ) to design a more efficient public-key scheme. Experiments on audio signals show great improvements considering Cachin's security criterion.Comment: 4 pages, 5 figure

Communication in the Presence of a State-Aware Adversary

We study communication systems over state-dependent channels in the presence of a malicious state-aware jamming adversary. The channel has a memoryless state with an underlying distribution. The adversary introduces a jamming signal into the channel. The state sequence is known non-causally to both the encoder and the adversary. Taking an Arbitrarily Varying Channel (AVC) approach, we consider two setups, namely, the discrete memoryless Gel'fand-Pinsker (GP) AVC and the additive white Gaussian Dirty Paper (DP) AVC. We determine the randomized coding capacity of both the AVCs under a maximum probability of error criterion. Similar to other randomized coding setups, we show that the capacity is the same even under the average probability of error criterion. Even with non-causal knowledge of the state, we prove that the state-aware adversary cannot affect the rate any worse than when it employs a memoryless strategy which depends only on the instantaneous state. Thus, the AVC capacity characterization is given in terms of the capacity of the worst memoryless channels with state, induced by the adversary employing such memoryless jamming strategies. For the DP-AVC, it is further shown that among memoryless jamming strategies, none impact the communication more than a memoryless Gaussian jamming strategy which completely disregards the knowledge of the state. Thus, the capacity of the DP-AVC equals that of a standard AWGN channel with two independent sources of additive white Gaussian noise, i.e., the channel noise and the jamming noise.Comment: 24 pages, 3 figure

Digital watermark technology in security applications

With the rising emphasis on security and the number of fraud related crimes around the world, authorities are looking for new technologies to tighten security of identity. Among many modern electronic technologies, digital watermarking has unique advantages to enhance the document authenticity. At the current status of the development, digital watermarking technologies are not as matured as other competing technologies to support identity authentication systems. This work presents improvements in performance of two classes of digital watermarking techniques and investigates the issue of watermark synchronisation. Optimal performance can be obtained if the spreading sequences are designed to be orthogonal to the cover vector. In this thesis, two classes of orthogonalisation methods that generate binary sequences quasi-orthogonal to the cover vector are presented. One method, namely "Sorting and Cancelling" generates sequences that have a high level of orthogonality to the cover vector. The Hadamard Matrix based orthogonalisation method, namely "Hadamard Matrix Search" is able to realise overlapped embedding, thus the watermarking capacity and image fidelity can be improved compared to using short watermark sequences. The results are compared with traditional pseudo-randomly generated binary sequences. The advantages of both classes of orthogonalisation inethods are significant. Another watermarking method that is introduced in the thesis is based on writing-on-dirty-paper theory. The method is presented with biorthogonal codes that have the best robustness. The advantage and trade-offs of using biorthogonal codes with this watermark coding methods are analysed comprehensively. The comparisons between orthogonal and non-orthogonal codes that are used in this watermarking method are also made. It is found that fidelity and robustness are contradictory and it is not possible to optimise them simultaneously. Comparisons are also made between all proposed methods. The comparisons are focused on three major performance criteria, fidelity, capacity and robustness. aom two different viewpoints, conclusions are not the same. For fidelity-centric viewpoint, the dirty-paper coding methods using biorthogonal codes has very strong advantage to preserve image fidelity and the advantage of capacity performance is also significant. However, from the power ratio point of view, the orthogonalisation methods demonstrate significant advantage on capacity and robustness. The conclusions are contradictory but together, they summarise the performance generated by different design considerations. The synchronisation of watermark is firstly provided by high contrast frames around the watermarked image. The edge detection filters are used to detect the high contrast borders of the captured image. By scanning the pixels from the border to the centre, the locations of detected edges are stored. The optimal linear regression algorithm is used to estimate the watermarked image frames. Estimation of the regression function provides rotation angle as the slope of the rotated frames. The scaling is corrected by re-sampling the upright image to the original size. A theoretically studied method that is able to synchronise captured image to sub-pixel level accuracy is also presented. By using invariant transforms and the "symmetric phase only matched filter" the captured image can be corrected accurately to original geometric size. The method uses repeating watermarks to form an array in the spatial domain of the watermarked image and the the array that the locations of its elements can reveal information of rotation, translation and scaling with two filtering processes

Near-capacity dirty-paper code design : a source-channel coding approach

This paper examines near-capacity dirty-paper code designs based on source-channel coding. We first point out that the performance loss in signal-to-noise ratio (SNR) in our code designs can be broken into the sum of the packing loss from channel coding and a modulo loss, which is a function of the granular loss from source coding and the target dirty-paper coding rate (or SNR). We then examine practical designs by combining trellis-coded quantization (TCQ) with both systematic and nonsystematic irregular repeat-accumulate (IRA) codes. Like previous approaches, we exploit the extrinsic information transfer (EXIT) chart technique for capacity-approaching IRA code design; but unlike previous approaches, we emphasize the role of strong source coding to achieve as much granular gain as possible using TCQ. Instead of systematic doping, we employ two relatively shifted TCQ codebooks, where the shift is optimized (via tuning the EXIT charts) to facilitate the IRA code design. Our designs synergistically combine TCQ with IRA codes so that they work together as well as they do individually. By bringing together TCQ (the best quantizer from the source coding community) and EXIT chart-based IRA code designs (the best from the channel coding community), we are able to approach the theoretical limit of dirty-paper coding. For example, at 0.25 bit per symbol (b/s), our best code design (with 2048-state TCQ) performs only 0.630 dB away from the Shannon capacity

Capacity and Random-Coding Exponents for Channel Coding with Side Information

Capacity formulas and random-coding exponents are derived for a generalized family of Gel'fand-Pinsker coding problems. These exponents yield asymptotic upper bounds on the achievable log probability of error. In our model, information is to be reliably transmitted through a noisy channel with finite input and output alphabets and random state sequence, and the channel is selected by a hypothetical adversary. Partial information about the state sequence is available to the encoder, adversary, and decoder. The design of the transmitter is subject to a cost constraint. Two families of channels are considered: 1) compound discrete memoryless channels (CDMC), and 2) channels with arbitrary memory, subject to an additive cost constraint, or more generally to a hard constraint on the conditional type of the channel output given the input. Both problems are closely connected. The random-coding exponent is achieved using a stacked binning scheme and a maximum penalized mutual information decoder, which may be thought of as an empirical generalized Maximum a Posteriori decoder. For channels with arbitrary memory, the random-coding exponents are larger than their CDMC counterparts. Applications of this study include watermarking, data hiding, communication in presence of partially known interferers, and problems such as broadcast channels, all of which involve the fundamental idea of binning.Comment: to appear in IEEE Transactions on Information Theory, without Appendices G and

Game-theoretic Analysis to Content-adaptive Reversible Watermarking

While many games were designed for steganography and robust watermarking, few focused on reversible watermarking. We present a two-encoder game related to the rate-distortion optimization of content-adaptive reversible watermarking. In the game, Alice first hides a payload into a cover. Then, Bob hides another payload into the modified cover. The embedding strategy of Alice affects the embedding capacity of Bob. The embedding strategy of Bob may produce data-extraction errors to Alice. Both want to embed as many pure secret bits as possible, subjected to an upper-bounded distortion. We investigate non-cooperative game and cooperative game between Alice and Bob. When they cooperate with each other, one may consider them as a whole, i.e., an encoder uses a cover for data embedding with two times. When they do not cooperate with each other, the game corresponds to a separable system, i.e., both want to independently hide a payload within the cover, but recovering the cover may need cooperation. We find equilibrium strategies for both players under constraints.Comment: 12 pages, 2 figure

Estimation of the Embedding Capacity in Pixel-pair based Watermarking Schemes

Estimation of the Embedding capacity is an important problem specifically in reversible multi-pass watermarking and is required for analysis before any image can be watermarked. In this paper, we propose an efficient method for estimating the embedding capacity of a given cover image under multi-pass embedding, without actually embedding the watermark. We demonstrate this for a class of reversible watermarking schemes which operate on a disjoint group of pixels, specifically for pixel pairs. The proposed algorithm iteratively updates the co-occurrence matrix at every stage, to estimate the multi-pass embedding capacity, and is much more efficient vis-a-vis actual watermarking. We also suggest an extremely efficient, pre-computable tree based implementation which is conceptually similar to the co-occurrence based method, but provides the estimates in a single iteration, requiring a complexity akin to that of single pass capacity estimation. We also provide bounds on the embedding capacity. We finally show how our method can be easily used on a number of watermarking algorithms and specifically evaluate the performance of our algorithms on the benchmark watermarking schemes of Tian [11] and Coltuc [6].Comment: This manuscript is submitted to Transactions of Image Processing, on september 5th 201

On Polar Coding for Binary Dirty Paper

The problem of communication over binary dirty paper (DP) using nested polar codes is considered. An improved scheme, focusing on low delay, short to moderate blocklength communication is proposed. Successive cancellation list (SCL) decoding with properly defined CRC is used for channel coding, and SCL encoding without CRC is used for source coding. The performance is compared to the best achievable rate of any coding scheme for binary DP using nested codes. A well known problem with nested polar codes for binary DP is the existence of frozen channel code bits that are not frozen in the source code. These bits need to be retransmitted in a second phase of the scheme, thus reducing transmission rate. We observe that the number of these bits is typically either zero or a small number, and provide an improved analysis, compared to that presented in the literature, on the size of this set and on its scaling with respect to the blocklength when the power constraint parameter is sufficiently large or the channel crossover probability sufficiently small.Comment: Accepted to ISIT 201