A new framework for efficient exact maximum-likelihood (ML) decoding of spherical lattice codes is developed. It employs a double-tree structure: The first is that which underlies established tree-search decoders; the second plays the crucial role of guiding the primary search by specifying admissible candidates and is our present focus. Lattice codes have long been of interest due to their rich structure, leading to decoding algorithms for unbounded lattices, as well as those with axis-aligned rectangular shaping regions. Recently, spherical Lattice Space-Time (LAST) codes were proposed to realize the optimal diversity-multiplexing tradeoff of MIMO channels. We address the so-called boundary control problem arising from the spherical shaping region defining these codes. This problem is complicated because of the varying number of candidates to consider at each search stage; it is not obvious how to address it effectively within the frameworks of existing decoders. Our proposed strategy is compatible with all sequential tree-search detectors, as well as auxiliary processing such as the MMSEGDFE and lattice reduction. We demonstrate the superior performance and complexity profiles achieved when applying the proposed boundary control in conjunction with two current efficient ML detectors and show an improvement of 1dB over the state-of-the-art at a comparable complexity.

This paper presents a new sub-optimal lattice decoder based on decomposition of the detection lattice into cosets and iterative application of LLL reduction to its primal and dual representations. From each coset, a candidate solution is chosen using linear equalization followed by integer quantization. These candidates are then compared and the best amongst them is returned. Because the cosets are identical save for distinct translation vectors, their sub-lattice decoders share common preprocessing and can operate very efficiently in parallel. Exclusive of pre-processing, the computational complexity of the proposed decoder is quadratic in the problem dimension and linear in the number of cosets. Simulation results demonstrate the near-ML bit error rate performance offered by the new decoder in the context of existing QAM-modulated MIMO detection schemes.

This paper develops a framework for the efficient maximum-likelihood decoding of lattice codes. Specifically we apply it to the spherical Lattice Space-Time (LAST) codes recently put forward by El Gamal et al. that have been proven to achieve the optimal diversity-multiplexing tradeoff of MIMO channels. Our solution addresses the so-called boundary control problem within the same search tree structure as existing suboptimal LAST decoders. We demonstrate its performance and complexity by applying two of the most efficient tree-based ML detectors currently reported in the literature to the spherical LAST code proposed for the 2 × 2 MIMO channel of block length 2. Our optimal decoders exhibit improved performance over the naive lattice decoder with MMSE-GDFE pre-processing at a comparable complexity.

This paper presents a novel pre-processing stage that offers significant improvement in the computational efficiency of sphere decoding by imposing a geometrically-inspired ordering on the columns of the channel matrix. By studying the performance of a genie decoder, which has knowledge of the optimal radius, we find that the optimal ordering depends not only on the channel matrix, but also on the received point. Analysis of this idealized problem leads to the proposal of an enhanced ordering. We demonstrate via simulation that it closely matches with the optimal ordering and more importantly that it results in a dramatic increase in sphere decoding efficiency over a 4/spl times/4 MIMO flat fading channel. We emphasize that the performance benefit is particularly great at low SNRs and for high modulation orders, two traditionally challenging regimes for sphere decoders. We conclude by briefly discussing the polynomial complexity of the new ordering algorithm.

This paper presents a new MIMO detector based on successive projection of the received signal onto the faces of the lattice induced by the channel matrix. Analysis of the relationship between successive algorithms like V-BLAST and the maximum likelihood (ML) sphere decoder, which share a common underlying tree structure, leads to the design of the successive projection algorithm (SPA). Although it is a suboptimal detector, we prove theoretically that when ML detection can be realized in a successive manner, i.e., without back-tracking, ML performance is also achieved by the SPA. The advantageous implications of this result are illustrated via simulation of the average bit error rates attained over a 4 times 4 MIMO flat fading channel. For instance, at a target error rate of 10-3using 16-QAM modulation, a 2.8 dB improvement over the popular V-BLAST detector is observed at a comparable complexity. We also demonstrate a parameterized SPA, which offers performance profiles approaching that of an ML detector

We present a theoretical framework for the linear collusion analysis of watermarked digital video sequences, and derive a new theorem equating a definition of statistical invisibility, collusion-resistance, and two practical watermark design rules. The proposed framework is simple and intuitive; the basic processing unit is the video frame and we consider second-order statistical descriptions of their temporal inter-relationships. Within this analytical setup, we define the linear frame collusion attack, the analytic notion of a statistically invisible video watermark, and show that the latter is an effective counterattack against the former. Finally, to show how the theoretical results detailed in this paper can easily be applied to the construction of collusion-resistant video watermarks, we encapsulate the analysis into two practical video watermark design rules that play a key role in the subsequent development of a novel collusion-resistant video watermarking algorithm discussed in a companion paper.

We develop a novel video watermarking framework based on the collusion-resistant design rules formulated in a companion paper. We propose to employ a spatially-localized image dependent approach to create a watermark whose pairwise frame correlations approximate those of the host video. To characterize the spread of its spatially-localized energy distribution, the notion of a watermark footprint is introduced. Then we explain how a particular type of image dependent footprint structure, comprised of subframes centered around a set of visually significant anchor points, can lead to two advantageous results: pairwise watermark frame correlations that more closely match those of the host video for statistical invisibility, and the ability to apply image watermarks directly to a frame sequence without sacrificing collusion-resistance. In the ensuing overview of the proposed video watermark, two new ideas are put forward: synchronizing the subframe locations using visual content rather than structural markers and exploiting the inherent spatial diversity of the subframe-based watermark to improve detector performance. Simulation results are presented to show that the proposed scheme provides improved resistance to linear frame collusion, while still being embedded and extracted using relatively low complexity frame-based algorithms.

This paper presents a novel video watermarking algorithm based on two key ideas: statistical invisibility and content-synchronized placement. We argue that statistical invisibility is essential to protect video watermarks from statistical collusion, and present a natural way to induce this property using a content-dependent spatially localized watermarking framework. We introduce the notion of a watermark footprint, the spatial locations over which its energy is spread. By defining localized footprints with regular structures, e.g., a set of subframes within each frame, current image watermarking techniques can immediately be applied at the subframe-level. We address the issue of reduced spatial redundancy by proposing an attack model based on bilinear interpolation, and embedding the watermark into regions with lower expected distortions. Results are presented to demonstrate the effectiveness of the algorithm.