Physical Layer Network Coding for Two-Way Relaying with QAM

The design of modulation schemes for the physical layer network-coded two way relaying scenario was studied in [1], [3], [4] and [5]. In [7] it was shown that every network coding map that satisfies the exclusive law is representable by a Latin Square and conversely, and this relationship can be used to get the network coding maps satisfying the exclusive law. But, only the scenario in which the end nodes use $M$-PSK signal sets is addressed in [7] and [8]. In this paper, we address the case in which the end nodes use $M$-QAM signal sets. In a fading scenario, for certain channel conditions $\gamma e^{j \theta}$, termed singular fade states, the MA phase performance is greatly reduced. By formulating a procedure for finding the exact number of singular fade states for QAM, we show that square QAM signal sets give lesser number of singular fade states compared to PSK signal sets. This results in superior performance of $M$-QAM over $M$-PSK. It is shown that the criterion for partitioning the complex plane, for the purpose of using a particular network code for a particular fade state, is different from that used for $M$-PSK. Using a modified criterion, we describe a procedure to analytically partition the complex plane representing the channel condition. We show that when $M$-QAM ($M >4$) signal set is used, the conventional XOR network mapping fails to remove the ill effects of $\gamma e^{j \theta}=1$, which is a singular fade state for all signal sets of arbitrary size. We show that a doubly block circulant Latin Square removes this singular fade state for $M$-QAM.Comment: 13 pages, 14 figures, submitted to IEEE Trans. Wireless Communications. arXiv admin note: substantial text overlap with arXiv:1203.326

Approximation of Entropy Numbers

The purpose of this article is to develop a technique to estimate certain bounds for entropy numbers of diagonal operator on spaces of p-summable sequences for finite p greater than 1. The approximation method we develop in this direction works for a very general class of operators between Banach spaces, in particular reflexive spaces. As a consequence of this technique we also obtain that the entropy number of a bounded linear operator T between two separable Hilbert spaces is equal to the entropy number of the adjoint of T. This gives a complete answer to the question posed by B. Carl [4] in the setting of separable Hilbert spaces.Comment: 10 page

Rejection-Cascade of Gaussians: Real-time adaptive background subtraction framework

Background-Foreground classification is a well-studied problem in computer vision. Due to the pixel-wise nature of modeling and processing in the algorithm, it is usually difficult to satisfy real-time constraints. There is a trade-off between the speed (because of model complexity) and accuracy. Inspired by the rejection cascade of Viola-Jones classifier, we decompose the Gaussian Mixture Model (GMM) into an adaptive cascade of Gaussians(CoG). We achieve a good improvement in speed without compromising the accuracy with respect to the baseline GMM model. We demonstrate a speed-up factor of 4-5x and 17 percent average improvement in accuracy over Wallflowers surveillance datasets. The CoG is then demonstrated to over the latent space representation of images of a convolutional variational autoencoder(VAE). We provide initial results over CDW-2014 dataset, which could speed up background subtraction for deep architectures.Comment: Accepted for National Conference on Computer Vision, Pattern Recognition, Image Processing and Graphics (NCVPRIPG 2019

Recent Techniques in Echocardiography: Two-Dimensional Echocardiography

Conventional M-mode echocardiography is a widely used noninvasive diagnostic technique. It allows bedside assessment of cardiac chamber dimensions, valve motion and left ventricular function. The limitations of this technique are that it (1) provides only a one-dimensional (icepick) view of the heart, (2) displays cardiac structures in an unfamiliar form that bears no resemblance to cardiac anatomy, and (3) does not provide information regarding spatial orientation of cardiac structures. These limitations led to the development of two-dimensional (2-D) real-time echocardiography in the last decade. The 2-D echo allows simultaneous visualization of cardiac structures in real time through multiple planes