Some fast elliptic solvers on parallel architectures and their complexities

The discretization of separable elliptic partial differential equations leads to linear systems with special block triangular matrices. Several methods are known to solve these systems, the most general of which is the Block Cyclic Reduction (BCR) algorithm which handles equations with nonconsistant coefficients. A method was recently proposed to parallelize and vectorize BCR. Here, the mapping of BCR on distributed memory architectures is discussed, and its complexity is compared with that of other approaches, including the Alternating-Direction method. A fast parallel solver is also described, based on an explicit formula for the solution, which has parallel computational complexity lower than that of parallel BCR

A Dorsal Hand Vein Recognition-based on Local Gabor Phase Quantization with Whitening Transformation

The hand vein pattern is a biometric feature in which the actual pattern is the shape of the vein network and its characteristics are the vein features. This paper investigates a new approach for dorsal hand vein pattern identification from grey level dorsal hand vein information. In this study Gabor filter quadrature pair is employed to compute locally in a window for every pixel position to extract the phase information. The phases of six frequency coefficients are quantized and it is used to form a descriptor code for the local region. These local descriptors are decorrelated using whitening transformation and a histogram is generated for every pixel which describes the local pattern.  Experiments are evaluated on North China University of Technology  dorsal hand vein image dataset with minimum distance classifier and the results are analyzed for recognition rate, run time and equal error rate. The proposed method gives 100 per cent recognition rate and 1 per cent EER for fusion of both left and right hands.Defence Science Journal, 2014, 64(2), pp. 159-167. DOI: http://dx.doi.org/10.14429/dsj.64.465

A general purpose subroutine for fast fourier transform on a distributed memory parallel machine

One issue which is central in developing a general purpose Fast Fourier Transform (FFT) subroutine on a distributed memory parallel machine is the data distribution. It is possible that different users would like to use the FFT routine with different data distributions. Thus, there is a need to design FFT schemes on distributed memory parallel machines which can support a variety of data distributions. An FFT implementation on a distributed memory parallel machine which works for a number of data distributions commonly encountered in scientific applications is presented. The problem of rearranging the data after computing the FFT is also addressed. The performance of the implementation on a distributed memory parallel machine Intel iPSC/860 is evaluated

Signal Shaping for BICM at Low SNR

The mutual information of bit-interleaved coded modulation (BICM) systems, sometimes called the BICM capacity, is investigated at low signal-to-noise ratio (SNR), i.e., in the wideband regime. A new linear transform that depends on bits' probabilities is introduced. This transform is used to prove the asymptotical equivalence between certain BICM systems with uniform and nonuniform input distributions. Using known results for BICM systems with a uniform input distribution, we completely characterize the combinations of input alphabet, input distribution, and binary labeling that achieve the Shannon limit -1.59 dB. The main conclusion is that a BICM system achieves the Shannon limit at low SNR if and only if it can be represented as a zero-mean linear projection of a hypercube, which is the same condition as for uniform input distributions. Hence, probabilistic shaping offers no extra degrees of freedom to optimize the low-SNR mutual information of BICM systems, in addition to what is provided by geometrical shaping. These analytical conclusions are confirmed by numerical results, which also show that for a fixed input alphabet, probabilistic shaping of BICM can improve the mutual information in the low and medium SNR range over any coded modulation system with a uniform input distribution

Pattern Recognition

A wealth of advanced pattern recognition algorithms are emerging from the interdiscipline between technologies of effective visual features and the human-brain cognition process. Effective visual features are made possible through the rapid developments in appropriate sensor equipments, novel filter designs, and viable information processing architectures. While the understanding of human-brain cognition process broadens the way in which the computer can perform pattern recognition tasks. The present book is intended to collect representative researches around the globe focusing on low-level vision, filter design, features and image descriptors, data mining and analysis, and biologically inspired algorithms. The 27 chapters coved in this book disclose recent advances and new ideas in promoting the techniques, technology and applications of pattern recognition

On the BICM Capacity

Optimal binary labelings, input distributions, and input alphabets are analyzed for the so-called bit-interleaved coded modulation (BICM) capacity, paying special attention to the low signal-to-noise ratio (SNR) regime. For 8-ary pulse amplitude modulation (PAM) and for 0.75 bit/symbol, the folded binary code results in a higher capacity than the binary reflected gray code (BRGC) and the natural binary code (NBC). The 1 dB gap between the additive white Gaussian noise (AWGN) capacity and the BICM capacity with the BRGC can be almost completely removed if the input symbol distribution is properly selected. First-order asymptotics of the BICM capacity for arbitrary input alphabets and distributions, dimensions, mean, variance, and binary labeling are developed. These asymptotics are used to define first-order optimal (FOO) constellations for BICM, i.e. constellations that make BICM achieve the Shannon limit -1.59 \tr{dB}. It is shown that the \Eb/N_0 required for reliable transmission at asymptotically low rates in BICM can be as high as infinity, that for uniform input distributions and 8-PAM there are only 72 classes of binary labelings with a different first-order asymptotic behavior, and that this number is reduced to only 26 for 8-ary phase shift keying (PSK). A general answer to the question of FOO constellations for BICM is also given: using the Hadamard transform, it is found that for uniform input distributions, a constellation for BICM is FOO if and only if it is a linear projection of a hypercube. A constellation based on PAM or quadrature amplitude modulation input alphabets is FOO if and only if they are labeled by the NBC; if the constellation is based on PSK input alphabets instead, it can never be FOO if the input alphabet has more than four points, regardless of the labeling.Comment: Submitted to the IEEE Transactions on Information Theor