Correlated Gaussian Sources over Orthogonal Gaussian Channels

We consider the transmission of correlated Gaussian sources over orthogonal Gaussian channels. It is shown that the Amplify and Forward (AF) scheme which simplifies the design of encoders and the decoder, performs close to the optimal scheme even at high SNR. Also, it outperforms a recently proposed scalar quantizer scheme both in performance and complexity. We also study AF when there is side information at the encoders and decoder.

Gaussian mixture model based switched split vector quantization of LSF parameters

We address the issue of rate-distortion (R/D) performance optimality of the recently proposed switched split vector quantization (SSVQ) method. The distribution of the source is modeled using Gaussian mixture density and thus, the non-parametric SSVQ is analyzed in a parametric model based framework for achieving optimum R/D performance. Using high rate quantization theory, we derive the optimum bit allocation formulae for the intra-cluster split vector quantizer (SVQ) and the inter-cluster switching. For the wide-band speech line spectrum frequency (LSF) parameter quantization, it is shown that the Gaussian mixture model (GMM) based parametric SSVQ method provides 1 bit/vector advantage over the non-parametric SSVQ method.

Non-Gaussian Cosmological Perturbations from Hybrid Inflation and Preheating

This thesis consists of four research papers and an introduction providing some background. The structure in the universe is generally considered to originate from quantum fluctuations in the very early universe. The standard lore of cosmology states that the primordial perturbations are almost scale-invariant, adiabatic, and Gaussian. A snapshot of the structure from the time when the universe became transparent can be seen in the cosmic microwave background (CMB). For a long time mainly the power spectrum of the CMB temperature fluctuations has been used to obtain observational constraints, especially on deviations from scale-invariance and pure adiabacity. Non-Gaussian perturbations provide a novel and very promising way to test theoretical predictions. They probe beyond the power spectrum, or two point correlator, since non-Gaussianity involves higher order statistics. The thesis concentrates on the non-Gaussian perturbations arising in several situations involving two scalar fields, namely, hybrid inflation and various forms of preheating. First we go through some basic concepts -- such as the cosmological inflation, reheating and preheating, and the role of scalar fields during inflation -- which are necessary for the understanding of the research papers. We also review the standard linear cosmological perturbation theory. The second order perturbation theory formalism for two scalar fields is developed. We explain what is meant by non-Gaussian perturbations, and discuss some difficulties in parametrisation and observation. In particular, we concentrate on the nonlinearity parameter. The prospects of observing non-Gaussianity are briefly discussed. We apply the formalism and calculate the evolution of the second order curvature perturbation during hybrid inflation. We estimate the amount of non-Gaussianity in the model and find that there is a possibility for an observational effect. The non-Gaussianity arising in preheating is also studied. We find that the level produced by the simplest model of instant preheating is insignificant, whereas standard preheating with parametric resonance as well as tachyonic preheating are prone to easily saturate and even exceed the observational limits. We also mention other approaches to the study of primordial non-Gaussianities, which differ from the perturbation theory method chosen in the thesis work.

Spectrophotometric and potentiometric investigations of copper (II)-Ethanolamine complexes - Part III. diethanolamine (Gaussian analysis of electronic spectra in mono and diethanolamine systems)

Spectrophotometric and potentiometric investigations have been carried out on copper-diethanolamine system. Job plots at 900, 900 and 580 mμ have indicated the formation of CuD++, CuD2++ and CuD3++. The n- pA curves obtained indicate the formation of CuD++, CuD2++, CuD3++, CuDOH+, CuD2OH+ and CuD3OH+. The n- pA curves have been analyzed to obtain the stability constants of these complexes. Absorption curves of pure complexes have been computed by a graphical method. Gaussian analysis of the absorption curves of pure and hydroxy complexes show the presence of a second band, indicating that the structure is that of a distorted octahedron.

Estimation of signals in colored non gaussian noise based on Gaussian Mixture models

Non-Gaussianity of signals/noise often results in significant performance degradation for systems, which are designed using the Gaussian assumption. So non-Gaussian signals/noise require a different modelling and processing approach. In this paper, we discuss a new Bayesian estimation technique for non-Gaussian signals corrupted by colored non Gaussian noise. The method is based on using zero mean finite Gaussian Mixture Models (GMMs) for signal and noise. The estimation is done using an adaptive non-causal nonlinear filtering technique. The method involves deriving an estimator in terms of the GMM parameters, which are in turn estimated using the EM algorithm. The proposed filter is of finite length and offers computational feasibility. The simulations show that the proposed method gives a significant improvement compared to the linear filter for a wide variety of noise conditions, including impulsive noise. We also claim that the estimation of signal using the correlation with past and future samples leads to reduced mean squared error as compared to signal estimation based on past samples only.

Coding for Two-User Gaussian MAC with PSK and PAM Signal Sets

Constellation Constrained (CC) capacity regions of a two-user Gaussian Multiple Access Channel(GMAC) have been recently reported. For such a channel, code pairs based on trellis coded modulation are proposed in this paper with MPSK and M-PAM alphabet pairs, for arbitrary values of M,toachieve sum rates close to the CC sum capacity of the GMAC. In particular, the structure of the sum alphabets of M-PSK and M-PAMmalphabet pairs are exploited to prove that, for certain angles of rotation between the alphabets, Ungerboeck labelling on the trellis of each user maximizes the guaranteed squared Euclidean distance of the sum trellis. Hence, such a labelling scheme can be used systematically,to construct trellis code pairs to achieve sum rates close to the CC sum capacity. More importantly, it is shown for the first time that ML decoding complexity at the destination is significantly reduced when M-PAM alphabet pairs are employed with almost no loss in the sum capacity.

Study of the random vibration of nonlinear systems by the Gaussian closure technique

A technique is developed to study random vibration of nonlinear systems. The method is based on the assumption that the joint probability density function of the response variables and input variables is Gaussian. It is shown that this method is more general than the statistical linearization technique in that it can handle non-Gaussian excitations and amplitude-limited responses. As an example a bilinear hysteretic system under white noise excitation is analyzed. The prediction of various response statistics by this technique is in good agreement with other available results.

Semi-Supervised Classification Using Sparse Gaussian Process Regression

Gaussian Processes (GPs) are promising Bayesian methods for classification and regression problems. They have also been used for semi-supervised learning tasks. In this paper, we propose a new algorithm for solving semi-supervised binary classification problem using sparse GP regression (GPR) models. It is closely related to semi-supervised learning based on support vector regression (SVR) and maximum margin clustering. The proposed algorithm is simple and easy to implement. It gives a sparse solution directly unlike the SVR based algorithm. Also, the hyperparameters are estimated easily without resorting to expensive cross-validation technique. Use of sparse GPR model helps in making the proposed algorithm scalable. Preliminary results on synthetic and real-world data sets demonstrate the efficacy of the new algorithm.

On Two-User Gaussian Multiple Access Channels With Finite Input Constellations

Constellation Constrained (CC) capacity regions of two-user Single-Input Single-Output (SISO) Gaussian Multiple Access Channels (GMAC) are computed for several Non-Orthogonal Multiple Access schemes (NO-MA) and Orthogonal Multiple Access schemes (O-MA). For NO-MA schemes, a metric is proposed to compute the angle(s) of rotation between the input constellations such that the CC capacity regions are maximally enlarged. Further, code pairs based on Trellis Coded Modulation (TCM) are designed with PSK constellation pairs and PAM constellation pairs such that any rate pair within the CC capacity region can be approached. Such a NO-MA scheme which employs CC capacity approaching trellis codes is referred to as Trellis Coded Multiple Access (TCMA). Then, CC capacity regions of O-MA schemes such as Frequency Division Multiple Access (FDMA) and Time Division Multiple Access (TDMA) are also computed and it is shown that, unlike the Gaussian distributed continuous constellations case, the CC capacity regions with FDMA are strictly contained inside the CC capacity regions with TCMA. Hence, for finite constellations, a NO-MA scheme such as TCMA is better than FDMA and TDMA which makes NO-MA schemes worth pursuing in practice for two-user GMAC. Then, the idea of introducing rotations between the input constellations is used to construct Space-Time Block Code (STBC) pairs for two-user Multiple-Input Single-Output (MISO) fading MAC. The proposed STBCs are shown to have reduced Maximum Likelihood (ML) decoding complexity and information-losslessness property. Finally, STBC pairs with reduced sphere decoding complexity are proposed for two-user Multiple-Input Multiple-Output (MIMO) fading MAC.

Coherent-mode decomposition of general anisotropic Gaussian Schell-model beams

We present a complete solution to the problem of coherent-mode decomposition of the most general anisotropic Gaussian Schell-model (AGSM) beams, which constitute a ten-parameter family. Our approach is based on symmetry considerations. Concepts and techniques familiar from the context of quantum mechanics in the two-dimensional plane are used to exploit the Sp(4, R) dynamical symmetry underlying the AGSM problem. We take advantage of the fact that the symplectic group of first-order optical system acts unitarily through the metaplectic operators on the Hilbert space of wave amplitudes over the transverse plane, and, using the Iwasawa decomposition for the metaplectic operator and the classic theorem of Williamson on the normal forms of positive definite symmetric matrices under linear canonical transformations, we demonstrate the unitary equivalence of the AGSM problem to a separable problem earlier studied by Li and Wolf [Opt. Lett. 7, 256 (1982)] and Gori and Guattari [Opt. Commun. 48, 7 (1983)]. This conn ction enables one to write down, almost by inspection, the coherent-mode decomposition of the general AGSM beam. A universal feature of the eigenvalue spectrum of the AGSM family is noted.

The Gaussian Toeplitz matrix

An analytical expression for the LL(T) decomposition for the Gaussian Toeplitz matrix with elements T(ij) = [1/(2-pi)1/2-sigma] exp[-(i - j)2/2-sigma-2] is derived. An exact expression for the determinant and bounds on the eigenvalues follows. An analytical expression for the inverse T-1 is also derived.

Residence time distribution for a class of Gaussian Markov processes

We study the distribution of residence time or equivalently that of "mean magnetization" for a family of Gaussian Markov processes indexed by a positive parameter alpha. The persistence exponent for these processes is simply given by theta=alpha but the residence time distribution is nontrivial. The shape of this distribution undergoes a qualitative change as theta increases, indicating a sharp change in the ergodic properties of the process. We develop two alternate methods to calculate exactly but recursively the moments of the distribution for arbitrary alpha. For some special values of alpha, we obtain closed form expressions of the distribution function. [S1063-651X(99)03306-1].

Subspace Based Speech Enhancement Using Gaussian Mixture Model

Traditional subspace based speech enhancement (SSE)methods use linear minimum mean square error (LMMSE) estimation that is optimal if the Karhunen Loeve transform (KLT) coefficients of speech and noise are Gaussian distributed. In this paper, we investigate the use of Gaussian mixture (GM) density for modeling the non-Gaussian statistics of the clean speech KLT coefficients. Using Gaussian mixture model (GMM), the optimum minimum mean square error (MMSE) estimator is found to be nonlinear and the traditional LMMSE estimator is shown to be a special case. Experimental results show that the proposed method provides better enhancement performance than the traditional subspace based methods.Index Terms: Subspace based speech enhancement, Gaussian mixture density, MMSE estimation.