The Higgs mechanism is the last piece of the SM to be discovered which is responsible for giving mass to the electroweak W± and Z bosons. Experimental evidence for the Higgs boson is therefore important and is currently explored at the Large Hadron Collider (LHC) at CERN. The ATLAS experiment (A Toroidal LHC ApparatuS) is analysing a wide range of physics processes from collisions produced by the LHC at a centre-of-mass energy of 7-8TeV and a peak luminosity of 7.73×10³³ cm−2s−1. This thesis concentrates on the discovery and mass measurement of the Higgs boson. The analysis using the H → ZZ(∗) → 4ℓ channel is presented, where ℓ denotes electrons or muons. Statistical methods with non-parametric models are successfully cross-checked with parametric models. The per-event errors studied to improve the mass determination decreases the total mass uncertainty by 9%. The other main focus is the performance of the initial, and possible upgraded, layouts of the ATLAS inner detector. The silicon cluster size, channel occupancy and track separation in jets are analysed for a detailed understanding of the inner detector. The inner detector is exposed to high particle fluxes and is crucial for tracking and vertexing. The simulation of the detector performance is improved by adjusting the cross talk of adjacent hit pixels and the Lorentz Angle in the digitisation. To improve the ATLAS detector for upgrade conditions, the performance is studied with pile-up of up to 200. Several possible layout configurations were considered before converging on the baseline one used for the Letter of Intent. This includes increased granularity in the Pixel and SCT and additional silicon detector layers. This layout was validated to accomplish the design target of an occupancy < 1% throughout the whole inner detector. The H → ZZ(∗) → 4ℓ analysis benefits from the excellent momentum resolution, particularly for leptons down to pT = 6GeV. The current inner detector is designed to provide momentum measurements of low pT charged tracks with resolution of σpT /pT = 0.05% pT ⊕ 1% over a range of |η| < 2.5. The discovery of a new particle in July 2012 which is compatible with the Standard model Higgs boson included the 3.6σ excess of events observed in the H → ZZ(∗) → 4ℓ channel at 125GeV. The per-event error was studied using a narrow mass range, concentrated around the signal peak (110GeV< mH < 150GeV). The error on the four-lepton invariant mass is derived and its probability density function (pdf) is multiplied by the conditional pdf of the four-lepton invariant mass given the error. Applying a systematics model dependent on the true mass of the discovered particle, the new fitting machinery was developed to exploit additional statistical methods for the mass measurement resulting in a discovery with 6.6σ at mH = 124.3+0.6−0.5(stat)+0.5−0.3(syst)GeV and μ = 1.7±0.5 using the full 2011 and 2012 datasets.

Although vector quantization (VQ) is an established topic in communication, its practical utility has been limited due to (i) prohibitive complexity for higher quality and bit-rate, (ii) structured VQ methods which are not analyzed for optimum performance, (iii) difficulty of mapping theoretical performance of mean square error (MSE) to perceptual measures. However, an ever increasing demand for various source signal compression, points to VQ as the inevitable choice for high efficiency. This thesis addresses all the three above issues, utilizing the power of parametric stochastic modeling of the signal source, viz., Gaussian mixture model (GMM) and proposes new solutions. Addressing some of the new requirements of source coding in network applications, the thesis also presents solutions for scalable bit-rate, rate-independent complexity and decoder scalability. While structured VQ is a necessity to reduce the complexity, we have developed, analyzed and compared three different schemes of compensation for the loss due to structured VQ. Focusing on the widely used methods of split VQ (SVQ) and KLT based transform domain scalar quantization (TrSQ), we develop expressions for their optimum performance using high rate quantization theory. We propose the use of conditional PDF based SVQ (CSVQ) to compensate for the split loss in SVQ and analytically show that it achieves coding gain over SVQ. Using the analytical expressions of complexity, an algorithm to choose the optimum splits is proposed. We analyze these techniques for their complexity as well as perceptual distortion measure, considering the specific case of quantizing the wide band speech line spectrum frequency (LSF) parameters. Using natural speech data, it is shown that the new conditional PDF based methods provide better perceptual distortion performance than the traditional methods. Exploring the use of GMMs for the source, we take the approach of separately estimating the GMM parameters and then use the high rate quantization theory in a simplified manner to derive closed form expressions for optimum MSE performance. This has led to the development of non-linear prediction for compensating the split loss (in contrast to the linear prediction using a Gaussian model). We show that the GMM approach can improve the recently proposed adaptive VQ scheme of switched SVQ (SSVQ). We derive the optimum performance expressions for SSVQ, in both variable bit rate and fixed bit rate formats, using the simplified approach of GMM in high rate theory. As a third scheme for recovering the split loss in SVQ and reduce the complexity, we propose a two stage SVQ (TsSVQ), which is analyzed for minimum complexity as well as perceptual distortion. Utilizing the low complexity of transform domain SVQ (TrSVQ) as well as the two stage approach in a universal coding framework, it is shown that we can achieve low complexity as well as better performance than SSVQ. Further, the combination of GMM and universal coding led to the development of a highly scalable coder which can provide both bit-rate scalability, decoder scalability and rate-independent low complexity. Also, the perceptual distortion performance is comparable to that of SSVQ. Since GMM is a generic source model, we develop a new method of predicting the performance bound for perceptual distortion using VQ. Applying this method to LSF quantization, the minimum bit rates for quantizing telephone band LSF (TB-LSF) and wideband LSF (WB-LSF) are derived.