A Theorem on Analytic Strong Multiplicity One

Let $K$ be an algebraic number field, and $\pi=\otimes\pi_{v}$ an irreducible, automorphic, cuspidal representation of \GL_{m}(\mathbb{A}_{K}) with analytic conductor $C(\pi)$. The theorem on analytic strong multiplicity one established in this note states, essentially, that there exists a positive constant $c$ depending on $\varepsilon>0, m,$ and $K$ only, such that $\pi$ can be decided completely by its local components $\pi_{v}$ with norm $N(v)<c\cdot C(\pi)^{2m+\varepsilon}.$Comment: accepted by J. Number Theor

Fully Scalable Video Coding Using Redundant-Wavelet Multihypothesis and Motion-Compensated Temporal Filtering

In this dissertation, a fully scalable video coding system is proposed. This system achieves full temporal, resolution, and fidelity scalability by combining mesh-based motion-compensated temporal filtering, multihypothesis motion compensation, and an embedded 3D wavelet-coefficient coder. The first major contribution of this work is the introduction of the redundant-wavelet multihypothesis paradigm into motion-compensated temporal filtering, which is achieved by deploying temporal filtering in the domain of a spatially redundant wavelet transform. A regular triangle mesh is used to track motion between frames, and an affine transform between mesh triangles implements motion compensation within a lifting-based temporal transform. Experimental results reveal that the incorporation of redundant-wavelet multihypothesis into mesh-based motion-compensated temporal filtering significantly improves the rate-distortion performance of the scalable coder. The second major contribution is the introduction of a sliding-window implementation of motion-compensated temporal filtering such that video sequences of arbitrarily length may be temporally filtered using a finite-length frame buffer without suffering from severe degradation at buffer boundaries. Finally, as a third major contribution, a novel 3D coder is designed for the coding of the 3D volume of coefficients resulting from the redundant-wavelet based temporal filtering. This coder employs an explicit estimate of the probability of coefficient significance to drive a nonadaptive arithmetic coder, resulting in a simple software implementation. Additionally, the coder offers the possibility of a high degree of vectorization particularly well suited to the data-parallel capabilities of modern general-purpose processors or customized hardware. Results show that the proposed coder yields nearly the same rate-distortion performance as a more complicated coefficient coder considered to be state of the art

Analytical Model for Outdoor Millimeter Wave Channels using Geometry-Based Stochastic Approach

The severe bandwidth shortage in conventional microwave bands has spurred the exploration of the millimeter wave (MMW) spectrum for the next revolution in wireless communications. However, there is still lack of proper channel modeling for the MMW wireless propagation, especially in the case of outdoor environments. In this paper, we develop a geometry-based stochastic channel model to statistically characterize the effect of all the first-order reflection paths between the transmitter and receiver. These first-order reflections are generated by the single-bounce of signals reflected from the walls of randomly distributed buildings. Based on this geometric model, a closed-form expression for the power delay profile (PDP) contributed by all the first-order reflection paths is obtained and then used to evaluate their impact on the MMW outdoor propagation characteristics. Numerical results are provided to validate the accuracy of the proposed model under various channel parameter settings. The findings in this paper provide a promising step towards more complex and practical MMW propagation channel modeling.Comment: Accepted to appear in IEEE Transactions on Vehicular Technolog