Re-proving Channel Polarization Theorems: An Extremality and Robustness Analysis

The general subject considered in this thesis is a recently discovered coding technique, polar coding, which is used to construct a class of error correction codes with unique properties. In his ground-breaking work, Ar{\i}kan proved that this class of codes, called polar codes, achieve the symmetric capacity --- the mutual information evaluated at the uniform input distribution ---of any stationary binary discrete memoryless channel with low complexity encoders and decoders requiring in the order of $O(N\log N)$ operations in the block-length $N$. This discovery settled the long standing open problem left by Shannon of finding low complexity codes achieving the channel capacity. Polar coding settled an open problem in information theory, yet opened plenty of challenging problems that need to be addressed. A significant part of this thesis is dedicated to advancing the knowledge about this technique in two directions. The first one provides a better understanding of polar coding by generalizing some of the existing results and discussing their implications, and the second one studies the robustness of the theory over communication models introducing various forms of uncertainty or variations into the probabilistic model of the channel.Comment: Preview of my PhD Thesis, EPFL, Lausanne, 2014. For the full version, see http://people.epfl.ch/mine.alsan/publication

Gridded circular patch antennas

The performance of circular microstrip patch antennas is presented where the conducting patch and ground plane are constructed from a grid. Improved cross polarization, mode suppression, and band-width are possible, but are accompanied by lower gain and reduced front-to-back ratios. A computer simulation reveals the current structure. The density and shape of the grid pattern are important parameters. Such antennas are can be manufactured within glass laminates. (C) 1999 John Wiley & Sons, Inc

One-dimensional Quantum Spin Dynamics of Bethe String States

Quantum dynamics of strongly correlated systems is a challenging problem. Although the low energy fractional excitations of one dimensional integrable models are often well-understood, exploring quantum dynamics in these systems remains challenging in the gapless regime, especially at intermediate and high energies. Based on the algebraic Bethe ansatz formalism, we study spin dynamics in a representative one dimensional strongly correlated model, {\it i.e. }, the antiferromagnetic spin-$\frac{1}{2}$ XXZ chain with the Ising anisotropy, via the form-factor formulae. Various excitations at different energy scales are identified crucial to the dynamic spin structure factors under the guidance of sum rules. At small magnetic polarizations, gapless excitations dominate the low energy spin dynamics arising from the magnetic-field-induced incommensurability. In contrast, spin dynamics at intermediate and high energies is characterized by the two- and three-string states, which are multi-particle excitations based on the commensurate N\'eel ordered background. Our work is helpful for experimental studies on spin dynamics in both condensed matter and cold atom systems beyond the low energy effective Luttinger liquid theory. Based on an intuitive physical picture, we speculate that the dynamic feature at high energies due to the multi-particle anti-bound state excitations can be generalized to non-integrable spin systems.Comment: 15 pages, to appear in Phys. Rev.

Theoretical interpretation of the experimental electronic structure of lens shaped, self-assembled InAs/GaAs quantum dots

We adopt an atomistic pseudopotential description of the electronic structure of self-assembled, lens shaped InAs quantum dots within the ``linear combination of bulk bands'' method. We present a detailed comparison with experiment, including quantites such as the single particle electron and hole energy level spacings, the excitonic band gap, the electron-electron, hole-hole and electron hole Coulomb energies and the optical polarization anisotropy. We find a generally good agreement, which is improved even further for a dot composition where some Ga has diffused into the dots.Comment: 16 pages, 5 figures. Submitted to Physical Review

A Limit on the Polarized Anisotropy of the Cosmic Microwave Background at Subdegree Angular Scales

A ground-based polarimeter, PIQUE, operating at 90 GHz has set a new limit on the magnitude of any polarized anisotropy in the cosmic microwave background. The combination of the scan strategy and full width half maximum beam of 0.235 degrees gives broad window functions with average multipoles, l = 211+294-146 and l = 212+229-135 for the E- and B-mode window functions, respectively. A joint likelihood analysis yields simultaneous 95% confidence level flat band power limits of 14 and 13 microkelvin on the amplitudes of the E- and B-mode angular power spectra, respectively. Assuming no B-modes, a 95% confidence limit of 10 microkelvin is placed on the amplitude of the E-mode angular power spectrum alone.Comment: 4 pages, 3 figures, submitted to Astrophysical Journal Letter

Nonperturbative signatures in pair production for general elliptic polarization fields

The momentum signatures in nonperturbative multiphoton pair production for general elliptic polarization electric fields are investigated by employing the real-time Dirac-Heisenberg-Wigner formalism. For a linearly polarized electric field we find that the positions of the nodes in momenta spectra of created pairs depend only on the electric field frequency. The polarization of external fields could not only change the node structures or even make the nodes disappear but also change the thresholds of pair production. The momentum signatures associated to the node positions in which the even-number-photon pair creation process is forbid could be used to distinguish the orbital angular momentum of created pairs on the momenta spectra. These distinguishable momentum signatures could be relevant for providing the output information of created particles and also the input information of ultrashort laser pulses.Comment: 8 pages, 4 figures, submitted to Europhysics Letter