Universal Polar Decoding with Channel Knowledge at the Encoder

Polar coding over a class of binary discrete memoryless channels with channel knowledge at the encoder is studied. It is shown that polar codes achieve the capacity of convex and one-sided classes of symmetric channels

The density function for the value-distribution of Lerch zeta-functions and its applications

The probabilistic study of the value-distribution of zeta-functions is one of the modern topics in analytic number theory. In this paper, we study a probability density function related to the value-distribution of Lerch zeta-functions. We prove a limit theorem with an effective error term, and moreover, we obtain an asymptotic formula on the number of zeros of Lerch zeta-functions on the right side of the critical line by applying the density function.Comment: 28 page

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

Discrete value-distribution of Artin LL-functions associated with cubic fields

Arising from the factorizations of Dedekind zeta-functions of non-Galois cubic fields, we obtain Artin $L$-functions of two-dimensional irreducible representations. In this paper, we study the distribution of values of such Artin $L$-functions as the cubic fields are varying. We prove that various mean values of the Artin $L$-functions are represented by integrals involving a density function which can be explicitly constructed. The result is applied to the study on the distribution of class numbers of cubic fields.Comment: 47 page

Is today's architecture about real space, virtual space or what?

Nowadays digital technologies and information and telecommunication technologies are widely used in every aspect of our lives. This article focuses on the digital technologies and their effect on the place-making activities. First an overview of the digital technologies for the creation, occupancy and management of a building is given. Secondly, the concepts of space and virtual space are discussed. Through these discussions, the concept of places and its virtual alternatives and recombination the use of space are described. Finally some concluding remarks are made on whether today’s place making activities about real space or it extends beyond that