Representation theory for high-rate multiple-antenna code design

Multiple antennas can greatly increase the data rate and reliability of a wireless communication link in a fading environment, but the practical success of using multiple antennas depends crucially on our ability to design high-rate space-time constellations with low encoding and decoding complexity. It has been shown that full transmitter diversity, where the constellation is a set of unitary matrices whose differences have nonzero determinant, is a desirable property for good performance. We use the powerful theory of fixed-point-free groups and their representations to design high-rate constellations with full diversity. Furthermore, we thereby classify all full-diversity constellations that form a group, for all rates and numbers of transmitter antennas. The group structure makes the constellations especially suitable for differential modulation and low-complexity decoding algorithms. The classification also reveals that the number of different group structures with full diversity is very limited when the number of transmitter antennas is large and odd. We, therefore, also consider extensions of the constellation designs to nongroups. We conclude by showing that many of our designed constellations perform excellently on both simulated and real wireless channels

Wavelet multiresolution analyses adapted for the fast solution of boundary value ordinary differential equations

We present ideas on how to use wavelets in the solution of boundary value ordinary differential equations. Rather than using classical wavelets, we adapt their construction so that they become (bi)orthogonal with respect to the inner product defined by the operator. The stiffness matrix in a Galerkin method then becomes diagonal and can thus be trivially inverted. We show how one can construct an O(N) algorithm for various constant and variable coefficient operators

Codes for differential signaling with many antennas

We construct signal constellations for differential transmission with multiple basestation antennas. The signals are derived using the theory of fixed-point-free groups and are especially suitable for mobile cellular applications because they do not require the handset to have more than one antenna or to know the time-varying propagation environment. Yet we achieve full transmitter diversity and excellent performance gains over a single-antenna system

Multiple antennas and representation theory

Multiple antennas can greatly increase the data rate and reliability of a wireless communication link in a fading environment, but the practical success of using multiple antennas depends crucially on our ability to design high-rate space-time constellations with low encoding and decoding complexity. It has been shown that full transmitter diversity, where the constellation is a set of unitary matrices whose differences have nonzero determinant, is a desirable property for good performance. We use the powerful theory of fixed-point-free groups and their representations to design high-rate constellations with full diversity. Furthermore, we thereby classify all full-diversity constellations that form a group, for all rates and numbers of transmitter antennas. The group structure makes the constellations especially suitable for differential modulation and low-complexity decoding algorithms. The classification also reveals that the number of different group structures with full diversity is very limited when the number of transmitter antennas is large and odd. We therefore also consider extensions of the constellation designs to nongroups. We conclude by showing that many of our designed constellations perform excellently on both simulated and real wireless channels

Interpolating Subdivision for Meshes of Arbitary Topology

Subdivision is a powerful paradigm for the generation of surfaces of arbitrary topology. Given an initial triangular mesh the goal is to produce a smooth and visually pleasing surface whose shape is controlled by the initial mesh. Of particular interest are interpolating schemes since they match the original data exactly, and are crucial for fast mutliresolution and wavelet techniques. Dyn, Gregory, and Levin introduced the Butterfly scheme [17], which yields C1 surfaces in the topologically regular setting. Unfortunately it exhibits undesirable artifacts in the case of an irregular topology. We examine these failures and derive an improved scheme, which retains the simplicity of the Butterfly scheme, is interpolating, and results in smoother surfaces

Wavelets and the Lifting Scheme: A 5 Minute Tour

this paper, we give a brief introductory tour to the lifting scheme, an new method to construct wavelets. We show its advantages over classical constructions and give pointers to the literature. 1. Introductio

The Lifting Scheme: A Construction Of Second Generation Wavelets

this paper we introduce a more general setting where the wavelets are not necessarily translates and dilates of each other but still enjoy all the powerful properties of first generation wavelets. These wavelets are referred to as second generation wavelets. We present the lifting scheme, a simple, but quite powerful tool to construct second generation wavelets. Before we consider the generalization to the second generation case, let us review the properties of first generation wavelets which we would like to preserve. P1: Wavelets form a Riesz basis for L 2 (R) and an unconditional basis for a wide variety of function spaces F , such as Lebesgue, Lipschitz, Sobolev, and Besov spaces. If we denote the wavelet basis b

The Lifting Scheme: A Construction Of Second Generation Wavelets

. We present the lifting scheme, a simple construction of second generation wavelets, wavelets that are not necessarily translates and dilates of one fixed function. Such wavelets can be adapted to intervals, domains, surfaces, weights, and irregular samples. We show how the lifting scheme leads to a faster, in-place calculation of the wavelet transform. Several examples are included. Key words. wavelet, multiresolution, second generation wavelet, lifting scheme AMS subject classifications. 42C15 1. Introduction. Wavelets form a versatile tool for representing general functions or data sets. Essentially we can think of them as data building blocks. Their fundamental property is that they allow for representations which are efficient and which can be computed fast. In other words, wavelets are capable of quickly capturing the essence of a data set with only a small set of coefficients. This is based on the fact that most data sets have correlation both in time (or space) and frequenc..