1,073 research outputs found
On the Gaussian Many-to-One X Channel
In this paper, the Gaussian many-to-one X channel, which is a special case of
general multiuser X channel, is studied. In the Gaussian many-to-one X channel,
communication links exist between all transmitters and one of the receivers,
along with a communication link between each transmitter and its corresponding
receiver. As per the X channel assumption, transmission of messages is allowed
on all the links of the channel. This communication model is different from the
corresponding many-to-one interference channel (IC). Transmission strategies
which involve using Gaussian codebooks and treating interference from a subset
of transmitters as noise are formulated for the above channel. Sum-rate is used
as the criterion of optimality for evaluating the strategies. Initially, a many-to-one X channel is considered and three transmission strategies
are analyzed. The first two strategies are shown to achieve sum-rate capacity
under certain channel conditions. For the third strategy, a sum-rate outer
bound is derived and the gap between the outer bound and the achieved rate is
characterized. These results are later extended to the case. Next,
a region in which the many-to-one X channel can be operated as a many-to-one IC
without loss of sum-rate is identified. Further, in the above region, it is
shown that using Gaussian codebooks and treating interference as noise achieves
a rate point that is within bits from the sum-rate capacity.
Subsequently, some implications of the above results to the Gaussian
many-to-one IC are discussed. Transmission strategies for the many-to-one IC
are formulated and channel conditions under which the strategies achieve
sum-rate capacity are obtained. A region where the sum-rate capacity can be
characterized to within bits is also identified.Comment: Submitted to IEEE Transactions on Information Theory; Revised and
updated version of the original draf
Continued fractions which correspond to two series expansions and the strong Hamburger moment problem
Just as the denominator polynomials of a J-fraction are
orthogonal polynomials with respect to some moment functional, the
denominator polynomials of an M-fraction are shown to satisfy a skew
orthogonality relation with respect to a stronger moment functional.
Many of the properties of the numerators and denominators of an M-
fraction are also studied using this pseudo orthogonality relation
of the denominator polynomials. Properties of the zeros of the
denominator polynomials when the associated moment functional is
positive definite are also considered.
A type of continued fraction, referred to as a J-fraction, is
shown to correspond to a power series about the origin and to another
power series about infinity such that the successive convergents of
this fraction include two more additional terms of anyone of the
power series. Given the power series expansions, a method of
obtaining such a J-fraction, whenever it exists, is also looked at.
The first complete proof of the so called strong Hamburger moment
problem using a continued fraction is given. In this case the
continued fraction is a J-fraction.
Finally a special class of J-fraction, referred to as positive
definite J-fractions, is studied in detail.
The four chapters of this thesis are divided into sections.
Each section is given a section number which is made up of the
chapter number followed by the number of the section within the
chapter. The equations in the thesis have an equation number
consisting of the section number followed by the number of the
equation within that section.
In Chapter One, in addition to looking at some of the
historical and recent developments of corresponding continued
fractions and their applications, we also present some preliminaries.
Chapter Two deals with a different approach of understanding
the properties of the numerators and denominators of corresponding
(two point) rational functions and, continued fractions. This
approach, which is based on a pseudo orthogonality relation of the
denominator polynomials of the corresponding rational functions,
provides an insight into understanding the moment problems. In
particular, results are established which suggest a possible type
of continued fraction for solving the strong Hamburger moment
problem.
In the third chapter we study in detail the existence
conditions and corresponding properties of this new type of continued
fraction, which we call J-fractions. A method of derivation of one
of these 3-fractions is also considered. In the same chapter we also
look at the all important application of solving the strong Hamburger
moment problem, using these 3-fractions.
The fourth and final chapter is devoted entirely to the study
of the convergence behaviour of a certain class of J-fractions,
namely positive definite J-fractions. This study also provides some
interesting convergence criteria for a real and regular 3-fraction.
Finally a word concerning the literature on continued fractions
and moment problems. The more recent and up-to-date exposition on
the analytic theory of continued fractions and their applications is
the text of Jones and Thron [1980]. The two volumes of Baker and
Graves-Morris [1981] provide a very good treatment on one of the
computational aspects of the continued fractions, namely Pade
approximants. There are also the earlier texts of Wall [1948] and
Khovanskii [1963], in which the former gives an extensive insight
into the analytic theory of continued fractions while the latter,
being simpler, remains the ideal book for the beginner. In his
treatise on Applied and Computational Complex Analysis, Henrici
[1977] has also included an excellent chapter on continued fractions.
Wall [1948] also includes a few chapters on moment problems and
related areas. A much wider treatment of the classical moment
problems is provided in the excellent texts of Shohat and Tamarkin
[1943] and Akhieser [1965]
Multiband Detectors and Application of Nanostructured Anti-Reflection Coatings for Improved Efficiency
This work describes multiband photon detection techniques based on novel semiconductor device concepts and detector designs with simultaneous detection of dierent wavelength radiation such as UV and IR. One aim of this investigation is to examine UV and IR detection concepts with a view to resolve some of the issues of existing IR detectors such as high dark current, non uniformity, and low operating temperature and to avoid having additional optical components such as filters in multiband detection. Structures were fabricated to demonstrate the UV and IR detection concepts and determine detector parameters: (i) UV/IR detection based on GaN/AlGaN heterostructures, (ii) Optical characterization of p-type InP thin films were carried out with the idea of developing InP based detectors, (iii) Intervalence band transitions in InGaAsP/InP heterojunction interfacial workfunction internal photoemission (HEIWIP) detectors. Device concepts, detector structures, and experimental results are discussed. In order to reduce reflection, TiO2 and SiO2 nanostructured thin film characterization and application of these as anti-reflection coatings on above mentioned detectors is also discussed
Sieved para-orthogonal polynomials on the unit circle
We look at the para-orthogonal polynomials, chain sequences and quadrature formulas that follow from the kernel polynomials of sieved orthogonal polynomials on the unit circle
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