Information Theory and its applications in theory of computation
Information Theory and its applications in theory of computation
Information Theory and its applications in theory of computation
This set of lecture notes by Venkatesan Guruswami
and Mahdi Cheraghchi addresses the intersection of information theory and
theoretical computer science. The core topics to be covered in the lecture note
include entropy, Kraft's inequality, source coding theorem, conditional entropy,
and mutual information. It also covers KL-divergence, Chernoff bounds, data
processing, and Fano's inequalities. Key concepts include AEP, universal source
coding using the Lempel-Ziv algorithm, and proof of its optimality. It covers
discrete channels and channel capacity, the Noisy Channel Coding Theorem, and
how to construct capacity-achieving codes by concatenation and by polar codes.
Additional topics: Bregman's theorem, Shearer's Lemma, graph entropy, and
applications to optimal set disjointness lower bounds. This text offers a
wide-ranging view of how the basic principles of information theory shed light
on the construction of algorithms, and the establishment of bounds-on the
complexity of problems in the field of theoretical computation.
Author(s): Venkatesan
Guruswami and Mahdi Cheraghchi
By F. Bavaud, J. C. Chappelier, and J. Kohlas—This long
note contains a good survey of information theory and its applications. It
introduces the basic ideas of uncertainty and information, then also the more
practical extensions such as optimal coding schemes, followed by the theories
underlying versions of stationary processes and Markov chains. Other challenges,
as the note addresses, pertain to noisy transmission environments in coding.
Highlighted here are several advanced topics that follow, including,
importantly, error-correcting codes and cryptography. The resource will give
both a theoretical background and a practical overview of how to encode,
transmit, and secure information effectively. It is a very important guide for
those who seek a deep understanding of information theory and how it relates to
real problems of communication and data processing.
The lecture notes
of Prof. Dr. rer. nat. Rudolf Mathar give a clear and very compact introduction
into information theory. These notes are divided into three key parts: the
basics of information theory, source coding, and information channels. The
introduction treats the basic notions and definitions in information theory in a
very solid way. Source coding gives methods and different techniques that are
used in encoding information, while the information channels section discusses
the pattern in which information is carried and noise that affects it. This
resource is a good pick for students and professionals who seek structure in the
principles of information theory and its applications from a respected expert in
the field.
Author(s): Prof. Dr. rer. nat. Rudolf Mathar, Institute
for Theoretical Information Technology Kopernikusstr, Germany
Om Carter-Introduction to information theory and entropy: It goes in deep
to do some basic concepts of information theory, focusing on the concept of
entropy and its applications. It does so by first investigating the measure of
complexity and the elementary theories of probability before introducing some
key ideas in information theory. It ranges from basic issues, such as entropy
theory and the Gibbs inequality, up to Shannon's communication theory but also
to practical applications in many diversified fields. Other topics dealt with
are Bayes Theorem, analog channels, the Maximum Entropy Principle, and
applications to biology and physics. The Kullback-Leibler information measure
will be discussed in trying to cast light upon quantification of information and
its relations with different fields of science. This book should be ideal for
the general reader interested in information theory and its immense areas of
application..
The lecture notes Advanced
Information Theory Notes by Prof. Dr. sc. techn. Gerhard Kramer cover advanced
topics in information theory. Information theory within the context of these
notes starts with discrete and continuous random variables to base the student
in deeper understandings of complicated scenarios. The key areas include channel
coding, important for good data transmission; typical sequences and sets, which
are fundamental in the theoretical and practical applications of the coding. The
text also explores lossy source coding and distributed source coding, which look
into how data might be compressed and transmitted with much efficiency. It also
covers multiaccess channels, an important aspect in showing just how different
sources of data interact. Such a broad-ranging textbook seems particularly
suited to readers having a firm grounding in basic information theory, wanting
to advance into more advanced areas as well as applications.
This
is a wide-ranging text by Shlomo Shamai and Abdellatif Zaidi, covering both
foundational and advanced topics in information theory applied to data
communications and processing. It discusses basic issues, such as information
bottleneck problems, unsupervised clustering via methods of the variational
information bottleneck, and rate-distortion analysis. It proceeds to get into
subjects of a higher level of difficulty: non-orthogonal eMBB and URLLC radio
access, robust baseband compression techniques, and amplitude-constrained MIMO
channels. Efficient algorithms have been derived for multicasting, content
placement in cache networks, and the fundamental limits of caching. The title
will be a ready reference for researchers and practitioners interested in the
theory and practice of modern communication systems, comprehensively covering
recent advancement efforts and applications in information theory.
This set of lecture notes by Venkatesan Guruswami
and Mahdi Cheraghchi addresses the intersection of information theory and
theoretical computer science. The core topics to be covered in the lecture note
include entropy, Kraft's inequality, source coding theorem, conditional entropy,
and mutual information. It also covers KL-divergence, Chernoff bounds, data
processing, and Fano's inequalities. Key concepts include AEP, universal source
coding using the Lempel-Ziv algorithm, and proof of its optimality. It covers
discrete channels and channel capacity, the Noisy Channel Coding Theorem, and
how to construct capacity-achieving codes by concatenation and by polar codes.
Additional topics: Bregman's theorem, Shearer's Lemma, graph entropy, and
applications to optimal set disjointness lower bounds. This text offers a
wide-ranging view of how the basic principles of information theory shed light
on the construction of algorithms, and the establishment of bounds-on the
complexity of problems in the field of theoretical computation.
Author(s): Venkatesan
Guruswami and Mahdi Cheraghchi