Lecture Notes on statistics and information Theory
Lecture Notes on statistics and information Theory
Lecture Notes on statistics and information Theory
This
lecture note navigates through information theory, statistics and measure theory. It
covers fundamental concepts such as definitions, chain rules, data processing
inequalities, and divergences and extends to optimal procedures, LeCam’s and
Fano’s inequalities, and operational results like entropy and source coding. It
also focus on exponential families and statistical modeling, fitting procedures,
and lower bounds on testing parameters, sub-Gaussian and sub-exponential random
variables, martingale methods, uniformity covering topics such as
Kullback-Leibler divergence, PAC-Bayes bounds, interactive data analysis, and
error bounds.
This note serves as a comprehensive guide to fundamental concepts in
information theory and coding. This pdf provides discrete probability theory,
information theory, and coding principles. Beginning with Shannon's measure of
information, then delves into the efficient coding of information, the
methodology of typical sequences is introduced, emphasizing the distinction
between lossy and lossless source encoding. The text also discusses coding for
noisy digital channels, block coding principles and tree and trellis coding
principles.
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.
Prof. Tsachy Weissman's
lecture notes are an excellent summary of the core topics in the subject of
information theory. The document initiates with a basic overview of entropy and
relative entropy, followed by mutual information and asymptotic equipartition
property. Further, it discusses communications theory, channel capacity, and the
method of types. It also covers key topics such as typicality-conditioned and
joint, lossy compression, and rate-distortion theory. The notes also include
joint source-channel coding, where there is quite a good grasp of the principles
and applications of information theory. These notes will be very helpful for
students and professionals looking forward to structured, comprehensive
knowledge about the subject.
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 is a PDF document written by
J.G. Daugman on the fundamentals of the theory of information and coding.
Beginning with the very basic concept of probability and uncertainty, and the
concept of information, it arrives at entropies and their meaning. It deals with
the source coding theorems: prefix, variable-length, and fixed-length codes. It
looks into several kinds of channels, their properties, noise, and channel
capacity. The further topics delve into detail with continuous information,
noisy channel coding theorems, Fourier series elaborated on in making matters of
convergence, orthogonal representation, and useful Fourier theorems. The text
also expands into aspects such as sampling and aliasing, DFT, FFT algorithms,
and the quantized degrees-of-freedom in continuous signals and concludes with
discussions on the Gabor-Heisenberg-Weyl uncertainty relation and Kolmogorov
complexity for a general overview of some of the key principles of information
theory and coding.