This note will explore the basic
concepts of information theory. It is highly recommended for students planning
to delve into the fields of communications, data compression, and statistical
signal processing. Topics covered includes: Entropy and mutual information,
Chain rules and inequalities, Data processing, Fano's inequality, Asymptotic
equipartition property, Entropy rate, Source coding and Kraft inequality,
Optimal code length and roof code, Huffman codes, Shannon-Fano-Elias and
arithmetic codes, Maximum entropy, Channel capacity, Channel coding theorem,
Differential entropy, Gaussian channel, Parallel Gaussian channel and
water-filling, Quantization and rate-distortion.
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.
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.
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.
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 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.
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