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.
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.
This book explains basics of thermodynamics, including thermodynamic
potentials, microcanonical and canonical distributions, and evolution in the
phase space, The inevitability of irreversibility, basics of information theory,
applications of information theory, new second law of thermodynamics and quantum
information.
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.