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MATH/MTHE 477/877
Data Compression and Source Coding
Winter 2017
 Course Outline

Efficient transmission and storage of information is of critical
importance in many branches of science
and engineering. The means by which to achieve this is source coding
(a.k.a. data compression), a discipline
that studies the compact representation of information bearing signals
(such as text, speech, still image, and
video) for the purpose of storage or transmission. Source coding is
part of the general theory of communication,
and is closely related to and information theory, signal processing,
as well as probability and random
processes.
In this course the fundamentals of the theory and practice of data
compression will be studied. The following is a list of topics
that will be covered in more or less detail.
 Fundamentals of RateDistortion Theory: The
ratedistortion
function and its properties, the lossy source coding theorem.
 Lossless Coding: Arithmetic coding, lossless universal
coding, Kolmogorov complexity, LempelZiv coding.
 Scalar Quantization: uniform and nonuniform quantization, companding quantization,
predictive quantization, speech coding fundamentals, CELP.
 Frequency Domain Coding: Transform coding, bit
allocation, subband coding, wavelet coding, image coding
fundamentals, JPEG, JPEG2000.
 Vector Quantization and High Resolution Theory:
Optimality conditions, design algorithms (LloydMax and related
methods), lattice quantization, Bennett's integral, the ZadorGersho
formula.