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Description: This graduate course
provides an introductory treatment of codes on graphs and their decoding
algorithms. Codes on graphs such as low-density parity check (LDPC) codes and
iterative decoding have revolutionized communications, and are becoming
standard in many systems, but their importance goes beyond applications in
communications.
The course
provides a unified framework of treating iterative decoding algorithms. It
gives a rigorous treatment of codes on graphs, their topology, and message
passing algorithms, such as belief propagation, sum-product, min-sum
algorithms, forward-backward type algorithms, as well as detailed case
studies of their applications.
Prerequisite(s):
None, but familiarity with probability concepts is desirable.
Objectives:
To give the student a fundamentals of modern error
control coding theory. After completion of the course, the student should
be able to design coding systems based on LDPC codes on graphs, and possess
sufficient background to tackle the leading publications in the field.
Credits:
This is a one-month short course.
Grading policy: Graded work
will include projects and presentations.
Instructor: Dr. Bane Vasic,
Professor of Electrical and Computer Engineering and Mathematics at the
University of Arizona, IEEE Fellow, da-vinci
Fellow, Fulbright Scholar.
Topics
covered:
Review of
mathematical tools and information theory
Orthogonal functions, probability theory, random processes,
Markov processes, information measures, channel capacity, channel coding,
Shannon coding theorems.
Optimum receivers
for additive white Gaussian noise (AWGN) channel
Maximum a posteriori (MAP) and maximum likelihood (ML)
detection, matched filter demodulation, sequence detectors, symbol by
symbol MAP detector for channels with memory, receiver performance
Error control
coding fundamentals
Finite fields, generator and parity check matrices, block and
convolutional codes, Hamming codes, syndrome decoding
Codes on graphs
and iterative decoding
Probabilistic
graphical models, exact and approximate inference, belief propagation,
low-density parity check (LDPC) codes, iterative decoding, linear programming
decoding
References:
Books
[1]
Tom Richardson, and Ruediger Urbanke, Modern Coding Theory
[2]
S. Lin and W. Ryan, Channel Codes: Classical and Modern
[3]
D. J. C. Mackay, Information Theory, Inference &
Learning Algorithms
Papers
[1]
F. Kschischang, B. Frey and
H. Loeliger, ``Factor Graphs and the Sum Product
Algorithm``
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