CMSC 653: Coding Theory & Applications
Instructor: S.J. Lomonaco, Jr.
Spring 1998
Course Description:
The course will consists of two parts, the first
part on algebraic coding theory, the second part on quantum error-correcting
codes.
Part I.
Introduction to BSC, BEC, and information theory. Linear Codes, standard
array, maximum likelihood decoding, distance bounds, generator & parity
check matrices, error-syndrome table. A brief overview of rings and ideals.
Cyclic codes, generator & parity check polynomials, linear sequential
circuits (LSCs), implementation of cyclic codes in terms of LSCs.
Finite fields, applications of finite fields to cyclic codes. BCH
codes, the BCH decoding algorithm. A brief overview of convolutional codes.
Part II.
A quick overview of quantum
mechanics, quantum
information theory, and quantum
cryptography. Various quantum error-correcting codes. Shor's and Grover's
algorithms.
Text:
There is no specific text. Students will
be given reading assignments from various references.
Supplementary Reading Material
from:
-
Berlekamp, Elwyn R., "Algebraic Coding Theory,"
McGraw-Hill, New York (1968)
-
Braunstein, Samuel L.,
Quantum Computation Tutorial
to be found at: http://chemphys.weizmann.ac.il/~schmuel/comp/comp.html
-
Gill, Arthur, "Linear Sequential Circuits,"
McGraw-Hill, New York (1966).
-
Hill, Raymond, "A First Course in Coding Theory,"
Oxford University Press, New York (1993).
-
Lomonaco, Samuel J., Jr.,
Lecture Notes
to be found at http://www.cs.umbc.edu/~lomonaco/lecturenotes/index.html
-
MacWilliams, F.J., and N.J.A. Sloane, "The Theory
of Error-Correcting Codes," North-Holland Publishing Company, New York
(1977)
-
Peterson, W. Wesley, and E.J. Weldon, Jr., "Error-Correcting
Codes," MIT Press, Cambridge (1986).
-
Pless, Vera, "Introduction to the Theory of Error-Correcting
Codes," John Wiley (1982)
-
Preskill, John,
Lecture Notes
to be found at: http://www.theory.caltech.edu/people/preskill/ph229/#lecture
-
Roman, Steven, "Coding and Information Theory,"
Springer-Verlag, New York (1992).
-
Williams, Colin P., and Scott H. Clearwater,
"Explorations in Quantum Computing," Springer-Verlag, New York (1997).
-
Los Alamos Archive on
Quantum Physics
to be found at: http://xxx.lanl.gov/archive/quant-ph
-
Stanford Quantum Computation
Archive
to be found at: http://feynman.stanford.edu/qcomp/
-
Journal papers on shift registers and linear sequential
circuits
-
Journal papers on quantum error-correcting codes
-
Other references to be supplied later
Grading:
The Course grade will be computed as follows:
25% Exam I
25% Exam II
25% Homework Avg
25% Final Exam
Prerequisites:
CMSC
203, MATH 221, Reasonable Mathematical & Algorithmic Maturity, and
an Intense Desire to Learn
Last Modified: January 27, 1998