CMSC 653: Coding Theory & Applications

Course Description:

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:

1. Berlekamp, Elwyn R., "Algebraic Coding Theory," McGraw-Hill, New York (1968)
2. Braunstein, Samuel L., Quantum Computation Tutorial to be found at: http://chemphys.weizmann.ac.il/~schmuel/comp/comp.html
3. Gill, Arthur, "Linear Sequential Circuits," McGraw-Hill, New York (1966).
4. Hill, Raymond, "A First Course in Coding Theory," Oxford University Press, New York (1993).
5. Lomonaco, Samuel J., Jr., Lecture Notes to be found at http://www.cs.umbc.edu/~lomonaco/lecturenotes/index.html

6. MacWilliams, F.J., and N.J.A. Sloane, "The Theory of Error-Correcting Codes," North-Holland Publishing Company, New York (1977)
7. Peterson, W. Wesley, and E.J. Weldon, Jr., "Error-Correcting Codes," MIT Press, Cambridge (1986).
8. Pless, Vera, "Introduction to the Theory of Error-Correcting Codes," John Wiley (1982)
9. Preskill, John, Lecture Notes to be found at: http://www.theory.caltech.edu/people/preskill/ph229/#lecture

10. Roman, Steven, "Coding and Information Theory," Springer-Verlag, New York (1992).
11. Williams, Colin P., and Scott H. Clearwater, "Explorations in Quantum Computing," Springer-Verlag, New York (1997).
12. Los Alamos Archive on Quantum Physics to be found at: http://xxx.lanl.gov/archive/quant-ph
13. Stanford Quantum Computation Archive to be found at: http://feynman.stanford.edu/qcomp/
14. Journal papers on shift registers and linear sequential circuits
15. Journal papers on quantum error-correcting codes
16. 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