# Nigel Boston

## Contact Information

3619 Engineering Hall, 303 Van Vleck

Telephone: 265-3817, 263-4753.

E-mail: boston@math.wisc.edu

Office Hours: 303VV Tues 2-3:30; 3619 EH Weds 2-3:30; or by appointment.

Barg's Notes

## Other Useful References

My favorite text is Blahut's ``Algebraic Codes for Data Transmission". Another reference book is ``Fundamentals of Error Correcting Codes" by Huffman and Pless. The classical reference was ``The Theory of Error-Correcting Codes" by MacWilliams and Sloane. A comprehensive reference is ``Handbook of Coding Theory" by Pless and Huffman. More recent developments are beautifully covered in ``Modern Coding Theory" by Richardson and Urbanke.

## Course Overview

Coding theory is the efficient use of redundancy to ensure the correction of errors in data transmission. It is a marvelous application of clever uses of algebra and combinatorics to problems of practical importance (satellite imagery, scratched CD's). We will follow Barg's excellent course notes - see http://www.ece.umd.edu/~abarg/626 - covering topics such as linear codes, Reed-Solomon codes, list decoding, cyclic codes, ensembles of random codes, iterative decoding, belief propagation, and LDPC codes, culminating in describing capacity - achieving codes for the binary erasure channel, which answers a basic question posed by Shannon 60 years ago.

## Sections

• Main Lecture: TR 11:00-12:15, B105 Van Vleck.

Homeworks will count for 35% of the final grade, the midterm for 25%, and the final exam for 40%. If you score 90% or higher, you will get an A; if you score 80% or higher, you will at least get a B; if you score 70% or higher, you will at least get a C; if you score 60% or higher, you will at least get a D.

## Homework Assignments

Homework will be set most Thursdays and due the following Thursday. You are encouraged to discuss the exercises with your classmates but the work you hand in should be your own. You will be expected to read the sections of the notes to be covered in advance of class.
• Homework, due Thursday, Feb 7: exercises from first 4 lectures.
• Homework, due Thursday, Feb 21: exercises from lectures 5 and 6.
• Homework, due Thursday, Feb 28: exercises from lectures 7, 10, and 11, plus qns 1 and 3 from problems.
• Homework, due Thursday, March 6: qns 13, 14, 16, 17 from the problem sheet above.
• Homework, due Tuesday, March 25: qns 23, 24, 25, 30 from the problem sheet above.
• Homework, due Thursday, April 10: qns 34, 37, 40 from the problem sheet.
• Homework, due Thursday, April 17: qns 26,48 from the problem sheet.
• Homework, due Thursday, May 1: qns 51, 56 from the problem sheet.

## Exams

• Midterm- 11:00am, Thursday, Mar 27.
• Final- 2:45pm, Tuesday, May 13.