Arya Mazumdar arya@cs.umass.edu

MoWe 14:30 - 15:45 CS 140

By appointment

The main prerequisites for this class are mathematical maturity, exposure to basic mathematical courses such as COMPSCI 240 and COMPSCI 250 and a solid grounding in linear algebra and probability theory. Students without such background can seek permission of the instructor.

Coding Theory has been playing an important role in Theoretical Computer Science in topics such as probabilistically checkable proofs, list decoding and local testability. It has also applications in other areas of computer science such networking and security. This course will be useful to students interested in any of these areas and will expose them to a wide range of mathematical tools and techniques. The specific topics covered will include:

Introduction to Coding Theory, Linear Codes

Algebraic Codes, Cyclic codes

Reed-Solomon Codes and List Decoding

Reed-Muller Codes

Random Coding and Asymptotical Goodness

Bounds on Codes

LDPC and Expander Codes

Polar Codes, Threshold phenomenon in random graphs, Capacity

Applications in Inference: Sparse-Graph Codes, Iterative Message-passing Decoding, Neural Networks, Compressed Sensing, group Testing

Applications in Networks and Security: Network Coding, Index coding, Graph theory, Lovasz theta, Spectral methods, Secret Sharing Schemes

The Following mathematical tools will be discussed wherever relevant:

Groups and fields

Elements of combinatorics and graph theory, Regular graphs, graph spectra, expansion, Turan’s theorems, hypergraphs

Concentration inequalities (Chernoff bounds, Bernstein and Hoeffding, martingales)

Association schemes and orthogonal polynomials

No required textbook. The following references are useful. Several papers and hand-outs will be distributed.

Ron M. Roth, Introduction to Coding Theory, Cambridge University Press, 2016.

F. MacWilliams and N. Sloane, The Theory of Error-Correcting Codes, North-Holland.

There will be 4 home assignments. Assignments are to be solved in a group of two. 1 midterm (individual effort) and 1 final exam (take home, individual effort).

Assignment 1 (Group effort) Feb 6: 10%

Assignment 2 (Group effort) Feb 27: 10%

Assignment 3 (Group effort) Apr 10: 10%

Midterm (In-class, Individual) Mar 20: 20%

Final (Take home, Individual) May 1: 20%

Project Report ((Group effort): 20%

Scribing (Group effort): 10%

Scribing and other efforts will be graded immediately upon receiving and will be available in Moodle.

A group of two students will submit a single homework that will reflect the collaborative effort of that group of students. Assignments must be submitted at the beginning of the class on the deadline or by email or in Moodle. Late submission by a day (e-submission only) will incur a 20% penalty. Submissions will not be accepted if there is any more delay without substantial reason (such as a doctor's note).

A group of two students will scribe the notes for one (or two) lectures in TeX. Template for lecture notes will be provided. Scribed notes must be submitted by email to the instructor within 3 days of the lecture. Late submission by a day will incur a 20% penalty. Any more delay without a Doctor's note will incur full penalty.

March 20, Monday, In-Class, Open Book, Open Notes

May 1, Take Home, Return at instructor's office by 15:00, May 3 (or by email)

Due 23:59 May 7 by email.

Lectures and assignments are immediately available on moodle and in this page with some delay.

The University of Massachusetts Amherst is committed to providing an equal educational opportunity for all students. If you have a documented physical, psychological, or learning disability on file with Disability Services (DS), you may be eligible for reasonable academic accommodations to help you succeed in this course. If you have a documented disability that requires an accommodation, please notify me within the first two weeks of the semester so that we may make appropriate arrangements.