MTH 810-001: Error Correcting Codes
|Time and Place:||MWF 11:30 am -- 12:20 pm via Zoom|
|Physical Office:||C342 WH|
|Office Hours:||Just after each class (MWF 12:21 pm -- 1:11 pm), and by appointment|
Topics covered will include general Error Correcting Code (ECC) basics (rate, distance, etc.), Hamming Codes and Bounds, Linear Codes, Reed-Solomon Codes, BCH codes, Reed-Muller Codes, the Gilbert-Varshamov bound, and a few modern applications (time permitting).
Course website for MTH810-001:
The course website has the course schedule, the syllabus, and required reading. Any papers covered in class will also be posted there and/or on the course D2L page.
Essential Coding Theory, by Venkatesan Guruswami, Atri Rudra, and Madhu Sudan. Available here.
Exercises will be assigned in class most days. They will *not* be collected or checked other than as part of the final oral exam for the class (see below) if the student has not chosen to do a project.
Alternatively, students may elect to work on projects (approved in advance by the instructor) instead of completing the homework assignments. A written report on the project will then be required before the end of the semester which will be defended as part of the final oral exam. The written project report will count for all the homework assigned while the student was completing their optional and instructor approved research project.
Students are encouraged to work with their peers on homework assignments. Math is a collaborative discipline and two or three minds are often better than one. However, your final homework solutions must be written up individually in your own words and then kept to help you during the final oral exam. The solutions will be useless to you if you don't understand how they work!
Final Oral Exam:
Students must either meet with the instructor in person (if classes are in session, all parties wearing a mask, and staying socially distanced) or via zoom with the camera on. The instructor will then ask the student to solve several HW problems that were assigned in class, or else to discuss their project (if they chose to do one). The student's HW grade will be based on their participation in the exam, together with the quality of their solutions. The oral exam will be open notes -- it is expected that the student will consult their project report and/or personal homework solutions as part of the exam. In short, the purpose of this exam is to convince the instructor that the student completed ``most'' of the assigned homework (if they did not do a project), or else to describe their project, summarize their project's conclusions, as well as to answer instructor questions about their project.
The time and place (or zoom link) for the final oral exam will be scheduled with the instructor individually, or in small groups. All exams should take place sometime between April 23 and April 30, 2021, and should be scheduled before April Fools Day (April 1). Each oral exam will be 30 minutes in duration for each student. The instructor reserves the right to waive this oral exam requirement, or to shorten its duration, for any student as necessary for scheduling purposes.
Please ask questions, answer questions, make constructive comments, and generally "show your face" by attending class with your video on whenever possible. In particular, participation in class requires that you regularly attend class. If anyone has reasons why they can not turn their video on during class they should talk to the instructor about it during the first week of the semester so that we can arrange for alternative accommodations.
Your final grade will be assigned based on the completed homework (and/or project report), as well as on your participation (i.e., lecture attendance).
- Homework (and/or final project) grade from the Final Oral Exam -- 80%
- Class Participation -- 20%
Some of the homework exercises will be challenging -- it is only expected that your homework solutions demonstrate effort.