Error Correcting Codes: Combinatorics, Algorithms and Applications CSE 545 January 11, 2010
Let’s do some introductions n Atri Rudra q q 123 Bell Hall atri@buffalo. edu 645 -2464 Office hours: By Appointment
Handouts for today n Syllabus n Feedback form q Also fill in the sheet being passed around with your name/email
Plug for feedback forms n Completing the form is voluntary & anonymous n Purpose of the form q q n Fix number of homeworks For me to get an idea of your technical background Last 5 minutes of the lecture to complete it
Course webpage http: //www. cse. buffalo. edu/~atri/courses/coding-theory/
Course blog (codingtheory. wordpress. com) n n Used for announcements YOU are responsible for checking the blog for updates
Why use a blog? n n Easy access Easier to link to URLs and displaying math
What will appear on the blog? n An entry for each lecture/homework q n Comments section to ask questions or post comments A post on some interesting side story/comment
Other stuff on the blog
Questions/Comments? n If something is broken on the blog (e. g. you cannot post a comment), let me know
Makeup classes n Some classes will be canceled q q n Need one 50 mins makeup lecture q n I will be traveling 1 class for now Indicate your preferences in the feedback form January 15 class is cancelled
References n n No text book Main source: Notes from Fall 07 course q n Links on the course blog/webpage Standard coding theory texts q q Mac. Williams and Sloane van Lint Blahut Handbook of coding theory
Pre-requisites n No formal pre-requisites q n Mathematical maturity q q n Probably no one will have all the pre-req’s Comfortable with proofs Willing to pick up basics of new areas Will spend one lecture on the pre-req’s q q Linear Algebra Finite Fields Probability Algorithms/ Asymptotic Analysis Go slower in the first half of the course
Grades and such like n Scribing/Proof-reading notes q n Homework(s) q n 30 -40% 40 -25% Updating Wikipedia q 30 -35%
Updating Wikipedia n You need a choose a coding theory topic q Either the entry is not present or the entry is “barebones”
More details n Deadlines q q March 22: Let me know your choice March 29: Submit one page “report” on what you intend to do April 19: Submit your final version in the in-house wiki More details in the syllabus
In-house wiki n You get to play on an in-house Wiki q You will need some La. Te. X knowledge
Scribing notes n n n Some lecture notes will be scribed by a student (maybe give some extra details) At most once during the course Use La. Te. X q n n n Style file on the webpage They are due in a week Notes will be graded on timeliness & quality See syllabus for more details
Proof-reading notes n n Proof-read existing notes 6 -7 during the course q n n n Depends on the class strength Email me typos, suggestions for improvement They are due in by noon before next lecture Notes will be graded on timeliness & quality Will ask for a volunteer See syllabus for more details
Questions/Comments? n Check out the syllabus for more details
Homework n n 1 or 3 depending on your choice Collaboration generally allowed q q q n Work in groups of size at most 3 Write up your own solutions Acknowledge your collaborators No source other than lecture notes Breaking these rules will be considered as cheating More details when they are handed out
My homework philosophy for 545 n n NOT to make sure you understand what I teach in the lectures Homework problems either q q Proofs that were not done in the class; or Material that is not covered in the class n Closely related to something that is
Questions/Comments? n Check out the syllabus for more details
Some comments n Decide on a Wikipedia topic early q q n Different topics might need different prep. work Come talk to me Homeworks might take time q Do not wait for the last moment
Some of my teaching “quirks” n Neighbor talk time n Periodic feedback forms
Academic Dishonesty n n All your submissions must be your own work Penalty: q q q n YOUR responsibility to know what is cheating, plagarism etc. q n Minimum: zero credit on the particular assignment Highly likely: An F grade Possible: F “due to academic dishonesty” on your transcript If not sure, come talk to me Excuses like “I have a job, ” “This was OK earlier/in my country, ” etc. WON’T WORK
If grades are all you care about n You’ll be fine if q q You do your assignments with honesty Make a reasonable attempt at them
Questions/Comments? n Check out the syllabus for more details
Let the fun begin!
Coding theory http: //catalyst. washington. edu/
What does this say? n W*lcome to the cl*ss. I h*pe you w*ll h*ve as mu*h f*n as I wi*l hav* t*ach*ng it! n Welcome to the class. I hope you will have as much fun as I will have teaching it!
Why did the example work? n n English has in built redundancy Can tolerate “errors”
The setup C(x) x y = C(x)+error n Mapping C q q Error-correcting code or just code Encoding: x C(x) Decoding: y x x C(x) is a codeword Give up
Communication n Internet q n n Cell phones Satellite broadcast q n Checksum used in multiple layers of TCP/IP stack TV Deep space telecommunications q Mars Rover
“Unusual” applications n Data Storage q q q n CDs and DVDs RAID ECC memory Paper bar codes q UPS (Maxi. Code) Codes are all around us
Other applications of codes n n Outside communication/storage domain Tons of applications in theory q q q Complexity Theory Cryptography Algorithms
The birth of coding theory n Claude E. Shannon q q q n “A Mathematical Theory of Communication” 1948 Gave birth to Information theory Richard W. Hamming q q “Error Detecting and Error Correcting Codes” 1950
Structure of the course n Part I: Combinatorics q n Part II: Algorithms q n What can and cannot be done with codes How to use codes efficiently Part III: Applications q Applications in (theoretical) Computer Science
The fundamental tradeoff n Correct as many errors as possible while using as little redundancy as possible q Intuitively, contradictory goals
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