Error Correcting Codes Combinatorics Algorithms and Applications CSE

Error Correcting Codes: Combinatorics, Algorithms and Applications CSE 545 January 12, 2009

Let’s do some introductions n Atri Rudra q q 123 Bell Hall atri@cse. buffalo. edu 645 -3180 x 117 Office hours: TBA

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 n Purpose of the form q q n Fix office hours 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 n Change in office hours An entry for each lecture/homework q n n Comments section to ask questions or post comments A list of suggested papers for presentation 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 60 mins makeup lecture q n I will be traveling 1 class for now Indicate your preferences in the feedback form February 13 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

Grades and such like n Updating Wikipedia/ Scribing notes q n Homework(s) q n 30 -40% 40 -25% Paper Presentations 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 You get to play on an in-house Wiki q q n Wiki should be up in a couple of weeks You will need some La. Te. X knowledge Deadlines q q q March 23: Let me know your choice March 30: Submit one page “report” on what you intend to do April 20: Submit your final version in the in-house wiki

Scribing notes n n Some lecture notes will be scribed by a student (maybe give some extra details) At most once during the course q n Use La. Te. X q n n Depends on the class strength Style file on the webpage They are due in a week Notes will be graded on timeliness & quality

Questions/Comments? n Check out the syllabus for more details

Homework n n 1 -2 depending on other course load Collaboration generally allowed q q n Work in groups of size at most 3 Write up your own solutions Acknowledge your collaborators Breaking these rules will be considered as cheating More details when they are handed out

My homework philosophy for 545 n NOT to make sure you understand what I teach in the lectures q n Assumption: You’re motivated enough 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

Paper presentation n Pick a paper to present List will be on the blog by the end of 2 nd week You can choose your own paper q n Dates for presentation q n Need my approval April 28 and April 29 (Reading days) Deadlines q April 13 or April 24 n n if you choose your own paper or not FCFS on the suggested list

Questions/Comments? n Check out the syllabus for more details

Some comments n Decide on a Wikipedia/paper 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

Rudra is the angry form of Shiva Sanjay Patel, “The Little Book of Hindu Deities, ” Plume, 2006

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 n Please drop the course 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