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Error Correcting Codes: Combinatorics, Algorithms and Applications

Error Correcting Codes: Combinatorics, Algorithms and Applications. CSE 545 January 14, 2013. Let ’ s do some introductions. Atri Rudra 319 Davis Hall atri@buffalo.edu 645-2464 Office hours: By Appointment. Handouts for today. Syllabus Linked from the blog Feedback form

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Error Correcting Codes: Combinatorics, Algorithms and Applications

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  1. Error Correcting Codes: Combinatorics, Algorithms and Applications CSE 545 January 14, 2013

  2. Let’s do some introductions • Atri Rudra • 319 Davis Hall • atri@buffalo.edu • 645-2464 • Office hours: By Appointment

  3. Handouts for today • Syllabus • Linked from the blog • Feedback form • Link on the blog

  4. Plug for feedback forms • Completing the form is voluntary & anonymous • Purpose of the form • For me to get an idea of your technical background • You can complete it later

  5. Course blog (codingtheory.wordpress.com) • Used for announcements • YOU are responsible for checking the blog for updates

  6. One Stop Shop for the course • Easy access • Easier to link to URLs and displaying math

  7. What will appear on the blog? • An entry for each lecture/homework • Comments section to ask questions or post comments • A post on some interesting side story/comment

  8. Other stuff on the blog

  9. Piazza for discussion Please use your UB email ID to sign up

  10. Questions/Comments? • If something doesn’t work (e.g. you cannot post a comment), let me know

  11. References • Draft of a book I’m writing • With Guruswami+Sudan • Standard coding theory texts • MacWilliams and Sloane • van Lint • Blahut • Handbook of coding theory

  12. Pre-requisites • No formal pre-requisites • Probably no one will have all the pre-req’s • Mathematical maturity • Comfortable with proofs • Willing to pick up basics of new areas • Will spend one lecture on the pre-req’s • Linear Algebra • Finite Fields • Probability • Algorithms/ Asymptotic Analysis Go slower in the first half of the course

  13. Grades and such like • Proof-reading • 20% • Homeworks • 45-35% • Updating Wikipedia • 35-45%

  14. Updating Wikipedia • You need a choose a coding theory topic • Either the entry is not present or the entry is “bare-bones”

  15. More details • Deadlines • March 20: Let me know your choice • March 27: Submit one page “report” on what you intend to do • More deadlines/details in the syllabus • To be done in group • Group size to be determined next week

  16. In-house wiki • You get to play on an in-house Wiki • You will need some LaTeX knowledge

  17. Proof-reading • Proof-read relevant part of the book • 3-4 during the course • 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

  18. Questions/Comments? • Check out the syllabus for more details

  19. Homework • 3 short ones • Collaboration generally allowed • 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

  20. My homework philosophy for 545 • NOT to make sure you understand what I teach in the lectures • Homework problems either • Proofs that were not done in the class; or • Material that is not covered in the class • Closely related to something that is

  21. Questions/Comments? • Check out the syllabus for more details

  22. Some comments • Decide on a Wikipedia topic early • Different topics might need different prep. work • Come talk to me • Homeworks might take time • Do not wait for the last moment

  23. Academic Dishonesty • All your submissions must be your own work • Penalty: • Minimum: zero credit on the particular assignment • Highly likely: An F grade • Possible: F“due to academic dishonesty” on your transcript • YOUR responsibility to know what is cheating, plagarism etc. • If not sure, come talk to me • Excuses like “I have a job,”“This was OK earlier/in my country,” etc. WON’T WORK

  24. If grades are all you care about • You’ll be fine if • You do your assignments honestly • Make a reasonable attempt at them

  25. Questions/Comments? • Check out the syllabus for more details

  26. Let the fun begin!

  27. Coding theory http://catalyst.washington.edu/

  28. What does this say? • 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! • Welcome to the class. I hope you will have as much fun as I will have teaching it!

  29. Why did the example work? • English has in built redundancy • Can tolerate “errors”

  30. The setup C(x) x y = C(x)+error • Mapping C • Error-correcting code or just code • Encoding: xC(x) • Decoding: yx • C(x) is a codeword x Give up

  31. Communication • Internet • Checksum used in multiple layers of TCP/IP stack • Cell phones • Satellite broadcast • TV • Deep space telecommunications • Mars Rover

  32. “Unusual” applications • Data Storage • CDs and DVDs • RAID • ECC memory • Paper bar codes • UPS (MaxiCode) Codes are all around us

  33. Other applications of codes • Outside communication/storage domain • Tons of applications in theory • Complexity Theory • Cryptography • Algorithms Coding theory is a good tool to have in your arsenal

  34. The birth of coding theory • Claude E. Shannon • “A Mathematical Theory of Communication” • 1948 • Gave birth to Information theory • Richard W. Hamming • “Error Detecting and Error Correcting Codes” • 1950

  35. Structure of the course • Part I: Combinatorics • What can and cannot be done with codes • Part II: Algorithms • How to use codes efficiently • Part III: Applications • Applications in (theoretical) Computer Science

  36. 1 1 1 0 0 1 0 0 0 0 1 1 Redundancy vs. Error-correction • Repetition code: Repeat every bit say 100 times • Good error correcting properties • Too much redundancy • Parity code: Add a parity bit • Minimum amount of redundancy • Bad error correcting properties • Two errors go completely undetected • Neither of these codes are satisfactory

  37. Two main challenges in coding theory • Problem with parity example • Messages mapped to codewords which do not differ in many places • Need to pick a lot of codewords that differ a lot from each other • Efficient decoding • Naive algorithm: check received word with all codewords

  38. The fundamental tradeoff • Correct as many errors as possible with as little redundancy as possible Can one achieve the “optimal” tradeoff with efficient encoding and decoding ?

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