Error Correcting Codes: Combinatorics, Algorithms and Applications

Error Correcting Codes: Combinatorics, Algorithms and Applications

CSE 545

January 12, 2009

Lets do some introductionsAtri Rudra123 Bell [email protected] x 117 Office hours: TBA

Handouts for todaySyllabus

Feedback formAlso fill in the sheet being passed around with your name/email

Plug for feedback formsCompleting the form is voluntary

Purpose of the formFix office hoursFor 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)Used for announcementsYOU are responsible for checking the blog for updates

Why use a blog?Easy accessEasier to link to URLs and displaying math

What will appear on the blog?Change in office hoursAn entry for each lecture/homeworkComments section to ask questions or post commentsA list of suggested papers for presentationA post on some interesting side story/comment

Other stuff on the blog

Questions/Comments?If something is broken on the blog (e.g. you cannot post a comment), let me know

Makeup classesSome classes will be canceledI will be traveling1 class for nowNeed one 60 mins makeup lectureIndicate your preferences in the feedback form

February 13 class is cancelled

ReferencesNo text bookMain source: Notes from Fall 07 courseLinks on the course blog/webpageStandard coding theory textsMacWilliams and Sloanevan LintBlahutHandbook of coding theory

Pre-requisitesNo formal pre-requisitesProbably no one will have all the pre-reqsMathematical maturityComfortable with proofsWilling to pick up basics of new areasWill spend one lecture on the pre-reqsLinear AlgebraFinite FieldsProbabilityAlgorithms/ Asymptotic Analysis

Grades and such likeUpdating Wikipedia/ Scribing notes30-40%

Homework(s)40-25%

Paper Presentations30-35%

Updating WikipediaYou need a choose a coding theory topicEither the entry is not present or the entry is bare-bones

More detailsYou get to play on an in-house WikiWiki should be up in a couple of weeksYou will need some LaTeX knowledgeDeadlinesMarch 23: Let me know your choiceMarch 30: Submit one page report on what you intend to doApril 20: Submit your final version in the in-house wiki

Scribing notesSome lecture notes will be scribed by a student (maybe give some extra details)At most once during the courseDepends on the class strengthUse LaTeXStyle file on the webpageThey are due in a weekNotes will be graded on timeliness & quality

Questions/Comments?Check out the syllabus for more details

Homework1-2 depending on other course loadCollaboration generally allowedWork in groups of size at most 3Write up your own solutionsAcknowledge your collaboratorsBreaking these rules will be considered as cheatingMore details when they are handed out

My homework philosophy for 545NOT to make sure you understand what I teach in the lecturesAssumption: Youre motivated enoughHomework problems eitherProofs that were not done in the class; orMaterial that is not covered in the classClosely related to something that is

Paper presentationPick a paper to presentList will be on the blog by the end of 2nd weekYou can choose your own paperNeed my approvalDates for presentationApril 28 and April 29 (Reading days)DeadlinesApril 13 or April 24 if you choose your own paper or notFCFS on the suggested list

Questions/Comments?Check out the syllabus for more details

Some commentsDecide on a Wikipedia/paper topic earlyDifferent topics might need different prep. workCome talk to meHomeworks might take timeDo not wait for the last moment

Some of my teaching quirksNeighbor talk time

Periodic feedback forms

Rudra is the angry form of ShivaSanjay Patel, The Little Book of Hindu Deities, Plume, 2006

Academic DishonestyAll your submissions must be your own workPenalty:Minimum: zero credit on the particular assignmentHighly likely: An F gradePossible: F due to academic dishonesty on your transcriptYOUR responsibility to know what is cheating, plagarism etc.If not sure, come talk to meExcuses like I have a job, This was OK earlier/in my country, etc. WONT WORK

If grades are all you care aboutPlease drop the courseYoull be fine ifYou do your assignments with honestyMake a reasonable attempt at them

Questions/Comments?Check out the syllabus for more details

Let the fun begin!

Coding theoryhttp://catalyst.washington.edu/

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!

Why did the example work?English has in built redundancyCan tolerate errors

The setupC(x)xy = C(x)+errorxGive upMapping CError-correcting code or just codeEncoding: x C(x)Decoding: y xC(x) is a codeword

CommunicationInternetChecksum used in multiple layers of TCP/IP stackCell phonesSatellite broadcastTVDeep space telecommunicationsMars Rover

Unusual applicationsData StorageCDs and DVDsRAIDECC memory

Paper bar codesUPS (MaxiCode)

Codes are all around us

Other applications of codesOutside communication/storage domainTons of applications in theoryComplexity TheoryCryptographyAlgorithms

The birth of coding theoryClaude E. ShannonA Mathematical Theory of Communication1948Gave birth to Information theory

Richard W. HammingError Detecting and Error Correcting Codes1950

Structure of the coursePart I: CombinatoricsWhat can and cannot be done with codes

Part II: AlgorithmsHow to use codes efficiently

Part III: ApplicationsApplications in theoretical Computer Science

The fundamental tradeoffCorrect as many errors as possible while using as little redundancy as possibleIntuitively, contradictory goals

Put codeword in color. And say form now on will talk about codeword.