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http://faculty.chemeketa.edu/ascholer/cs160/Files/ecGrid.html. Error Detection and Correction. Fixing 0101X011. Computer Errors. RAM isn't perfect. Computer Errors. Networks aren't either. Computer Errors. How the heck do you read 1s and 0's off this?. Pinpoint. How did I do it?.
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http://faculty.chemeketa.edu/ascholer/cs160/Files/ecGrid.htmlhttp://faculty.chemeketa.edu/ascholer/cs160/Files/ecGrid.html
Error Detection and Correction Fixing 0101X011
Computer Errors • RAM isn't perfect
Computer Errors • Networks aren't either
Computer Errors • How the heck do you read 1s and 0's off this?
Pinpoint • How did I do it?
Pinpoint • Message / Check BitEvery Row & Col should have odd # of black squares
Pinpoint • How did I do it? Every Row & Col should have odd # of black squares
Real Life Checksum • Last digit of credit card number calculated to http://tywkiwdbi.blogspot.com/2012/06/checksum-number-on-credit-card.html
Real Life Stair Case • ISBN – books: http://www-math.ucdenver.edu/~wcherowi/jcorner/isbn.html
Hamming Code • Use extra bits to "space out" messages • 4 bit message with 3 error correction bits:
Hamming Code • 7 bits could be 27 = 128 codes • Only use 16 of them
Hamming Code • Every good message has distance of 3+ from other good messages:
Our Message • We get: 0110110 • Which message was it meant to be?
Errors • Assuming • Started with valid code word • Only one error • Then • 1 bit from one valid word • 2+ bits from another valid code word Valid Code A Valid Code B Valid Code C Error
Our Message • We get: 0110110 • Find the closest match: • The message was supposed to be 0110010
Hamming Code • Hamming Codes as pinpoint parity checks: http://www.systems.caltech.edu/EE/Faculty/rjm/SAMPLE_20040708.html
Hamming Code Overhead • Message size : 4 bits • Code word: 7 bits 75% overhead… 512bit message can be encoded with 522bits: 2% overhead!