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Understanding Error Detection and Correction Through Hamming Codes

Explore how Hamming codes help detect and correct computer errors, with practical examples and real-life applications. Learn about using extra bits for error correction and the concept of message parity checks.

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Understanding Error Detection and Correction Through Hamming Codes

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  1. http://faculty.chemeketa.edu/ascholer/cs160/Files/ecGrid.htmlhttp://faculty.chemeketa.edu/ascholer/cs160/Files/ecGrid.html

  2. Error Detection and Correction Fixing 0101X011

  3. Computer Errors • RAM isn't perfect

  4. Computer Errors • Networks aren't either

  5. Computer Errors • How the heck do you read 1s and 0's off this?

  6. Pinpoint • How did I do it?

  7. Pinpoint • Message / Check BitEvery Row & Col should have odd # of black squares

  8. Pinpoint • How did I do it? Every Row & Col should have odd # of black squares

  9. Real Life Checksum • Last digit of credit card number calculated to http://tywkiwdbi.blogspot.com/2012/06/checksum-number-on-credit-card.html

  10. Real Life Stair Case • ISBN – books: http://www-math.ucdenver.edu/~wcherowi/jcorner/isbn.html

  11. Hamming Codes

  12. Hamming Code • Use extra bits to "space out" messages • 4 bit message with 3 error correction bits:

  13. Hamming Code • 7 bits could be 27 = 128 codes • Only use 16 of them

  14. Hamming Code • Every good message has distance of 3+ from other good messages:

  15. Our Message • We get: 0110110 • Which message was it meant to be?

  16. 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

  17. Our Message • We get: 0110110 • Find the closest match: • The message was supposed to be 0110010

  18. Hamming Code • Hamming Codes as pinpoint parity checks: http://www.systems.caltech.edu/EE/Faculty/rjm/SAMPLE_20040708.html

  19. Hamming Code Overhead • Message size : 4 bits • Code word: 7 bits 75% overhead… 512bit message can be encoded with 522bits: 2% overhead!

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