1 / 19

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.

cbutler
Download Presentation

Understanding Error Detection and Correction Through Hamming Codes

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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!

More Related