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faculty.chemeketa/ascholer/cs160/Files/ecGrid.html

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?. A message. 4 bit message:.

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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. A message • 4 bit message:

  7. A message • 4 bit message: • An errror:

  8. Trick 1 : Repetition • To avoid misunderstanding, repeat yourself…

  9. Trick 1 : Repetition • An error:

  10. Trick 1 : Repetition • Most common message wins:

  11. Trick 1 : Repetition • What if every message is wrong:

  12. Trick 1 : Repetition • Most common bit wins: Corrected

  13. Trick 1 : Repetition • More errors: "Corrected"

  14. Trick 1 : Repetition • Best 3 out of 5? Corrected

  15. Overhead • Message size : 4 bits • Including repetition : 12 bits

  16. Overhead • Message size : 4 bits • Including repetition : 12 bits 200% overhead 10Mb download is now 30Mb!

  17. Trick 2 : Redundancy • Redundancy : more information than strictly required • Common linguistic trick: He took his seat She took her seat They took their seats

  18. Trick 2 : Redundancy • Redundancy : more information than strictly required • Common linguistic trick: He took his seat She took her seat They took theirseats

  19. Trick 2 : Redundancy • Repetion is redundancy • Can we be redundant more efficently?

  20. Hamming Distance • Hamming Distance : number of different bits

  21. Normal Binary • 4 bits : 16 possible values:

  22. Normal Binary • Using all patterns – any error looks like a different message • 1 bit errors for 1010

  23. Normal Binary • Only use half the patterns • All "good" patterns have a distance of 2 from each other

  24. Normal Binary • "Good" patterns have distance of 2:1 bit error is obviously an error • 1 bit errors for 1010

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

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

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

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

  29. 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

  30. Our Message • We get: 0110110 • Find the code with distance of 1

  31. Errors • Assuming 1 error bit, we can identify correct message:

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

  33. Trick 3 : Checksums • Parity • Odd or even number of 1's • 1 extra bit used to make odd num of 1's datacheckbit 1001100100 00001 11100

  34. Trick 3 : Checksums • Message: 00001 • All 1 bit errors: 10001 01001001010001100000

  35. Trick 3 : Checksums • Checksum for decimal number: • Add digits, mod by 10: Message: 46756 • 4 + 6 + 7 + 5 + 6 = 28 • 28 mod (clock size) 10 = 8 Coded message: 467568

  36. Trick 3 : Checksums Coded message: 467568 Error message: 461568 Check: 461568 • 4 + 6 + 1 + 5 + 6 = 22 • 22 mod (clock size) 10 = 2!!! we have a problem

  37. Two Errors Coded message: 467568 Error message: 421568 Check: 421568 • 4 + 2 + 1 + 5 + 6 = 18 • 18 mod (clock size) 10 = 8!!! we missed it

  38. Staircse Code • Multiply each digit by its place: 12345Message: 46756 • 4 x 1+ 6 x 2+ 7 x 3+ 5 x 4+ 6 x 5= 87 • 87 mod (clock size) 10 = 7 Coded message: 467567

  39. Two Errors w Stair Case Coded message: 467567 Error message: 421567 12345Check: 421567 • 4 x 1 + 2 x 2 + 1 x 3 + 5 x 4 + 6 x 5 = 61 • 61 mod (clock size) 10 = 1!!! we caught it

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

  41. Trick 4: Pinpoint • How did I do it?

  42. Trick 4: Pinpoint • How did I do it? Every Row & Col should have odd # of black squares

  43. Trick 4: Pinpoint • How did I do it? Every Row & Col should have odd # of black squares

  44. Trick 4: Pinpoint • Message / Checksum

  45. Trick 4 : Pinpoint • With decimal values:

  46. Trick 4 : Pinpoint • With decimal values:

  47. Trick 4 : Pinpoint • With decimal values: 4 9

  48. Trick 4 : Pinpoint • With decimal values: 4 off by 2 9 off by 2

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

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

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