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Error Correcting Codes

Error Correcting Codes. Christopher Motl 01.29.2008. Overview. Definitions Current Uses Future of Error-correcting codes. Can You Hear Me Now?. Error Detection. Ability to detect errors Parity bit, Checksum, Cyclic redundancy check, Hashing. Error Correction.

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Error Correcting Codes

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  1. Error Correcting Codes • Christopher Motl • 01.29.2008

  2. Overview • Definitions • Current Uses • Future of Error-correcting codes

  3. Can You Hear Me Now?

  4. Error Detection • Ability to detect errors • Parity bit, Checksum, Cyclic redundancy check, Hashing

  5. Error Correction • Ability to detect and correct errors • Automatic repeat request, Error-correcting code

  6. Coding Theory • “a branch of mathematics and computer science dealing with the error-prone process of transmitting data across noisy channels, via clever means, so that a large number of errors that occur can be corrected.” • Two areas of coding theory • Source coding (data compression) • Channel coding (forward error correction)

  7. Forward Error Correction • “a system of error control for data transmission, whereby the sender adds redundant data to its messages” • Reduces need to retransmit data

  8. Forward Error Correction • Block Coding • Primary type of channel coding used in earlier mobile communication systems. • Convolutional Coding • Often used to improve the performance of digital radio, mobile phones, satellite links, and Bluetooth implementations.

  9. Major Uses • Mariner • Voyager • Mars Pathfinder • Mars Exploration Rovers • Cassini Probe

  10. Mariner Example • 5 bits of data • 32 bits transmitted • Up to 7 errors can be corrected

  11. Common Uses • Parchive • High Speed Modems • Barcode - Post Office / UPS • CD / DVD / Hard Drive • Cell Phones • TCP/IP • ISBN

  12. Turbo Codes • Most recent development • Combines convolutional codes • Qualcomm EVDO • Deep space satellite communications

  13. Recap • What is an Error-correcting code? • What are they used for? • What is in store?

  14. Homework • What is the difference between error detection and error correction? • What area of mathematics and computer science deals with the transmission of data across noisy channels?

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