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Intro to Error Correcting Codes

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• Prelude: Coding Theory
  • Coding Theory:

    Coding Theory = a discipline of Mathematics that study the properties of codes and their fitness for specific applications.

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  • Use of codes:

    Data compression Data encryption Error correction

    Wikipedia: click here

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• Error correction codes
  • Key to error correction:

    Redundancy....

    Example: a naive error correction code

    For every bit that you send, repeat it 3 times Example: Message: 1011 Transmitted as: 111000111111 The receiver use "majority voting" on groups of 3 bits to decode the message

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  • More sophisticated error correction codes:

    Hamming code: Can correct single bit errors Reed-Solomon code: Can correct 2 bits errors

    I will only show you how to use Hamming code

    No proofs.... (beyond the scope of this course !)