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Principle of error detection and correction

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• Illustrative question
  • Example of transmitted data:

    11111111

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  • Example of received data:

    11110111

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    Question:

    How can we tell whether some bit(s) is/are incorrect (without know what the transmitted data was) ???

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• Principle of error detection/correction methods

  • Principe to detect/correct of errors:

    Embed extra bits into the transmitted message The insert extra bit creates a certain pattern in the bits stream (usually conforming to some (mathematical) property) The receiver checks for the embedded pattern in the received data: Pattern was found   ⇒   message assumed to be correct Pattern was not found   ⇒   message assumed to be in error

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• Mathematics: coding theory
  • FYI:

    The mathematical theory that deal with design patterns in the transmission is called coding theory.

    I will only discuss some commonly used codes

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• Commonly used error detection/correction schemes
  • Commonly used schemes:

    Error detection schemes: Parity checks Cyclic Redundancy Check   (CRC)            Error Correction Schemes: Hamming's code (can correct 1 bit error) Solomon-Reed's code (can correct 2 bit errors)