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Multi-dimensional parity-based error detection schemes

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• Two-dimensional parity
  • Two-dimensional Parity scheme

    2-dimensional parity scheme: Form a MxN matrix of bits Add a (even or odd) parity bit to each row and to each column

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  • Example:

    Original data (unprotected): 1111000 1010101 1111111 1. For a matrix of bits: 1111000 1010101 1111111 2. Add parity bits: 11110000 10101010 11111111 10100101

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  • Properties of the 2-dimensional parity scheme:

    The 2-dimensional parity scheme can correct all 1 bit errors Example: Transmitted data: 11110000 10101010 11111111 10100101 Received with one bit in error: 11110000 10101010 11011111 <---- odd parity 10100101 ^ | odd parity The receiver can tell which bit was in error from the parity check !!! Therefore: The receiver can take the initiative to correct the received message ! The 2-dimensional parity scheme can detect all 2 bit errors...        but it cannot correct the error. Example: Transmitted data: 11110000 10101010 11111111 10100101 Received with 2 bits in error: 11110000 10111010 <---- odd parity 11011111 <---- odd parity 10100101 ^^ || odd parity The errors can be detected. However, the receiver cannot correct the error: The cause of error is ambiguous: Original data: 11110000 10011010 11111111 10100101 Error pattern #1: 11110000 10001010 <---- odd parity 11011111 <---- odd parity 10100101 ^^ || odd parity Error pattern #2: 11110000 10111010 <---- odd parity 11101111 <---- odd parity 10100101 ^^ || odd parity Both cases will result in the same parity pattern !!! The receiver cannot tell which of these 2 error cases has occured.... So the receiver can not correct the error