CS485 Sylabus

### Multi-dimensional parity-based error detection schemes

• 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

• Example:

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

• 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