Error Detection and Correction: Two Dimensional Parity
Suppose that a packet’s payload consists of 10 eight-bit values (e.g., representing ten ASCII-encoded characters) shown below. (Here, we have arranged the ten eight-bit values as five sixteen-bit values):
Figure 101111010 11010111
10100000 11111011
10111110 10011100
01111101 10001110
01000110 01101010
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11111010 01101101 101100111 11001010 1
01101110 00111000 1
01111011 10100000 0
01110101 11101011 1
11111111 11010100 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01001110 00111110 001101111 11000110 0
10100110 10110100 0
01001101 01100101 0
01101010 01010101 0
00100001 01111100 0
Question List
1. For figure 1, compute the two-dimensional parity bits for the 16 columns. Combine the bits into one string
2. For figure 1, compute the two-dimensional parity bits for the 5 rows (starting from the top). Combine the bits into one string
3. For figure 1, compute the parity bit for the parity bit row from question 1. Assume that the result should be even.
4. For figure 2, indicate the row and column with the flipped bit (format as: x,y), assuming the top-left bit is 0,0
5. For figure 3, is it possible to detect and correct the bit flips? Yes or No
Solution
The full solution for figure 1 is shown below:
01111010 11010111 1
10100000 11111011 1
10111110 10011100 0
01111101 10001110 0
01000110 01101010 1
01011111 01010100 1
1. The parity bits for the 16 columns is: 01011111 01010100
2. The parity bits for the 5 rows is: 11001
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (6,2):
11111010 01101101 1
01100111 11001010 1
01101110 00111000 1
01111011 10100000 0
01110101 11101011 1
11111111 11010100 0
For figure 3, the bits that were flipped are (0,0) and (7,5):
01001110 00111110 0
01101111 11000110 0
10100110 10110100 0
01001101 01100101 0
01101010 01010101 0
00100001 01111100 0
5. No, with 2D parity, you can detect the presence of two flipped bits, but you can't know their exact locations in order to correct them.
That's incorrect
That's correct
The answer was: 0101111101010100
The answer was: 11001
The answer was: 1
The answer was: 6,2
The answer was: No