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 111111001 00100101
11110101 00111000
01101101 11010101
10111001 10001111
10100110 01101010
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11100001 11110110 110001001 11100101 0
10101001 10011000 1
01111010 01011000 0
11110110 10010000 0
01011101 01000011 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00111101 11000111 101011100 11111010 1
01111110 01001100 1
01010001 00000010 0
10011010 11111000 1
10010100 00001011 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:
11111001 00100101 1
11110101 00111000 1
01101101 11010101 0
10111001 10001111 0
10100110 01101010 0
01111110 00101101 0
1. The parity bits for the 16 columns is: 01111110 00101101
2. The parity bits for the 5 rows is: 11000
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (3,0):
11100001 11110110 1
10001001 11100101 0
10101001 10011000 1
01111010 01011000 0
11110110 10010000 0
01011101 01000011 0
For figure 3, the bits that were flipped are (8,0) and (1,1):
00111101 11000111 1
01011100 11111010 1
01111110 01001100 1
01010001 00000010 0
10011010 11111000 1
10010100 00001011 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: 0111111000101101
The answer was: 11000
The answer was: 0
The answer was: 3,0
The answer was: No