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 101101001 11111001
00000111 00110000
00101111 01110010
11111110 01100000
01100001 10110010
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10111100 11101011 110100111 01111000 1
00101001 11000100 0
11110111 11000011 0
00111001 11100111 0
11101100 01110011 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10011111 10001100 111101000 10001010 0
11000111 01100000 0
11000000 00000000 0
10101111 10001000 0
11001111 11100110 1
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:
01101001 11111001 0
00000111 00110000 1
00101111 01110010 1
11111110 01100000 1
01100001 10110010 1
11011110 01101001 0
1. The parity bits for the 16 columns is: 11011110 01101001
2. The parity bits for the 5 rows is: 01111
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (3,3):
10111100 11101011 1
10100111 01111000 1
00101001 11000100 0
11110111 11000011 0
00111001 11100111 0
11101100 01110011 0
For figure 3, the bits that were flipped are (3,1) and (12,2):
10011111 10001100 1
11101000 10001010 0
11000111 01100000 0
11000000 00000000 0
10101111 10001000 0
11001111 11100110 1
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: 1101111001101001
The answer was: 01111
The answer was: 0
The answer was: 3,3
The answer was: No