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 110110100 11100010
01010011 11101011
00110110 11100011
10010111 10100001
01010110 00110001
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11111100 01110001 011010111 00101010 1
10101001 10011001 0
01111100 10001011 1
01110000 00101000 0
10101110 01100001 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10111100 11111101 100001010 10001000 0
11001001 11111000 1
10110001 10101010 1
10001100 11100011 0
01000011 10000100 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:
10110100 11100010 0
01010011 11101011 0
00110110 11100011 1
10010111 10100001 0
01010110 00110001 1
00010000 01111010 0
1. The parity bits for the 16 columns is: 00010000 01111010
2. The parity bits for the 5 rows is: 00101
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (2,4):
11111100 01110001 0
11010111 00101010 1
10101001 10011001 0
01111100 10001011 1
01110000 00101000 0
10101110 01100001 0
For figure 3, the bits that were flipped are (7,0) and (9,3):
10111100 11111101 1
00001010 10001000 0
11001001 11111000 1
10110001 10101010 1
10001100 11100011 0
01000011 10000100 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: 0001000001111010
The answer was: 00101
The answer was: 0
The answer was: 2,4
The answer was: No