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 111101101 01110001
10010000 10001101
11000101 11001100
01110101 01010101
00000000 10011110
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11001000 00111111 101100101 01011100 0
01000001 10011000 0
10111110 11110000 0
00000100 00101101 1
01010110 01100110 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01000111 01101111 000101100 11001110 1
01011100 11000100 0
11110010 11110001 0
00010100 10101000 1
11010001 00001100 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:
11101101 01110001 0
10010000 10001101 0
11000101 11001100 0
01110101 01010101 1
00000000 10011110 1
11001101 11111011 0
1. The parity bits for the 16 columns is: 11001101 11111011
2. The parity bits for the 5 rows is: 00011
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (9,2):
11001000 00111111 1
01100101 01011100 0
01000001 10011000 0
10111110 11110000 0
00000100 00101101 1
01010110 01100110 0
For figure 3, the bits that were flipped are (11,2) and (10,1):
01000111 01101111 0
00101100 11001110 1
01011100 11000100 0
11110010 11110001 0
00010100 10101000 1
11010001 00001100 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: 1100110111111011
The answer was: 00011
The answer was: 0
The answer was: 9,2
The answer was: No