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 111111110 10110001
11110001 10101001
01000110 01000000
10001101 01100101
11101101 01000010
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01110100 10111010 000001110 01001110 1
10100001 00101100 0
10111011 00010000 1
00011001 01110101 0
01111001 10111001 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10100100 11001101 001111011 00000010 0
10100000 10110110 0
11000100 01001110 1
01100001 00011111 0
01011000 00101000 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:
11111110 10110001 1
11110001 10101001 1
01000110 01000000 0
10001101 01100101 0
11101101 01000010 0
00101001 01111111 0
1. The parity bits for the 16 columns is: 00101001 01111111
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 (13,0):
01110100 10111010 0
00001110 01001110 1
10100001 00101100 0
10111011 00010000 1
00011001 01110101 0
01111001 10111001 0
For figure 3, the bits that were flipped are (6,1) and (0,2):
10100100 11001101 0
01111011 00000010 0
10100000 10110110 0
11000100 01001110 1
01100001 00011111 0
01011000 00101000 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: 0010100101111111
The answer was: 11000
The answer was: 0
The answer was: 13,0
The answer was: No