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 100111000 00011010
01011110 01100100
11000101 10111010
00100111 01111111
11001110 10111000
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11110100 00001000 000010111 10111110 0
00110101 10111101 0
00110100 01001100 0
01110000 10100110 1
10010010 11100101 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11011111 11111110 101100011 11111001 1
01010110 01101101 1
11100001 11110001 1
00100100 10110101 1
00101111 10101100 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:
00111000 00011010 0
01011110 01100100 0
11000101 10111010 1
00100111 01111111 1
11001110 10111000 1
01001010 00000011 1
1. The parity bits for the 16 columns is: 01001010 00000011
2. The parity bits for the 5 rows is: 00111
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (13,5):
11110100 00001000 0
00010111 10111110 0
00110101 10111101 0
00110100 01001100 0
01110000 10100110 1
10010010 11100101 1
For figure 3, the bits that were flipped are (14,0) and (8,1):
11011111 11111110 1
01100011 11111001 1
01010110 01101101 1
11100001 11110001 1
00100100 10110101 1
00101111 10101100 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: 0100101000000011
The answer was: 00111
The answer was: 1
The answer was: 13,5
The answer was: No