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 110001000 11001100
10100100 10100101
01001001 00100001
11110001 10111000
11010000 01100101
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01110001 11011101 011011010 00000101 1
11001111 00100001 0
10111000 10100100 1
00011011 10101111 0
11000111 11110010 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00011101 00100000 011011110 10010110 0
11001011 10011001 1
01011100 11100111 0
10111000 01101110 1
11101100 10100101 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:
10001000 11001100 0
10100100 10100101 1
01001001 00100001 1
11110001 10111000 1
11010000 01100101 1
01000100 10010101 0
1. The parity bits for the 16 columns is: 01000100 10010101
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 (16,5):
01110001 11011101 0
11011010 00000101 1
11001111 00100001 0
10111000 10100100 1
00011011 10101111 0
11000111 11110010 1
For figure 3, the bits that were flipped are (15,0) and (14,5):
00011101 00100000 0
11011110 10010110 0
11001011 10011001 1
01011100 11100111 0
10111000 01101110 1
11101100 10100101 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: 0100010010010101
The answer was: 01111
The answer was: 0
The answer was: 16,5
The answer was: No