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 111101001 11011100
10111011 10101110
00000101 11101001
11010101 10100111
00011001 10010110
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01100101 01010000 001001011 11110011 0
01100010 11001010 0
10101011 00110101 1
01101010 11100100 0
10001111 10111000 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11001000 10000110 011000101 00010101 0
01011000 01100000 0
11101111 10001101 1
00000100 01100001 0
11111110 00111111 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:
11101001 11011100 0
10111011 10101110 1
00000101 11101001 1
11010101 10100111 0
00011001 10010110 1
10011011 10101010 1
1. The parity bits for the 16 columns is: 10011011 10101010
2. The parity bits for the 5 rows is: 01101
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (6,2):
01100101 01010000 0
01001011 11110011 0
01100010 11001010 0
10101011 00110101 1
01101010 11100100 0
10001111 10111000 1
For figure 3, the bits that were flipped are (10,2) and (1,1):
11001000 10000110 0
11000101 00010101 0
01011000 01100000 0
11101111 10001101 1
00000100 01100001 0
11111110 00111111 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: 1001101110101010
The answer was: 01101
The answer was: 1
The answer was: 6,2
The answer was: No