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 111011000 11001111
11011001 00000101
00010110 11001101
00101101 00110111
01101001 11001000
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01110111 01001101 001111011 01111101 0
11000010 10100011 0
00100000 10110000 0
01100010 01011100 1
10001100 01111101 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11001110 00011001 001011110 01001110 1
01110001 00010100 0
01001111 00100010 1
00000100 01010001 1
10101110 00110001 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:
11011000 11001111 0
11011001 00000101 1
00010110 11001101 0
00101101 00110111 1
01101001 11001000 1
01010011 11111000 1
1. The parity bits for the 16 columns is: 01010011 11111000
2. The parity bits for the 5 rows is: 01011
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (14,2):
01110111 01001101 0
01111011 01111101 0
11000010 10100011 0
00100000 10110000 0
01100010 01011100 1
10001100 01111101 1
For figure 3, the bits that were flipped are (15,5) and (5,4):
11001110 00011001 0
01011110 01001110 1
01110001 00010100 0
01001111 00100010 1
00000100 01010001 1
10101110 00110001 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: 0101001111111000
The answer was: 01011
The answer was: 1
The answer was: 14,2
The answer was: No