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 100011110 11100101
00001110 10010110
10000101 11100101
00110101 10010010
11010001 10110010
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10100000 00101010 101001110 10001010 0
11001111 10101100 0
01111100 10111001 0
11000101 01001000 0
10011000 11111100 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11011111 10001111 001100010 00100101 0
11010010 00010010 1
10111011 01010010 1
00010110 11101111 1
01100010 00000101 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:
00011110 11100101 1
00001110 10010110 1
10000101 11100101 0
00110101 10010010 1
11010001 10110010 0
01110001 10110110 1
1. The parity bits for the 16 columns is: 01110001 10110110
2. The parity bits for the 5 rows is: 11010
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (15,1):
10100000 00101010 1
01001110 10001010 0
11001111 10101100 0
01111100 10111001 0
11000101 01001000 0
10011000 11111100 1
For figure 3, the bits that were flipped are (2,2) and (0,4):
11011111 10001111 0
01100010 00100101 0
11010010 00010010 1
10111011 01010010 1
00010110 11101111 1
01100010 00000101 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: 0111000110110110
The answer was: 11010
The answer was: 1
The answer was: 15,1
The answer was: No