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 111001101 00111110
00000100 11001010
10010000 11100101
01011000 00111011
01111100 01111000
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10000000 01101100 101001011 01000100 0
11101000 00101100 1
00111101 11001001 1
01111110 00000000 1
01100001 11001101 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11001110 00101110 101100000 11000000 0
00110101 01100101 1
00101000 10000011 0
11011110 01000001 0
01101101 01000011 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:
11001101 00111110 0
00000100 11001010 1
10010000 11100101 1
01011000 00111011 0
01111100 01111000 1
01111101 01010010 1
1. The parity bits for the 16 columns is: 01111101 01010010
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 (7,4):
10000000 01101100 1
01001011 01000100 0
11101000 00101100 1
00111101 11001001 1
01111110 00000000 1
01100001 11001101 0
For figure 3, the bits that were flipped are (14,3) and (12,2):
11001110 00101110 1
01100000 11000000 0
00110101 01100101 1
00101000 10000011 0
11011110 01000001 0
01101101 01000011 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: 0111110101010010
The answer was: 01101
The answer was: 1
The answer was: 7,4
The answer was: No