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 110010011 01110111
11100110 01001100
00001101 01000000
01000011 00101000
10100100 10101000
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10010001 11010010 110010001 01001010 0
10101101 00111001 1
01111001 10011101 0
00110011 10010100 0
11100111 10101001 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01111110 10100100 110011110 01001011 0
00011111 00111100 1
01001011 11101001 1
01001001 10011111 1
01111101 10100111 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:
10010011 01110111 0
11100110 01001100 0
00001101 01000000 0
01000011 00101000 1
10100100 10101000 0
10011111 11111011 1
1. The parity bits for the 16 columns is: 10011111 11111011
2. The parity bits for the 5 rows is: 00010
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (15,4):
10010001 11010010 1
10010001 01001010 0
10101101 00111001 1
01111001 10011101 0
00110011 10010100 0
11100111 10101001 0
For figure 3, the bits that were flipped are (14,1) and (0,5):
01111110 10100100 1
10011110 01001011 0
00011111 00111100 1
01001011 11101001 1
01001001 10011111 1
01111101 10100111 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: 1001111111111011
The answer was: 00010
The answer was: 1
The answer was: 15,4
The answer was: No