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 101011100 00111010
01000010 00101000
01101100 00100001
10000101 01101001
01101110 10001101
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10101000 01101101 001010011 00011010 1
01100111 01100011 1
11000110 01000101 0
10111000 11011100 1
11000010 10001101 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10110111 01011101 110000110 01011100 1
00010100 10010100 1
01100110 11011001 1
11010110 10101111 0
10010100 11100010 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:
01011100 00111010 0
01000010 00101000 0
01101100 00100001 0
10000101 01101001 1
01101110 10001101 1
10011001 11010111 0
1. The parity bits for the 16 columns is: 10011001 11010111
2. The parity bits for the 5 rows is: 00011
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (2,3):
10101000 01101101 0
01010011 00011010 1
01100111 01100011 1
11000110 01000101 0
10111000 11011100 1
11000010 10001101 1
For figure 3, the bits that were flipped are (15,4) and (7,5):
10110111 01011101 1
10000110 01011100 1
00010100 10010100 1
01100110 11011001 1
11010110 10101111 0
10010100 11100010 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: 1001100111010111
The answer was: 00011
The answer was: 0
The answer was: 2,3
The answer was: No