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 110000101 01010111
10000011 00000010
11010000 10001101
10010011 00010111
01100001 01111000
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01101111 00001011 101100001 00000100 0
10111101 01101001 0
10100100 01011001 1
11111101 00011100 0
11101010 00100001 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11101110 10110111 100100001 11110000 1
10111101 01110011 1
10000110 00010100 1
11010110 01001101 1
01100010 01101100 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:
10000101 01010111 0
10000011 00000010 0
11010000 10001101 1
10010011 00010111 0
01100001 01111000 1
00100100 10110111 0
1. The parity bits for the 16 columns is: 00100100 10110111
2. The parity bits for the 5 rows is: 00101
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (14,5):
01101111 00001011 1
01100001 00000100 0
10111101 01101001 0
10100100 01011001 1
11111101 00011100 0
11101010 00100001 0
For figure 3, the bits that were flipped are (15,1) and (1,0):
11101110 10110111 1
00100001 11110000 1
10111101 01110011 1
10000110 00010100 1
11010110 01001101 1
01100010 01101100 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: 0010010010110111
The answer was: 00101
The answer was: 0
The answer was: 14,5
The answer was: No