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 111010111 00101101
01110011 11110010
01001011 10001111
01110111 00101010
11101000 10011011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01101010 00010110 100100010 11001111 0
01010101 00101111 1
00111110 00001100 1
00001000 10111100 0
00101011 01100110 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10101110 10001011 011011000 11000101 0
01010101 01101001 1
11000111 00000100 0
01100011 11100001 0
10000111 10100010 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:
11010111 00101101 0
01110011 11110010 0
01001011 10001111 1
01110111 00101010 1
11101000 10011011 1
01110000 11100001 1
1. The parity bits for the 16 columns is: 01110000 11100001
2. The parity bits for the 5 rows is: 00111
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (10,5):
01101010 00010110 1
00100010 11001111 0
01010101 00101111 1
00111110 00001100 1
00001000 10111100 0
00101011 01100110 1
For figure 3, the bits that were flipped are (10,0) and (9,2):
10101110 10001011 0
11011000 11000101 0
01010101 01101001 1
11000111 00000100 0
01100011 11100001 0
10000111 10100010 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: 0111000011100001
The answer was: 00111
The answer was: 1
The answer was: 10,5
The answer was: No