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 100100111 00110011
01110111 11100000
01110000 10110001
01101010 10011011
01100110 01101001
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01100011 00011010 100001111 00011110 0
00010110 01010101 0
00110100 11010011 0
00011110 11011100 1
11010000 01011110 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00111110 11100000 011000110 10110000 1
11111011 10001000 0
10000000 10010101 0
10001011 11110111 1
00001010 10111110 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:
00100111 00110011 0
01110111 11100000 1
01110000 10110001 1
01101010 10011011 1
01100110 01101001 0
00101100 10010000 1
1. The parity bits for the 16 columns is: 00101100 10010000
2. The parity bits for the 5 rows is: 01110
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (0,2):
01100011 00011010 1
00001111 00011110 0
00010110 01010101 0
00110100 11010011 0
00011110 11011100 1
11010000 01011110 0
For figure 3, the bits that were flipped are (6,3) and (13,2):
00111110 11100000 0
11000110 10110000 1
11111011 10001000 0
10000000 10010101 0
10001011 11110111 1
00001010 10111110 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: 0010110010010000
The answer was: 01110
The answer was: 1
The answer was: 0,2
The answer was: No