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 111101001 11110101
01001010 00111110
11001000 00011011
01111110 01010000
11010100 01011011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01100001 10000111 100010011 10000101 1
10000101 11000101 1
11101011 10001011 0
01101101 00011100 0
11110001 01010000 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01010010 01110001 100010100 00010101 0
01001000 01001011 1
10111010 10010000 1
01101011 11110001 0
11011110 01000110 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:
11101001 11110101 1
01001010 00111110 0
11001000 00011011 1
01111110 01010000 0
11010100 01011011 1
11000001 11011011 1
1. The parity bits for the 16 columns is: 11000001 11011011
2. The parity bits for the 5 rows is: 10101
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (0,1):
01100001 10000111 1
00010011 10000101 1
10000101 11000101 1
11101011 10001011 0
01101101 00011100 0
11110001 01010000 1
For figure 3, the bits that were flipped are (12,1) and (7,2):
01010010 01110001 1
00010100 00010101 0
01001000 01001011 1
10111010 10010000 1
01101011 11110001 0
11011110 01000110 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: 1100000111011011
The answer was: 10101
The answer was: 1
The answer was: 0,1
The answer was: No