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 101000001 00100110
11000011 00100011
11100001 01100011
00001011 01110100
11110110 01111000
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01100110 10001011 011010011 00000101 1
01011110 00101001 1
11100011 01001111 0
10110011 10000110 0
10111011 01101100 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10011001 01011011 010111000 10111011 0
11001101 10101110 0
00111101 11101000 1
01110101 10010101 0
10000100 01110011 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:
01000001 00100110 1
11000011 00100011 1
11100001 01100011 0
00001011 01110100 1
11110110 01111000 0
10011110 01101010 1
1. The parity bits for the 16 columns is: 10011110 01101010
2. The parity bits for the 5 rows is: 11010
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (14,2):
01100110 10001011 0
11010011 00000101 1
01011110 00101001 1
11100011 01001111 0
10110011 10000110 0
10111011 01101100 0
For figure 3, the bits that were flipped are (9,0) and (2,4):
10011001 01011011 0
10111000 10111011 0
11001101 10101110 0
00111101 11101000 1
01110101 10010101 0
10000100 01110011 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: 1001111001101010
The answer was: 11010
The answer was: 1
The answer was: 14,2
The answer was: No