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 100011011 01100000
01100110 11110011
10101101 01111011
00010100 11000000
01100011 00101010
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01110001 10010110 001011000 01111111 1
01010000 11010111 0
01001010 00111110 0
11000100 10000110 0
11110111 10001110 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11011100 10001010 010101011 01010100 1
01011000 00000100 1
01000100 11111010 0
00110000 11001011 1
01011011 11101000 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:
00011011 01100000 0
01100110 11110011 0
10101101 01111011 1
00010100 11000000 0
01100011 00101010 1
10100111 00000010 0
1. The parity bits for the 16 columns is: 10100111 00000010
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 (12,1):
01110001 10010110 0
01011000 01111111 1
01010000 11010111 0
01001010 00111110 0
11000100 10000110 0
11110111 10001110 1
For figure 3, the bits that were flipped are (14,1) and (15,2):
11011100 10001010 0
10101011 01010100 1
01011000 00000100 1
01000100 11111010 0
00110000 11001011 1
01011011 11101000 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: 1010011100000010
The answer was: 00101
The answer was: 0
The answer was: 12,1
The answer was: No