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 100111001 11010100
01001101 10011001
11000101 01001111
10011100 00101010
11001110 11111110
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01101111 00000000 001011100 00100011 1
11101001 00001010 1
01011101 11110011 1
00010110 11111000 1
10010001 00100000 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01010010 01011101 100111000 10100011 1
11110000 00101010 1
11111000 00000001 0
01101011 01100001 0
10011001 10110100 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:
00111001 11010100 0
01001101 10011001 0
11000101 01001111 1
10011100 00101010 1
11001110 11111110 0
11100011 11010110 0
1. The parity bits for the 16 columns is: 11100011 11010110
2. The parity bits for the 5 rows is: 00110
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (14,4):
01101111 00000000 0
01011100 00100011 1
11101001 00001010 1
01011101 11110011 1
00010110 11111000 1
10010001 00100000 0
For figure 3, the bits that were flipped are (0,5) and (3,0):
01010010 01011101 1
00111000 10100011 1
11110000 00101010 1
11111000 00000001 0
01101011 01100001 0
10011001 10110100 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: 1110001111010110
The answer was: 00110
The answer was: 0
The answer was: 14,4
The answer was: No