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 111110011 01101011
10101110 11110110
00011100 11001101
11000111 10110010
10100000 11100011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01101111 11110100 100010010 01000101 1
11011100 10101010 1
01101110 10010110 0
00000001 00001000 0
11001010 10000101 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10000001 01111101 001111100 11011111 0
00111010 01101000 0
01100011 00100101 1
11001011 01011111 1
01101110 10110010 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:
11110011 01101011 1
10101110 11110110 1
00011100 11001101 0
11000111 10110010 1
10100000 11100011 1
00100110 00000001 0
1. The parity bits for the 16 columns is: 00100110 00000001
2. The parity bits for the 5 rows is: 11011
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (5,3):
01101111 11110100 1
00010010 01000101 1
11011100 10101010 1
01101110 10010110 0
00000001 00001000 0
11001010 10000101 1
For figure 3, the bits that were flipped are (7,5) and (14,2):
10000001 01111101 0
01111100 11011111 0
00111010 01101000 0
01100011 00100101 1
11001011 01011111 1
01101110 10110010 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: 0010011000000001
The answer was: 11011
The answer was: 0
The answer was: 5,3
The answer was: No