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 101100110 01000101
00111001 11101000
01100111 10110101
11111001 01100101
11001010 10101010
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00101011 11010110 101110010 00001001 0
11111110 00010000 0
10100011 11101010 0
11111011 11010001 1
01111111 11110100 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11100101 11101001 010000111 11101110 0
11101011 01111011 0
00010001 00100101 0
11000010 00000100 1
01011000 01011100 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:
01100110 01000101 1
00111001 11101000 0
01100111 10110101 0
11111001 01100101 0
11001010 10101010 0
00001011 11010111 1
1. The parity bits for the 16 columns is: 00001011 11010111
2. The parity bits for the 5 rows is: 10000
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (0,3):
00101011 11010110 1
01110010 00001001 0
11111110 00010000 0
10100011 11101010 0
11111011 11010001 1
01111111 11110100 0
For figure 3, the bits that were flipped are (15,4) and (6,3):
11100101 11101001 0
10000111 11101110 0
11101011 01111011 0
00010001 00100101 0
11000010 00000100 1
01011000 01011100 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: 0000101111010111
The answer was: 10000
The answer was: 1
The answer was: 0,3
The answer was: No