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 110100111 11110011
11101110 10101011
10000000 01100011
10110010 01010100
01001111 00111001
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00111111 10110111 010100101 11011001 1
10110101 00000010 0
10101011 01110100 0
11101110 11100100 0
01101000 11111100 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00110111 01011001 011111110 11011001 0
10101000 10001101 0
01000000 10010110 1
00110100 01110010 1
01010001 11101001 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:
10100111 11110011 1
11101110 10101011 1
10000000 01100011 1
10110010 01010100 1
01001111 00111001 1
00110100 01010110 1
1. The parity bits for the 16 columns is: 00110100 01010110
2. The parity bits for the 5 rows is: 11111
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (6,3):
00111111 10110111 0
10100101 11011001 1
10110101 00000010 0
10101011 01110100 0
11101110 11100100 0
01101000 11111100 1
For figure 3, the bits that were flipped are (1,2) and (5,0):
00110111 01011001 0
11111110 11011001 0
10101000 10001101 0
01000000 10010110 1
00110100 01110010 1
01010001 11101001 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: 0011010001010110
The answer was: 11111
The answer was: 1
The answer was: 6,3
The answer was: No