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 100110000 10000101
00001101 00011011
10100010 10000001
10011001 11000111
10100000 10111110
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10011101 11000110 101111101 11110101 0
10101011 11101010 1
10101011 11110110 1
10100100 00010110 0
01000101 00111001 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00010010 00001001 000110001 10010110 1
10100110 11100111 1
01110100 01011111 0
01110011 11100110 0
10010010 11000001 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:
00110000 10000101 1
00001101 00011011 1
10100010 10000001 1
10011001 11000111 1
10100000 10111110 0
10100110 01100110 0
1. The parity bits for the 16 columns is: 10100110 01100110
2. The parity bits for the 5 rows is: 11110
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (7,2):
10011101 11000110 1
01111101 11110101 0
10101011 11101010 1
10101011 11110110 1
10100100 00010110 0
01000101 00111001 1
For figure 3, the bit that was flipped is (3,2):
00010010 00001001 0
00110001 10010110 1
10100110 11100111 1
01110100 01011111 0
01110011 11100110 0
10010010 11000001 0
5. Yes, with 2D parity, you can detect and correct the a single flipped bit
That's incorrect
That's correct
The answer was: 1010011001100110
The answer was: 11110
The answer was: 0
The answer was: 7,2
The answer was: Yes