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 111111111 00111011
00010010 11100110
01000001 01110010
11010111 00001110
00100001 00010000
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00111100 10111111 110100100 10010110 1
11101001 10010001 0
10010101 00001010 0
10001000 11000010 1
00101100 01110000 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00011001 11110101 000001011 11010110 0
00011001 01111110 1
11100001 00000001 1
11000111 10101100 1
00101101 11110001 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:
11111111 00111011 1
00010010 11100110 1
01000001 01110010 0
11010111 00001110 1
00100001 00010000 1
01011010 10110001 0
1. The parity bits for the 16 columns is: 01011010 10110001
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 (1,5):
00111100 10111111 1
10100100 10010110 1
11101001 10010001 0
10010101 00001010 0
10001000 11000010 1
00101100 01110000 1
For figure 3, the bit that was flipped is (15,0):
00011001 11110101 0
00001011 11010110 0
00011001 01111110 1
11100001 00000001 1
11000111 10101100 1
00101101 11110001 1
5. Yes, with 2D parity, you can detect and correct the a single flipped bit
That's incorrect
That's correct
The answer was: 0101101010110001
The answer was: 11011
The answer was: 0
The answer was: 1,5
The answer was: Yes