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 100111001 00001100
00010000 10101111
11001110 10101111
01110100 01000100
01110000 01101101
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00011111 10111110 101110000 11011011 1
11111001 00000100 1
00110101 01010110 0
11100111 01110011 1
01000110 01000100 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11110011 11000010 101000001 01101110 1
00000110 10001100 0
10101100 10101101 1
00000011 00100100 0
00011011 10101001 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:
00111001 00001100 0
00010000 10101111 1
11001110 10101111 1
01110100 01000100 0
01110000 01101101 0
11100011 00100101 0
1. The parity bits for the 16 columns is: 11100011 00100101
2. The parity bits for the 5 rows is: 01100
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (6,5):
00011111 10111110 1
01110000 11011011 1
11111001 00000100 1
00110101 01010110 0
11100111 01110011 1
01000110 01000100 0
For figure 3, the bit that was flipped is (16,2):
11110011 11000010 1
01000001 01101110 1
00000110 10001100 0
10101100 10101101 1
00000011 00100100 0
00011011 10101001 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: 1110001100100101
The answer was: 01100
The answer was: 0
The answer was: 6,5
The answer was: Yes