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 110001001 10100110
00111101 11101011
11111110 00110010
11000111 11011110
10010000 11001110
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01110100 00000111 100110011 11011001 1
11100100 10110101 0
00011111 00110011 1
10000101 00000010 0
00111001 01011000 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11101001 11100110 010110111 11011111 1
01011101 00101011 1
10001111 00101000 1
11100011 11011100 1
01101111 11110110 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:
10001001 10100110 1
00111101 11101011 1
11111110 00110010 0
11000111 11011110 1
10010000 11001110 1
00011101 01101111 0
1. The parity bits for the 16 columns is: 00011101 01101111
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 (14,2):
01110100 00000111 1
00110011 11011001 1
11100100 10110101 0
00011111 00110011 1
10000101 00000010 0
00111001 01011000 1
For figure 3, the bit that was flipped is (11,4):
11101001 11100110 0
10110111 11011111 1
01011101 00101011 1
10001111 00101000 1
11100011 11011100 1
01101111 11110110 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: 0001110101101111
The answer was: 11011
The answer was: 0
The answer was: 14,2
The answer was: Yes