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 111101000 10001000
11100011 11001010
01101111 11110010
10111000 00001000
01011001 00001011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00011111 11100001 101011100 01110110 1
10110000 10010010 0
10110110 10000111 1
00011101 01011010 1
01011010 11011000 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11001011 01011110 000101010 10110101 0
11001101 00111000 1
01000001 00110110 0
10100010 10001111 0
11001111 01100010 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:
11101000 10001000 0
11100011 11001010 1
01101111 11110010 1
10111000 00001000 1
01011001 00001011 1
10000101 10110011 0
1. The parity bits for the 16 columns is: 10000101 10110011
2. The parity bits for the 5 rows is: 01111
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (6,4):
00011111 11100001 1
01011100 01110110 1
10110000 10010010 0
10110110 10000111 1
00011101 01011010 1
01011010 11011000 0
For figure 3, the bit that was flipped is (12,2):
11001011 01011110 0
00101010 10110101 0
11001101 00111000 1
01000001 00110110 0
10100010 10001111 0
11001111 01100010 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: 1000010110110011
The answer was: 01111
The answer was: 0
The answer was: 6,4
The answer was: Yes