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 101000101 00101000
01001111 10100001
01000000 11110111
11001100 11000101
11110011 00111101
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10010000 01101011 100011000 00011000 0
00000010 10111100 0
11000100 00001111 1
00110001 10000010 1
01111011 01000010 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01110010 11000100 110000101 10010100 0
00001000 00010110 0
11001000 00001000 0
00010111 11111011 0
00100000 10110001 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:
01000101 00101000 1
01001111 10100001 0
01000000 11110111 0
11001100 11000101 0
11110011 00111101 1
01110101 10000110 0
1. The parity bits for the 16 columns is: 01110101 10000110
2. The parity bits for the 5 rows is: 10001
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (5,5):
10010000 01101011 1
00011000 00011000 0
00000010 10111100 0
11000100 00001111 1
00110001 10000010 1
01111011 01000010 1
For figure 3, the bit that was flipped is (13,4):
01110010 11000100 1
10000101 10010100 0
00001000 00010110 0
11001000 00001000 0
00010111 11111011 0
00100000 10110001 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: 0111010110000110
The answer was: 10001
The answer was: 0
The answer was: 5,5
The answer was: Yes