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 100101111 00111111
00010110 10110011
00010101 01011011
11011000 11000101
01011011 01111001
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10010100 00101000 110001110 11000111 0
00110000 01101000 1
01110110 00001111 1
01000111 11110000 0
00011011 00111000 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10100010 00110101 000001010 10110001 0
01101111 00111001 0
01111010 00010111 1
11000011 11011110 0
01111110 00110100 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:
00101111 00111111 1
00010110 10110011 0
00010101 01011011 0
11011000 11000101 0
01011011 01111001 0
10101111 01101011 1
1. The parity bits for the 16 columns is: 10101111 01101011
2. The parity bits for the 5 rows is: 10000
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (9,1):
10010100 00101000 1
10001110 11000111 0
00110000 01101000 1
01110110 00001111 1
01000111 11110000 0
00011011 00111000 1
For figure 3, the bit that was flipped is (9,0):
10100010 00110101 0
00001010 10110001 0
01101111 00111001 0
01111010 00010111 1
11000011 11011110 0
01111110 00110100 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: 1010111101101011
The answer was: 10000
The answer was: 1
The answer was: 9,1
The answer was: Yes