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 111101001 00111001
10101010 10101100
11100100 10101101
10101011 11111010
10001100 01110010
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01001001 00010110 011000111 10111101 1
10001011 00001011 1
00000111 11001001 0
10000111 01000110 1
10000101 10101111 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00000110 01010001 000001100 00100110 1
11001101 10111101 1
00000001 11110100 0
11010011 01000000 0
00010001 01111110 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:
11101001 00111001 1
10101010 10101100 0
11100100 10101101 1
10101011 11111010 1
10001100 01110010 1
10000000 10110000 0
1. The parity bits for the 16 columns is: 10000000 10110000
2. The parity bits for the 5 rows is: 10111
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (8,3):
01001001 00010110 0
11000111 10111101 1
10001011 00001011 1
00000111 11001001 0
10000111 01000110 1
10000101 10101111 1
For figure 3, the bit that was flipped is (5,0):
00000110 01010001 0
00001100 00100110 1
11001101 10111101 1
00000001 11110100 0
11010011 01000000 0
00010001 01111110 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: 1000000010110000
The answer was: 10111
The answer was: 0
The answer was: 8,3
The answer was: Yes