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 111001000 01110000
01001110 11011010
00011111 10100111
00000000 01101111
11001100 10001000
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11101010 10001011 101101000 00111011 0
00010010 10010011 0
01000101 00001101 1
10010000 01000011 1
00000101 01101101 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11010101 01000000 010100111 10010000 1
10101111 01001111 1
00000001 00010101 0
11010110 11100101 0
00001010 01101111 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:
11001000 01110000 0
01001110 11011010 1
00011111 10100111 0
00000000 01101111 0
11001100 10001000 0
01010101 11101010 1
1. The parity bits for the 16 columns is: 01010101 11101010
2. The parity bits for the 5 rows is: 01000
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (1,3):
11101010 10001011 1
01101000 00111011 0
00010010 10010011 0
01000101 00001101 1
10010000 01000011 1
00000101 01101101 1
For figure 3, the bit that was flipped is (16,5):
11010101 01000000 0
10100111 10010000 1
10101111 01001111 1
00000001 00010101 0
11010110 11100101 0
00001010 01101111 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: 0101010111101010
The answer was: 01000
The answer was: 1
The answer was: 1,3
The answer was: Yes