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 110100010 10110000
01111001 00011011
11001000 01101101
11000000 01100111
00010101 00100000
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00100111 10000110 101011100 01110011 1
10000010 10001000 0
01111100 10101111 0
00001111 11001011 1
10011010 00011001 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00101101 00010100 110100101 11011101 0
11011100 11001110 0
11101111 00001110 0
10000000 10110110 0
00111011 10111110 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:
10100010 10110000 0
01111001 00011011 1
11001000 01101101 0
11000000 01100111 1
00010101 00100000 0
11000110 10000001 0
1. The parity bits for the 16 columns is: 11000110 10000001
2. The parity bits for the 5 rows is: 01010
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (3,3):
00100111 10000110 1
01011100 01110011 1
10000010 10001000 0
01111100 10101111 0
00001111 11001011 1
10011010 00011001 1
For figure 3, the bit that was flipped is (15,0):
00101101 00010100 1
10100101 11011101 0
11011100 11001110 0
11101111 00001110 0
10000000 10110110 0
00111011 10111110 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: 1100011010000001
The answer was: 01010
The answer was: 0
The answer was: 3,3
The answer was: Yes