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 110100001 00111001
11000000 11100101
01110100 11101011
00011000 10001111
11000011 10000001
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01111100 00000001 000111110 01100001 0
10111000 10100110 0
01010000 10100101 0
01110011 10001010 1
11011001 11101000 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01000101 01101011 001010001 11011001 1
01100011 01000111 0
01000110 10011100 1
01111011 01000110 1
01001010 00101101 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:
10100001 00111001 1
11000000 11100101 1
01110100 11101011 0
00011000 10001111 1
11000011 10000001 0
11001110 00111001 1
1. The parity bits for the 16 columns is: 11001110 00111001
2. The parity bits for the 5 rows is: 11010
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (15,4):
01111100 00000001 0
00111110 01100001 0
10111000 10100110 0
01010000 10100101 0
01110011 10001010 1
11011001 11101000 1
For figure 3, the bit that was flipped is (14,1):
01000101 01101011 0
01010001 11011001 1
01100011 01000111 0
01000110 10011100 1
01111011 01000110 1
01001010 00101101 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: 1100111000111001
The answer was: 11010
The answer was: 1
The answer was: 15,4
The answer was: Yes