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 101111100 00111111
11001000 11000011
10001001 10101110
01010001 00100111
01000110 00000000
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01000101 11001011 011001010 00101110 1
11000000 10110100 0
11010011 01110011 0
11010101 11011110 1
01001001 11101100 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01100011 01110001 011110000 11111111 0
00111000 00100100 1
10111000 10110001 0
11010011 00100100 1
11000000 00111111 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:
01111100 00111111 1
11001000 11000011 1
10001001 10101110 0
01010001 00100111 1
01000110 00000000 1
00101010 01110101 0
1. The parity bits for the 16 columns is: 00101010 01110101
2. The parity bits for the 5 rows is: 11011
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (11,1):
01000101 11001011 0
11001010 00101110 1
11000000 10110100 0
11010011 01110011 0
11010101 11011110 1
01001001 11101100 0
For figure 3, the bit that was flipped is (16,5):
01100011 01110001 0
11110000 11111111 0
00111000 00100100 1
10111000 10110001 0
11010011 00100100 1
11000000 00111111 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: 0010101001110101
The answer was: 11011
The answer was: 0
The answer was: 11,1
The answer was: Yes