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 101110101 11111111
00100001 01101001
10111000 10100010
01001010 10111110
10111010 10100001
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01101010 11010100 011110110 00001111 0
01100000 11010000 1
01110011 10011110 0
01010011 10101100 1
11001100 00111001 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10100111 11011001 011000000 00110011 0
01101101 11100101 0
00101111 01100111 0
11100110 00110010 1
11010011 01011010 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:
01110101 11111111 1
00100001 01101001 0
10111000 10100010 1
01001010 10111110 1
10111010 10100001 0
00011100 00101011 1
1. The parity bits for the 16 columns is: 00011100 00101011
2. The parity bits for the 5 rows is: 10110
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (3,4):
01101010 11010100 0
11110110 00001111 0
01100000 11010000 1
01110011 10011110 0
01010011 10101100 1
11001100 00111001 0
For figure 3, the bit that was flipped is (3,4):
10100111 11011001 0
11000000 00110011 0
01101101 11100101 0
00101111 01100111 0
11100110 00110010 1
11010011 01011010 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: 0001110000101011
The answer was: 10110
The answer was: 1
The answer was: 3,4
The answer was: Yes