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 01010001
10101100 11000110
01111000 10001010
00100111 01010110
00001001 11001100
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11010111 00100011 100100111 01000010 0
01111001 00011110 1
00101010 00111011 0
10101100 01100000 1
00101111 00100100 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10010110 10111110 001110111 00111001 0
01110001 11111111 0
10001111 11100010 0
00000011 00100100 0
00001100 10111110 0
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 01010001 0
10101100 11000110 0
01111000 10001010 1
00100111 01010110 0
00001001 11001100 0
10001111 10000111 1
1. The parity bits for the 16 columns is: 10001111 10000111
2. The parity bits for the 5 rows is: 00100
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (2,4):
11010111 00100011 1
00100111 01000010 0
01111001 00011110 1
00101010 00111011 0
10101100 01100000 1
00101111 00100100 1
For figure 3, the bit that was flipped is (3,3):
10010110 10111110 0
01110111 00111001 0
01110001 11111111 0
10001111 11100010 0
00000011 00100100 0
00001100 10111110 0
5. Yes, with 2D parity, you can detect and correct the a single flipped bit
That's incorrect
That's correct
The answer was: 1000111110000111
The answer was: 00100
The answer was: 1
The answer was: 2,4
The answer was: Yes