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 101000001 01100110
11001100 01110111
11011100 01110010
11010001 01011001
11100110 01110110
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00110111 00001101 011010110 10010110 1
01111100 11101001 0
01101101 01101010 1
00011110 01001101 0
11101110 01010100 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
00101110 01101010 011000100 00010111 0
00010010 01100011 0
10010000 11100010 0
10100000 00100100 0
11001010 11011000 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:
01000001 01100110 0
11001100 01110111 0
11011100 01110010 1
11010001 01011001 0
11100110 01110110 0
01100110 01001100 1
1. The parity bits for the 16 columns is: 01100110 01001100
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 (15,5):
00110111 00001101 0
11010110 10010110 1
01111100 11101001 0
01101101 01101010 1
00011110 01001101 0
11101110 01010100 0
For figure 3, the bit that was flipped is (6,1):
00101110 01101010 0
11000100 00010111 0
00010010 01100011 0
10010000 11100010 0
10100000 00100100 0
11001010 11011000 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: 0110011001001100
The answer was: 00100
The answer was: 1
The answer was: 15,5
The answer was: Yes