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 101010111 11001011
00101110 01111110
11101101 00001100
01001000 00100000
01000110 01100100
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
01100000 11111101 111111001 00011110 0
01111110 11001001 0
11110110 11011100 0
10001001 10100100 0
10011000 01010110 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11011011 00110100 111011100 00011000 0
00110001 00100011 0
11101110 11000110 0
11000110 11010100 1
00010111 00011101 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:
01010111 11001011 0
00101110 01111110 0
11101101 00001100 0
01001000 00100000 1
01000110 01100100 0
10011010 11111101 1
1. The parity bits for the 16 columns is: 10011010 11111101
2. The parity bits for the 5 rows is: 00010
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (13,3):
01100000 11111101 1
11111001 00011110 0
01111110 11001001 0
11110110 11011100 0
10001001 10100100 0
10011000 01010110 1
For figure 3, the bits that were flipped are (7,4) and (4,1):
11011011 00110100 1
11011100 00011000 0
00110001 00100011 0
11101110 11000110 0
11000110 11010100 1
00010111 00011101 0
5. No, with 2D parity, you can detect the presence of two flipped bits, but you can't know their exact locations in order to correct them.
That's incorrect
That's correct
The answer was: 1001101011111101
The answer was: 00010
The answer was: 1
The answer was: 13,3
The answer was: No