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 101011011 01110001
11010001 11001010
10001010 01100100
01000010 11001001
11011010 10001001
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
11111001 00011000 001100010 01100111 1
10011011 11100001 1
01110101 10101100 1
00111001 01011011 1
01001100 01101101 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01100001 10011101 100000111 11100110 0
11010101 00011110 1
01010101 10100000 0
11011111 01100010 1
00111001 10100101 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:
01011011 01110001 1
11010001 11001010 0
10001010 01100100 0
01000010 11001001 0
11011010 10001001 0
10011000 10011111 1
1. The parity bits for the 16 columns is: 10011000 10011111
2. The parity bits for the 5 rows is: 10000
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (13,1):
11111001 00011000 0
01100010 01100111 1
10011011 11100001 1
01110101 10101100 1
00111001 01011011 1
01001100 01101101 0
For figure 3, the bits that were flipped are (14,0) and (16,4):
01100001 10011101 1
00000111 11100110 0
11010101 00011110 1
01010101 10100000 0
11011111 01100010 1
00111001 10100101 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: 1001100010011111
The answer was: 10000
The answer was: 1
The answer was: 13,1
The answer was: No