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 100010101 10001111
00101000 10100001
01001111 01100011
11000100 01110010
00000011 01001011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00000100 11101010 010001100 01101011 0
10011100 00100000 0
10110100 00000101 0
01101101 01110001 1
11011101 11010101 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
11000000 10110100 101110001 10101011 1
11100001 00010000 1
10110001 00110110 1
00110000 10000000 1
11110001 10111101 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:
00010101 10001111 0
00101000 10100001 1
01001111 01100011 1
11000100 01110010 1
00000011 01001011 0
10110101 01110100 1
1. The parity bits for the 16 columns is: 10110101 01110100
2. The parity bits for the 5 rows is: 01110
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (3,2):
00000100 11101010 0
10001100 01101011 0
10011100 00100000 0
10110100 00000101 0
01101101 01110001 1
11011101 11010101 1
For figure 3, the bits that were flipped are (13,0) and (2,3):
11000000 10110100 1
01110001 10101011 1
11100001 00010000 1
10110001 00110110 1
00110000 10000000 1
11110001 10111101 1
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: 1011010101110100
The answer was: 01110
The answer was: 1
The answer was: 3,2
The answer was: No