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 111111001 01101001
00100011 00010010
00001010 10111101
00100000 11111011
00101100 10100100
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
10110000 00010011 000001101 10001100 0
11101001 01101011 0
01010000 00000101 1
11011001 00010110 0
11011101 10100111 1
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
01100101 00101101 000101001 11000001 0
10001101 00000111 1
01101100 01000100 1
11111010 01100010 0
11010111 11000101 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:
11111001 01101001 0
00100011 00010010 1
00001010 10111101 0
00100000 11111011 0
00101100 10100100 0
11011100 10011001 1
1. The parity bits for the 16 columns is: 11011100 10011001
2. The parity bits for the 5 rows is: 01000
3. The parity bit for the parity row is: 1
4. The bit that was flipped in figure 2 is (9,3):
10110000 00010011 0
00001101 10001100 0
11101001 01101011 0
01010000 00000101 1
11011001 00010110 0
11011101 10100111 1
For figure 3, the bits that were flipped are (12,3) and (0,4):
01100101 00101101 0
00101001 11000001 0
10001101 00000111 1
01101100 01000100 1
11111010 01100010 0
11010111 11000101 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: 1101110010011001
The answer was: 01000
The answer was: 1
The answer was: 9,3
The answer was: No