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 110010111 10100100
00000000 10101011
10000000 10110100
10001101 01100110
11111100 00110011
Figure 2
Both the payload and parity bits are shown. One of these bits is flipped.
00101010 01010100 000010100 11101001 1
11001000 10111001 1
00011101 01000010 0
01101000 11010111 1
10000011 10010001 0
Figure 3
Both the payload and parity bits are shown; Either one or two of the bits have been flipped.
10001111 00001111 111110011 01001000 1
10100101 11000101 0
10111001 00001011 1
10001101 01111111 1
01101101 11110100 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:
10010111 10100100 0
00000000 10101011 1
10000000 10110100 1
10001101 01100110 0
11111100 00110011 0
01100110 11101110 0
1. The parity bits for the 16 columns is: 01100110 11101110
2. The parity bits for the 5 rows is: 01100
3. The parity bit for the parity row is: 0
4. The bit that was flipped in figure 2 is (16,2):
00101010 01010100 0
00010100 11101001 1
11001000 10111001 1
00011101 01000010 0
01101000 11010111 1
10000011 10010001 0
For figure 3, the bits that were flipped are (0,3) and (14,1):
10001111 00001111 1
11110011 01001000 1
10100101 11000101 0
10111001 00001011 1
10001101 01111111 1
01101101 11110100 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: 0110011011101110
The answer was: 01100
The answer was: 0
The answer was: 16,2
The answer was: No